AU2014218436A1 - Droplet Actuator Configurations and Methods of Conducting Droplet Operations - Google Patents

Abstract

A droplet actuator with a droplet formation electrode configuration associated with a droplet operations surface, wherein the electrode configuration comprises one or more 5 electrodes configured to control volume of a droplet during formation of a sub-droplet on the droplet operations surface. Methods of making and using the droplet actuator are also provided. 210a 214 218a 210b As- -Figure 2A 234 218b 222 210a 214 218a 210b _ ___ - Figue_2 234 218b 222 210a214 18a210b 230a FF 230b Axis ure -- - FF- - Figure 2C 234 218b 222

Description

DROPLET ACTUATOR CONFIGURATIONS AND METHODS OF CONDUCTING DROPLET OPERATIONS Field of the Invention 5 The invention relates to droplet actuators in which droplet operations are mediated by electrodes, and particularly to modifications of droplet actuators and electrode configurations on droplet actuators for enhancing the loading, dispensing, splitting and/or disposing of droplets. The invention also relates to modified droplet actuators in which 0 electrical field gradients are used to conduct or enhance droplet operations. Background Droplet actuators are used to conduct a wide variety of droplet operations. A droplet 5 actuator typically includes two substrates separated by a gap. The substrates include electrodes for conducting droplet operations. The space is typically filled with a filler fluid that is immiscible with the fluid that is to be manipulated on the droplet actuator. The formation and movement of droplets is controlled by electrodes for conducting a variety of droplet operations, such as droplet transport and droplet dispensing. Because there is a need to 0 produce droplets having more accurate and/or precise volumes for both samples and reagents, there is a need for alternative approaches to metering droplets in a droplet actuator. There is also a need for improved approaches to loading droplet operations fluids, such as samples and/or reagents, into and removing such fluids from a droplet actuator. 25 Summary of the Invention In an aspect, the present invention provides a droplet actuator comprising: (a) a top substrate assembly comprising reservoir; (b) a bottom substrate assembly separated from the top substrate to form a 30 gap; (c) electrodes associated with the top substrate assembly and/or the bottom substrate assembly and configured to conduct one or more droplet operations; (d) a fluid path configured for: 35 (i) flowing fluid from the reservoir into the gap, where the droplet is subjected to one or more droplet operations mediated by one or more of the electrodes; and/or 1 (ii) transporting fluid using the electrodes into contact with the opening and causing the fluid to substantially exit the gap and enter the reservoir. In one embodiment, the top substrate assembly comprises: 5 (a) a top substrate; and (b) a reservoir substrate associated with the top substrate and comprising the reservoir formed therein. In one embodiment, the present invention comprises a reservoir electrode associated with the bottom substrate. 0 In one embodiment, the opening overlaps an edge of the reservoir electrode. In one embodiment, the present invention further comprises a first droplet operations electrode associated with the bottom substrate and adjacent to the reservoir electrode, wherein the opening overlaps an edge of the first electrode and an edge of the droplet operations electrode. 5 In one embodiment, the present invention further comprises a first droplet operations electrode associated with the bottom substrate and at least partially inset into the reservoir electrode, wherein the opening overlaps an edge of the first electrode and an edge of the droplet operations electrode. In one embodiment, the present invention is configured to facilitate flow of droplets 0 from the gap into the reservoir. In one embodiment, the reservoir has a diameter which is greater than about 1 mm. In one embodiment, the reservoir has a diameter which is greater than about 2 mm. In one embodiment, the reservoir has a volume sufficient to hold a volume of liquid ranging from about 100 to about 300mL. 25 In one embodiment, the reservoir has a volume sufficient to hold a volume of liquid ranging from about 5 pL to about 5000 pL. In one embodiment, the reservoir has a volume sufficient to hold a volume of liquid ranging from about 10 pL to about 2000 pL. In one embodiment, the reservoir has a volume sufficient to hold a volume of liquid 30 ranging from about 50 pL to about 1500 pL. In one embodiment, the reservoir has dimensions which are substantially cylindrical. In one embodiment, the opening is substantially aligned about an axis of the cylindrical dimensions of the reservoir. In one embodiment, the gap comprises a filler fluid. 35 In one embodiment, the filler fluid comprises an oil. 2 In one embodiment, the reservoir comprises a region having a reduced diameter relative to a main volume of the reservoir, the region having a reduced diameter providing a fluid path between the main volume of the reservoir and the opening. In one embodiment, the restricted region of the reservoir has a height above the 5 bottom substrate that exceeds the dead height corresponding to the dead volume of the restricted region of the reservoir. In one embodiment, the main volume of the reservoir has a height above the bottom substrate that exceeds the dead height corresponding to the dead volume of the main volume of the reservoir. o In one embodiment, the present invention provides: (a) the restricted region of the reservoir has a first diameter and a first height above the bottom substrate; (b) the main volume of the reservoir has a second diameter, a second height above the bottom substrate; and 5 (c) the first diameter, first height, second diameter, and second height are selected such that a liquid volume equal to substantially all of the volume of the main volume of the reservoir is available for dispensing. In one embodiment, the main volume of the reservoir is elongated relative to a cylindrical main volume without substantially increasing dead volume relative to the 0 corresponding cylindrical main volume. In another aspect, the present invention provides a method of transporting a droplet out of a droplet actuator gap, the method comprising: (a) providing a droplet actuator comprising: (i) a top substrate assembly comprising reservoir; 25 (ii) a bottom substrate assembly separated from the top substrate to form a gap; (iii) electrodes associated with the top substrate assembly and/or the bottom substrate assembly and configured to conduct one or more droplet operations; 30 (iv) a fluid path configured for flowing fluid from the gap into the reservoir; (v) transporting fluid using the electrodes into contact with the opening and causing the fluid to substantially exit the gap and enter the reservoir. 35 In one embodiment, the top substrate assembly comprises: (a) a top substrate; and 3 (b) a reservoir substrate associated with the top substrate and comprising the reservoir formed therein. In one embodiment, the present invention comprises a reservoir electrode associated with the bottom substrate. 5 In one embodiment, the opening overlaps an edge of the reservoir electrode. In one embodiment, the present invention further comprises a first droplet operations electrode associated with the bottom substrate and adjacent to the reservoir electrode, wherein the opening overlaps an edge of the first electrode and an edge of the droplet operations electrode. o In one embodiment, the present invention further comprises a first droplet operations electrode associated with the bottom substrate and at least partially inset into the reservoir electrode, wherein the opening overlaps an edge of the first electrode and an edge of the droplet operations electrode. The invention, in one aspect, provides a droplet actuator comprising a droplet 5 formation electrode configuration. The droplet formation electrode configuration may be associated with a droplet operations surface. The electrode configuration may include one or more electrodes configured to control a position of an edge of a droplet during formation of a sub-droplet on the droplet operations surface. The electrode configuration may include one or more electrodes configured to control a volume of a droplet during formation of a o sub-droplet on the droplet operations surface. The electrode configuration may include one or more electrodes configured to control a footprint of a droplet or a region of a droplet during formation of a sub-droplet on the droplet operations surface. The edge of the droplet controlled during droplet formation may include an edge of a necking region of the droplet. The edge of the droplet controlled during droplet formation may 25 include an edge of the sub-droplet being formed. The control of the position of the edge of the droplet may the volume of the sub-droplet. The control of the footprint of the droplet may control the volume of the sub-droplet. The control of a region of the footprint of the droplet may control the volume of the sub-droplet. The control of the necking region of the footprint of the droplet may control the volume of the sub-droplet. The control may exerted by 30 controlling voltage applied to the electrode. The electrode configuration may include an intermediate electrode configuration. The intermediate electrode configuration may include one or more inner electrodes; and two or more outer electrodes arranged laterally with respect to the inner electrode; and electrodes flanking the intermediate electrode configuration. The intermediate electrode 35 configuration and electrodes flanking the intermediate electrode configuration may be arranged such that activation of the intermediate electrode configuration and the electrodes flanking the intermediate electrode configuration in the presence of the droplet causes the 4 droplet to elongate across the droplet forming electrode configuration. A reduction in voltage applied to two or more of the outer electrodes in the presence the elongated droplet may be effected to initiate necking of the elongated droplet. A reduction in voltage applied to the one or more inner electrodes following a reduction in voltage applied to the two or more outer 5 electrodes may be effected to break the elongated droplet, forming one or more sub-droplets. Deactivation of the two or more outer electrodes in the presence the elongated droplet may be effected to initiate necking of the elongated droplet. Deactivation of the one or more inner electrodes following deactivation of all outer electrodes may be effected to break the elongated droplet, forming one or more sub-droplets. The outer electrodes arranged laterally 0 with respect to the inner electrode may be electrically coupled and function as a single electrode. The droplet actuator may include a reservoir electrode adjacent to the droplet formation electrode configuration. The droplet actuator may include a droplet operations electrode adjacent to the droplet formation electrode configuration. 5 The electrode configuration may include one or more centrally located electrodes; and one or more necking electrodes adjacent to an edge of the droplet forming electrode configuration. The centrally located electrodes and necking electrodes may be configured to control droplet necking and splitting in a droplet splitting process effected by sequential deactivation of sets of electrodes beginning with the necking electrodes and continuing to the 0 centrally located electrodes. The droplet actuator wherein the electrode configuration may include a centrally located electrode that is generally I-shaped and/or hourglass shaped. The electrode configuration may be interposed in a path of electrodes. The electrode configuration and the path of electrodes may be arranged along a common axis. The electrode configuration may 25 include a central electrode arranged symmetrically about the common axis, and necking electrodes flanking the central electrode. The electrode configuration may include a second set of necking electrodes flanking the first set of necking electrodes. The necking electrodes have a shape which may be convex away from the axis. The necking electrodes may include electrode bars oriented in a substantially parallel orientation 30 relative to the central electrode. The electrode configuration may have a size which is approximately equal to the size of one or more adjacent electrodes in the path of electrodes. The electrode configuration may include four triangles arranged to form a square or rectangle. The electrode configuration may include an electrode that produces an electrical 35 field gradient that controls a position of an edge of the droplet during formation of the sub-droplet. The electrode that produces the electrical field gradient may a position of an edge of a necking region of the droplet during formation of a sub-droplet. The electrode that 5 produces the electrical field gradient may control a diameter of a necking region of the droplet during formation of a sub-droplet. The electrode that produces the electrical field gradient may control a footprint a necking region of the droplet during formation of a sub-droplet. 5 The electrode may produce an electrical field gradient at a first voltage that induces droplet necking; and an electrical field gradient at a second voltage that induces droplet splitting. The electrode may produce an electrical field gradient at a first voltage that induces droplet extension; an electrical field gradient at a second voltage that induces droplet necking; and an electrical field gradient at a third voltage that induces droplet splitting. o The field gradient may be established by a composition atop the electrode. The composition may include a dielectric composition. The composition may include a patterned material including regions having different thicknesses. The composition may include a patterned material including regions having different relative static permittivity or dielectric constant. The composition may include two or more patterned materials, each patterned 5 material having a different relative static permittivity or dielectric constant. The composition may include a dielectric material having a first dielectric constant and a dielectric material having a second dielectric constant which may be different from the first dielectric constant. The composition may include dielectric material doped in a patterned fashion with one or more substances that modify the dielectric constant of the dielectric material. o The field gradient may be established by means including shape of the electrode that produces the electrical field gradient. The field gradient may be established by means including variations in electrode thickness in the electrode that produces the electrical field gradient. The field gradient may be established by means including spatial orientation of the electrode in a z direction relative to a droplet operations surface of the droplet actuator. The 25 electrode that produces the electrical field gradient may include conductivity patterns established within the electrode. The electrode that produces the electrical field gradient may include two or more different conductive materials patterned to produce a predetermined field gradient. The electrode that produces the electrical field gradient may include a wire trace in which different regions the electrode that produces the electrical field gradient may include 30 different densities of wire spacing. The invention, in one aspect, provides a system including the droplet actuator and a processor programmed to control the supply of voltage to the one or more electrodes configured to control a position of an edge of the droplet during formation of the sub-droplet. The system may include a sensor for monitoring an edge of the droplet during formation of 35 the sub-droplet. The system may include a sensor for monitoring a footprint of the droplet during formation of the sub-droplet. The system may include a sensor for monitoring a footprint of a region of the droplet during formation of the sub-droplet. The region of the 6 droplet monitored by the system may correspond to volume of the dispensed sub-droplet. The sensor may detect a parameter associated with volume of the sub-droplet. The sensor may be selected to detect one or more electrical, chemical and/or physical properties of the droplet. The sensor may include an imaging device configured to image the droplet. The 5 processor may be configured to adjust voltage of one or more of the electrodes configured to control the position of the edge of the droplet during formation of the sub-droplet. The processor may be configured to adjust voltage of one or more of the electrodes configured to control a position of an edge of the droplet during formation of the sub-droplet. The invention, in one aspect, provides a droplet actuator including substrate 0 including a path or array of electrodes, the path or array including one or more electrodes formed using a wire trace. The wire trace configuration may include wires in a meandering path. Each turn in the meandering path may be substantially equal to other turns in the path. The wire trace configuration may include regions of differing wire density. The wire trace configuration may include a central axial region that may have greater wire density than an 5 outer region. The wire trace configuration may include an elongated electrode having a first end region and a second end region. The first end region may have greater wire density than the second end region. The wire density may gradually increase along the length of the elongated from the second end region to the first end region. The invention, in one aspect, provides a droplet actuator including an droplet 0 formation electrode configuration for forming a droplet. The droplet forming electrode configuration may include a droplet source; an intermediate electrode; and a terminal electrode. When a liquid is present at the droplet source, activation of the intermediate electrode and the terminal electrode may cause a droplet extension to flow across the intermediate electrode and onto the terminal electrode. Increasing voltage applied to the 25 terminal electrode may increase the length of the droplet extension. Deactivation of the intermediate electrode may break the droplet into two sub-droplets. The droplet source may include a droplet source electrode. The droplet source electrode may include a reservoir. The droplet source electrode may include a reservoir electrode. The droplet source electrode may include a droplet operations electrode. The 30 terminal electrode may be elongated relative to the intermediate electrode. The terminal electrode may have a substantially tapering shape. The terminal electrode may taper away from the droplet source electrode. The terminal electrode may taper towards the droplet source electrode. The terminal electrode may be substantially triangular in shape. An apex of the terminal electrode may be inset into a notch in the intermediate electrode. The terminal 35 electrode may taper from a widest region which may be oriented distally with respect to the intermediate electrode to a narrow region which may be oriented proximally with respect to the intermediate electrode. The terminal electrode may taper from a widest region which may 7 be oriented proximally with respect to the intermediate electrode to a narrow region which may be oriented distally with respect to the intermediate electrode. The widest region may be approximately equal in width to the diameter of the intermediate electrode taken along an axis of the electrode configuration. The narrow region may be narrower than the diameter of 5 the intermediate electrode taken along an axis of the electrode configuration. The droplet actuator may be provided as a component of a system including the droplet actuator; and a processor. The processor may be programmed to control voltage applied to electrodes of the electrode configuration. The processor may be programmed to control droplet volume by adjusting voltage applied to the terminal electrode. o The invention, in one aspect, provides a droplet actuator including an electrode configured to conduct a droplet operation. The electrode may be configured to produce an electric field gradient that effects a droplet operation by effecting a change in voltage applied to the electrode. The droplet actuator may include a dielectric material atop the electrode configured to establish a dielectric topography that controls the droplet operation upon 5 effecting the change in voltage applied to the electrode. The field gradient may be established by means including a patterned material atop the electrode. The patterned material atop the electrode may include a dielectric material including regions having different thicknesses. The patterned material atop the electrode may include a dielectric material including regions having different dielectric constants. The 0 patterned material atop the electrode may include a dielectric material including two or more patterned materials, each patterned material having a different dielectric constant. The patterned material atop the electrode may include a dielectric material having a composition which may be varied to produce the electric field gradient. The patterned material atop the electrode may include a first dielectric material of a first dielectric constant patterned on the 25 electrode and a second dielectric material of a second dielectric constant layered on the first dielectric material. The field gradient may be configured to control the droplet necking and splitting upon reduction of voltage applied to the electrode. Necking may be induced by a first reduction in voltage applied to the electrode configuration and breaking may be induced by a 30 second reduction in voltage applied to the electrode configuration. The field gradient may be established by means including electrode shape. The field gradient may be established by means including electrode thickness. The field gradient may be established by means including conductivity patterns established within the electrode. The electrode may include two or more different conductive materials patterned to produce a predetermined field 35 gradient. The field gradient may be established by means including a wire trace in which different regions of the electrode configuration have different densities of wire spacing. The field gradient may be established by a means including a pattern of conductive material 8 within the electrode. The field gradient may be established by a means including a pattern of nonconductive material within the electrode. The field gradient may be established by a means including a pattern of differently conductive material within the electrode. The electrode may produce a patterned field gradient that effects a droplet operation 5 upon activation, deactivation or an adjustment in voltage. A reduction in voltage may effect a droplet operation. An increase in voltage may effect extension of a droplet. An increase in voltage in the presence of a droplet on the electrode effects extension of the droplet. The invention, in one aspect, provides a method of controlling a position of an edge of a droplet during formation of a sub-droplet. The invention provides a method of controlling 0 a footprint of a droplet during formation of a sub-droplet. The invention provides a method of controlling a footprint of a region of a droplet during formation of a sub-droplet. A method of the invention, in one aspect, includes providing droplet actuator including a droplet formation electrode configuration associated with a droplet operations surface, wherein the electrode configuration may include one or more electrodes configured 5 to control a position of an edge of the droplet during formation of the sub-droplet on the droplet operations surface. A method of the invention includes forming the sub-droplet while using the electrode configuration to control the edge of the droplet. The method may include controlling an edge of a necking region of the droplet while forming the sub-droplet. The method may include controlling a footprint of a necking region of 0 the droplet while forming the sub-droplet. The method may include controlling a region of a footprint of a necking region of the droplet while forming the sub-droplet. The method may include controlling a diameter of a necking region of the droplet while forming the sub-droplet. The method may include controlling volume of a necking region of the droplet while forming the sub-droplet. The method may include controlling drainage of a necking 25 region of the droplet while forming the sub-droplet. The method may include controlling an edge of the sub-droplet while forming the sub-droplet. The method may include controlling the volume of the sub-droplet while forming the sub-droplet. The method may include controlling a footprint of the sub-droplet while forming the 30 sub-droplet. The method may include controlling a footprint of a region of the sub-droplet while forming the sub-droplet. Forming the sub-droplet may include voltage applied to the electrode configuration. Forming the sub-droplet may include voltage applied to an intermediate electrode configuration. Forming the sub-droplet may include voltage applied to a terminal electrode 35 configuration. Forming the sub-droplet may include voltage applied to an intermediate electrode of the electrode configuration. Forming the sub-droplet may include voltage applied to a terminal electrode of the electrode configuration. 9 The electrode configuration may include an intermediate electrode configuration. The intermediate electrode configuration may include one or more inner electrodes; two or more outer electrodes arranged laterally with respect to the inner electrode; and electrodes flanking the intermediate electrode configuration. The intermediate electrode configuration 5 and electrodes flanking the intermediate electrode configuration may be arranged such that activation of the intermediate electrode configuration and the electrodes flanking the intermediate electrode configuration in the presence of the droplet causes the droplet to elongate across the droplet forming electrode configuration. A reduction in voltage applied to two or more of the outer electrodes in the presence the elongated droplet may initiate 0 necking of the elongated droplet. A reduction in voltage applied to the one or more inner electrodes following a reduction in voltage applied to the two or more outer electrodes may break the elongated droplet, forming one or more sub-droplets. Deactivation of the two or more outer electrodes in the presence the elongated droplet may initiate necking of the elongated droplet. Deactivation of the one or more inner electrodes following deactivation of 5 all outer electrodes may break the elongated droplet, forming one or more sub-droplets. Two or more outer electrodes arranged laterally with respect to the inner electrode may be electrically coupled and function as a single electrode. The electrode configuration may include a reservoir electrode adjacent to the droplet formation electrode configuration. Forming the sub-droplet may include dispensing a smaller 0 volume droplet from a larger volume droplet. A droplet operations electrode may be included adjacent to the droplet formation electrode configuration. The electrode configuration may include one or more centrally located electrodes and one or more necking electrodes adjacent to an edge of the droplet forming electrode configuration. Forming the sub-droplet may include sequentially deactivating sets of electrodes beginning with the necking 25 electrodes and continuing to the centrally located electrodes. The electrode configuration may include a centrally located electrode that may be generally I-shaped and/or hourglass shaped. The electrode configuration may be interposed in a path of electrodes. The electrode configuration and the path of electrodes may be arranged along a common axis. 30 The electrode configuration may include a central electrode arranged symmetrically about the common axis and necking electrodes flanking the central electrode. A second set of necking electrodes may be provided flanking the first set of necking electrodes. The necking electrodes may have a shape which may be convex away from the axis. The necking electrodes may include electrode bars oriented in a substantially parallel orientation relative 35 to the central electrode. The electrode configuration may have a size which may be approximately equal to the size of one or more adjacent electrodes in the path of electrodes. The electrode configuration may include four triangles arranged to form a square or 10 rectangle. The electrode configuration may include an electrode that produces an electrical field gradient that controls a position of an edge of the droplet during formation of the sub-droplet. The method may include controlling the position of an edge of the droplet by using 5 the electrode configuration to establish an electrical field gradient that controls the position of an edge of a necking region of the droplet during formation of a sub-droplet. The method may include controlling the footprint of the droplet. The electrode configuration may establish an electrical field gradient that controls the footprint of a necking region of the droplet during formation of a sub-droplet. The footprint may be controlled by controlling voltage applied to 0 the electrode configuration to establish an electrical field gradient at a first voltage that induces droplet necking and an electrical field gradient at a second voltage that induces droplet splitting. The method may include including controlling voltage applied to the electrode configuration to establish an electrical field gradient at a first voltage that induces droplet 5 extension; an electrical field gradient at a second voltage that induces droplet necking; and an electrical field gradient at a third voltage that induces droplet splitting. The field gradient may be established by a composition atop the electrode. The composition may include a dielectric composition. The composition may include a patterned material including regions having different thicknesses. The composition may include a o patterned material including regions having different relative static permittivity or dielectric constant. The composition may include two or more patterned materials, each patterned material having a different relative static permittivity or dielectric constant. The composition may include: a dielectric material having a first dielectric constant and a dielectric material having a second dielectric constant which may be different from the first dielectric constant. 25 The materials having different dielectric constants may be patterned to induce a field gradient which effects a droplet operation upon a change in voltage applied to the electrode. The composition may include dielectric material doped in a patterned fashion with one or more substances that modify the dielectric constant of the dielectric material. The field gradient may be established by means including shape of the electrode that produces the electrical 30 field gradient. The field gradient may be established by means including variations in electrode thickness in the electrode that produces the electrical field gradient. The field gradient may be established by means including spatial orientation of the electrode in a z direction relative to a droplet operations surface of the droplet actuator. As already noted, the electrode that produces the electrical field gradient may 35 include conductivity patterns established within the electrode. The electrode that produces the electrical field gradient may include two or more different conductive materials patterned to produce a predetermined field gradient. The electrode that produces the electrical field 11 gradient may include a wire trace in which different regions the electrode that produces the electrical field gradient may include different densities of wire spacing. The method may be controlled by a system. The system may control forming the sub-droplet. The system may control the diameter of the necking region of the droplet. The 5 system may control the footprint of the necking region of the droplet. The system may control the footprint of a portion of the necking region of the droplet. The system may include a processor programmed to control the supply of voltage to the one or more electrodes of the electrode configuration. The system may include a sensor coupled to the processor. The method may include monitoring an edge of the droplet during formation of the sub-droplet 0 using the sensor coupled to the processor. The method may include adjusting voltage applied to an electrode or electrode configuration based on the parameter sensed by the sensor. The processor may be configured to control the volume of the dispensed sub-droplet by adjusting voltage of one or more electrodes of the electrode configuration in response to a sensed position of the edge of the droplet while forming of the sub-droplet in order to locate 5 the edge of the droplet at a predetermined position indicative of a desired sub-droplet volume. The invention, in one aspect, provides a method of forming a sub-droplet from a droplet, the method including controllably reducing the diameter of a necking region of a droplet in a necking-and-splitting process. The sub-droplet may have a predetermined 0 volume. The invention, in one aspect, provides a method forming a sub-droplet from a droplet, the method including controllably expanding the volume of the droplet atop a terminal electrode and initiating a droplet splitting process at an intermediate electrode upon reaching a predetermined volume atop the terminal electrode. The sub-droplet may have a 25 predetermined volume. The invention, in one aspect, provides a method of forming a sub-droplet, the method including providing an elongated droplet spanning an electrode configuration including a first electrode and a second electrode, the elongated droplet including a volume of liquid atop the first electrode and a volume of liquid atop the second electrode. The 30 method may include controllably expanding the volume of the elongated droplet atop the second electrode. The method may include splitting the droplet at the first electrode to yield the sub-droplet. The sub-droplet may have a predetermined volume. The invention, in one aspect, provides a method of forming a sub-droplet, the method including providing an elongated droplet spanning an electrode configured to 35 produce a field gradient including an intermediate region in which a relatively higher voltage may be required to effect electrowetting atop the intermediate region. The method may include applying a voltage to the electrode sufficient to cause a droplet to expand across the 12 intermediate region. The method may include sufficiently reducing the voltage to cause the droplet to break at the intermediate region. The field gradient may be established by means including electrode shape. The field gradient may be established by means including electrode thickness. The field gradient may be established by means including conductivity 5 patterns established within the electrode. The electrode may include two or more different conductive materials patterned to produce a predetermined field gradient. The field gradient may be established by means including a wire trace in which different regions of the electrode configuration have different densities of wire spacing. The field gradient may be established by a means including a pattern of conductive material within the electrode. The 0 field gradient may be established by a means including a pattern of nonconductive material within the electrode. The field gradient may be established by a means including a pattern of differently conductive material within the electrode. The electrode or electrode configuration may produce a patterned field gradient that effects a droplet operation upon activation, deactivation or an adjustment in voltage. 5 The invention, in one aspect, provides a method of forming a sub-droplet, the method including providing an elongated droplet spanning an electrode configuration including a terminal electrode region configured to produce a field gradient, wherein droplet volume atop the terminal region may be incrementally increased by increasing voltage applied to the terminal region. The method may include applying a voltage to the electrode 0 sufficient to cause a droplet to expand to a predetermined volume atop the terminal region. The method may include causing the droplet to break, thereby forming a sub-droplet atop the terminal region. The terminal region may be configured to permit increasing droplet volume atop the terminal region to a volume which may be greater than the volume of an adjacent unit sized droplet operations electrode. The field gradient may be established by means 25 including electrode shape. The field gradient may be established by means including electrode thickness. The field gradient may be established by means including conductivity patterns established within the electrode. The electrode may include two or more different conductive materials patterned to produce a predetermined field gradient. The field gradient may be established by means including a wire trace in which different regions of the 30 electrode configuration have different densities of wire spacing. The field gradient may be established by a means including a pattern of conductive material within the electrode. The field gradient may be established by a means including a pattern of nonconductive material within the electrode. The field gradient may be established by a means including a pattern of differently conductive material within the electrode. 35 The invention, in one aspect, provides a droplet actuator including: a top substrate assembly including reservoir; a bottom substrate assembly separated from the top substrate to form a gap; electrodes associated with the top substrate assembly and/or the bottom 13 substrate assembly and configured to conduct one or more droplet operations; and a fluid path. The fluid path may be configured for flowing fluid from the reservoir into the gap, where the droplet may be subjected to one or more droplet operations mediated by one or more of the electrodes; and/or transporting fluid using the electrodes into contact with the opening 5 and causing the fluid to substantially exit the gap and enter the reservoir. The top substrate assembly may include a top substrate and a reservoir substrate associated with the top substrate and including the reservoir formed therein. The droplet actuator may include a reservoir electrode associated with the bottom substrate. The opening may overlap an edge of the reservoir electrode. The droplet actuator may include a 0 first droplet operations electrode associated with the bottom substrate and adjacent to the reservoir electrode, wherein the opening overlaps an edge of the first electrode and an edge of the droplet operations electrode. The droplet actuator may include a first droplet operations electrode associated with the bottom substrate and at least partially inset into the reservoir electrode, wherein the opening overlaps an edge of the first electrode and an edge 5 of the droplet operations electrode. The droplet actuator may be configured to facilitate flow of droplets from the gap into the reservoir. The reservoir may have a diameter which may be greater than about 1 mm. The reservoir may have a diameter which may be greater than about 2 mm. The reservoir may have a volume sufficient to hold a volume of liquid ranging from about 100 to about 300mL. The reservoir may have a volume sufficient to hold a volume 0 of liquid ranging from about 5 pL to about 5000 pL. The reservoir may have a volume sufficient to hold a volume of liquid ranging from about 10 pL to about 2000 pL. The reservoir may have a volume sufficient to hold a volume of liquid ranging from about 50 pL to about 1500 pL. The reservoir may have dimensions which may be substantially cylindrical. The opening may be substantially aligned about an axis of the cylindrical dimensions of the 25 reservoir. The gap may include a filler fluid. The filler fluid may include an oil. The reservoir may include region having a reduced diameter relative to a main volume of the reservoir, the region having a reduced diameter providing a fluid path between the main volume of the reservoir and the opening. The restricted region of the reservoir may have a height above the bottom substrate that exceeds the dead height corresponding to the dead volume of the 30 restricted region of the reservoir. The main volume of the reservoir may have a height above the bottom substrate that exceeds the dead height corresponding to the dead volume of the main volume of the reservoir. The restricted region of the reservoir may have a first diameter and a first height above the bottom substrate; the main volume of the reservoir may have a second diameter, a second height above the bottom substrate; and the first diameter, first 35 height, second diameter, and second height may be selected such that a liquid volume equal to substantially all of the volume of the main volume of the reservoir may be available for dispensing. The main volume of the reservoir may be elongated relative to a cylindrical main 14 volume without substantially increasing dead volume relative to the corresponding cylindrical main volume. The invention, in one aspect, provides a method of transporting a droplet out of a droplet actuator gap. The method may include providing a droplet actuator including: a top 5 substrate assembly including reservoir; a bottom substrate assembly separated from the top substrate to form a gap; electrodes associated with the top substrate assembly and/or the bottom substrate assembly and configured to conduct one or more droplet operations; and a fluid path configured for flowing fluid from the gap into the reservoir. The method may include transporting fluid using the electrodes into contact with the opening and causing the fluid to 0 substantially exit the gap and enter the reservoir. The top substrate assembly may include a top substrate and a reservoir substrate associated with the top substrate and including the reservoir formed therein. A reservoir electrode may be associated with the bottom substrate. The opening may overlap an edge of the reservoir electrode. A first droplet operations electrode may be associated with the bottom substrate and adjacent to the reservoir 5 electrode. The opening may overlap an edge of the first electrode and an edge of the droplet operations electrode. A first droplet operations electrode may be associated with the bottom substrate and at least partially inset into the reservoir electrode. The opening may overlap an edge of the first electrode and an edge of the droplet operations electrode. The embodiments included in this Summary of the Invention are illustrative only. o Further embodiments will be apparent to one of skill in the art upon review of this Summary of the Invention and the ensuing sections and claims. Definitions 25 As used herein, the following terms have the meanings indicated. "Activate"with reference to one or more electrodes means effecting a change in the electrical state of the one or more electrodes which, in the presence of a droplet, results in a droplet operation. "Bead", with respect to beads on a droplet actuator, means any bead or particle that 30 is capable of interacting with a droplet on or in proximity with a droplet actuator. Beads may be any of a wide variety of shapes, such as spherical, generally spherical, egg shaped, disc shaped, cubical and other three dimensional shapes. The bead may, for example, be capable of being transported in a droplet on a droplet actuator or otherwise configured with respect to a droplet actuator in a manner which permits a droplet on the droplet actuator to 35 be brought into contact with the bead, on the droplet actuator and/or off the droplet actuator. Beads may be manufactured using a wide variety of materials, including for example, resins, and polymers. The beads may be any suitable size, including for example, microbeads, 15 microparticles, nanobeads and nanoparticles. In some cases, beads are magnetically responsive; in other cases beads are not significantly magnetically responsive. For magnetically responsive beads, the magnetically responsive material may constitute substantially all of a bead or one component only of a bead. The remainder of the bead may 5 include, among other things, polymeric material, coatings, and moieties which permit attachment of an assay reagent. Examples of suitable magnetically responsive beads are described in U.S. Patent Publication No. 2005-0260686, entitled, "Multiplex flow assays preferably with magnetic particles as solid phase", published on November 24, 2005, the entire disclosure of which is incorporated herein by reference for its teaching concerning 0 magnetically responsive materials and beads. The fluids may include one or more magnetically responsive and/or non-magnetically responsive beads. Examples of droplet actuator techniques for immobilizing magnetically responsive beads and/or non-magnetically responsive beads and/or conducting droplet operations protocols using beads are described in U.S. Patent Application No. 11/639,566, entitled "Droplet-Based Particle Sorting", filed on 5 December 15, 2006; U.S. Patent Application No. 61/039,183, entitled "Multiplexing Bead Detection in a Single Droplet", filed on March 25, 2008; U.S. Patent Application No. 61/047,789, entitled "Droplet Actuator Devices and Droplet Operations Using Beads", filed on April 25, 2008; U.S. Patent Application No. 61/086,183, entitled "Droplet Actuator Devices and Methods for Manipulating Beads", 0 filed on August 5, 2008; International Patent Application No. PCT/US2008/053545, entitled "Droplet Actuator Devices and Methods Employing Magnetic Beads", filed on February 11, 2008; International Patent Application No. PCT/US2008/058018, entitled "Bead-based Multiplexed Analytical Methods and Instrumentation", filed on March 24, 2008; International Patent Application No. PCT/US2008/058047, "Bead Sorting on a Droplet Actuator", filed on 25 March 23, 2008; and International Patent Application No. PCT/US2006/047486, entitled "Droplet-based Biochemistry", filed on December 11, 2006; the entire disclosures of which are incorporated herein by reference. "Droplet" means a volume of liquid on a droplet actuator that is at least partially bounded by filler fluid. For example, a droplet may be completely surrounded by filler fluid or 30 may be bounded by filler fluid and one or more surfaces of the droplet actuator. Droplets may, for example, be aqueous or non-aqueous or may be mixtures or emulsions including aqueous and non-aqueous components. Droplets may be wholly or partially in a droplet actuator gap. Droplets may take a wide variety of shapes; nonlimiting examples include generally disc shaped, slug shaped, truncated sphere, ellipsoid, spherical, partially 35 compressed sphere, hemispherical, ovoid, cylindrical, and various shapes formed during droplet operations, such as merging or splitting or formed as a result of contact of such shapes with one or more surfaces of a droplet actuator. For examples of droplet fluids that 16 may be subjected to droplet operations using the approach of the invention, see International Patent Application No. PCT/US 06/47486, entitled, "Droplet-Based Biochemistry", filed on December 11, 2006. In various embodiments, a droplet may include a biological sample, such as whole blood, lymphatic fluid, serum, plasma, sweat, tear, saliva, sputum, 5 cerebrospinal fluid, amniotic fluid, seminal fluid, vaginal excretion, serous fluid, synovial fluid, pericardial fluid, peritoneal fluid, pleural fluid, transudates, exudates, cystic fluid, bile, urine, gastric fluid, intestinal fluid, fecal samples, liquids containing single or multiple cells, liquids containing organelles, fluidized tissues, fluidized organisms, liquids containing multi-celled organisms, biological swabs and biological washes. Moreover, a droplet may include a 0 reagent, such as water, deionized water, saline solutions, acidic solutions, basic solutions, detergent solutions and/or buffers. Other examples of droplet contents include reagents, such as a reagent for a biochemical protocol, such as a nucleic acid amplification protocol, an affinity-based assay protocol, an enzymatic assay protocol, a sequencing protocol, and/or a protocol for analyses of biological fluids. 5 "Droplet Actuator" means a device for manipulating droplets. For examples of droplet actuators, see U.S. Patent 6,911,132, entitled 'Apparatus for Manipulating Droplets by Electrowetting-Based Techniques", issued on June 28, 2005 to Pamula et al.; U.S. Patent Application No. 11/343,284, entitled 'Apparatuses and Methods for Manipulating Droplets on a Printed Circuit Board", filed on filed on January 30, 2006; U.S. Patents 6,773,566, entitled 0 "Electrostatic Actuators for Micro fluidics and Methods for Using Same", issued on August 10, 2004 and 6,565,727, entitled "Actuators for Microfluidics Without Moving Parts", issued on January 24, 2000, both to Shenderov et al.; Pollack et al., International Patent Application No. PCT/US2006/047486, entitled "Droplet-Based Biochemistry", filed on December 11, 2006, the disclosures of which are incorporated herein by reference. Methods of the 25 invention may be executed using droplet actuator systems, e.g. as described in International Patent Application No. PCT/US2007/009379, entitled "Droplet manipulation systems", filed on May 9, 2007. In various embodiments, the manipulation of droplets by a droplet actuator may be electrode mediated, e.g. electrowetting mediated or dielectrophoresis mediated. Examples of other methods of controlling fluid flow that may be used in the droplet actuators 30 of the invention include devices that induce hydrodynamic fluidic pressure, such as those that operate on the basis of mechanical principles (e.g. external syringe pumps, pneumatic membrane pumps, vibrating membrane pumps, vacuum devices, centrifugal forces, and capillary action); electrical or magnetic principles (e.g. electroosmotic flow, electrokinetic pumps piezoelectric/ultrasonic pumps, ferrofluidic plugs, electrohydrodynamic pumps, and 35 magnetohydrodynamic pumps); thermodynamic principles (e.g. gas bubble generation/phase-change-induced volume expansion); other kinds of surface-wetting principles (e.g. electrowetting, and optoelectrowetting, as well as chemically, thermally, and 17 radioactively induced surface-tension gradient); gravity; surface tension (e.g. capillary action); electrostatic forces (e.g. electroosmotic flow); centrifugal flow (substrate disposed on a compact disc and rotated); magnetic forces (e.g. oscillating ions causes flow); magnetohydrodynamic forces; and vacuum or pressure differential. In certain embodiments, 5 combinations of two or more of the foregoing techniques may be employed in droplet actuators of the invention. "Droplet operation" means any manipulation of a droplet on a droplet actuator. A droplet operation may, for example, include: loading a droplet into the droplet actuator; dispensing one or more droplets from a source droplet; splitting, separating or dividing a o droplet into two or more droplets; transporting a droplet from one location to another in any direction; merging or combining two or more droplets into a single droplet; diluting a droplet; mixing a droplet; agitating a droplet; deforming a droplet; retaining a droplet in position; incubating a droplet; heating a droplet; vaporizing a droplet; cooling a droplet; disposing of a droplet; transporting a droplet out of a droplet actuator; other droplet operations described 5 herein; and/or any combination of the foregoing. The terms "merge", "merging", "combine", "combining" and the like are used to describe the creation of one droplet from two or more droplets. It should be understood that when such a term is used in reference to two or more droplets, any combination of droplet operations that are sufficient to result in the combination of the two or more droplets into one droplet may be used. For example, "merging droplet A 0 with droplet B", can be achieved by transporting droplet A into contact with a stationary droplet B, transporting droplet B into contact with a stationary droplet A, or transporting droplets A and B into contact with each other. The terms "splitting", "separating" and "dividing" are not intended to imply any particular outcome with respect to volume of the resulting droplets (i.e. the volume of the resulting droplets can be the same or different) or 25 number of resulting droplets (the number of resulting droplets may be 2, 3, 4, 5 or more). The term "mixing" refers to droplet operations which result in more homogenous distribution of one or more components within a droplet. Examples of "loading"droplet operations include microdialysis loading, pressure assisted loading, robotic loading, passive loading, and pipette loading. Droplet operations may be electrode-mediated. In some cases, droplet operations 30 are further facilitated by the use of hydrophilic and/or hydrophobic regions on surfaces and/or by physical obstacles. "Filler fluid" means a fluid associated with a droplet operations substrate of a droplet actuator, which fluid is sufficiently immiscible with a droplet phase to render the droplet phase subject to electrode-mediated droplet operations. The filler fluid may, for example, be 35 a low-viscosity oil, such as silicone oil. Other examples of filler fluids are provided in International Patent Application No. PCT/US2006/047486, entitled, "Droplet-Based Biochemistry", filed on December 11, 2006; and in International Patent Application 18 No. PCT/US2008/072604, entitled "Use of additives for enhancing droplet actuation", filed on August 8, 2008. The filler fluid may fill the entire gap of the droplet actuator or may coat one or more surfaces of the droplet actuator. "Immobilize" with respect to magnetically responsive beads, means that the beads 5 are substantially restrained in position in a droplet or in filler fluid on a droplet actuator. For example, in one embodiment, immobilized beads are sufficiently restrained in position to permit execution of a splitting operation on a droplet, yielding one droplet with substantially all of the beads and one droplet substantially lacking in the beads. "Magnetically responsive" means responsive to a magnetic field. "Magnetically 0 responsive beads" include or are composed of magnetically responsive materials. Examples of magnetically responsive materials include paramagnetic materials, ferromagnetic materials, ferrimagnetic materials, and metamagnetic materials. Examples of suitable paramagnetic materials include iron, nickel, and cobalt, as well as metal oxides, such as Fe 3 0 4 , BaFe 12

O

1 9 , CoO, NiO, Mn 2

O

3 , Cr 2

O

3 , and CoMnP. 5 "Washing"with respect to washing a magnetically responsive bead means reducing the amount and/or concentration of one or more substances in contact with the magnetically responsive bead or exposed to the magnetically responsive bead from a droplet in contact with the magnetically responsive bead. The reduction in the amount and/or concentration of the substance may be partial, substantially complete, or even complete. The substance may 0 be any of a wide variety of substances; examples include target substances for further analysis, and unwanted substances, such as components of a sample, contaminants, and/or excess reagent. In some embodiments, a washing operation begins with a starting droplet in contact with a magnetically responsive bead, where the droplet includes an initial amount and initial concentration of a substance. The washing operation may proceed using a variety 25 of droplet operations. The washing operation may yield a droplet including the magnetically responsive bead, where the droplet has a total amount and/or concentration of the substance which is less than the initial amount and/or concentration of the substance. Examples of suitable washing techniques are described in Pamula et al., U.S. Patent 7,439,014, entitled "Droplet-Based Surface Modification and Washing", granted on October 21, 2008, the entire 30 disclosure of which is incorporated herein by reference. The terms "top", "bottom", "over", "under", and "on" are used throughout the description with reference to the relative positions of components of the droplet actuator, such as relative positions of top and bottom substrates of the droplet actuator. It will be appreciated that the droplet actuator is functional regardless of its orientation in space. 35 When a liquid in any form (e.g. a droplet or a continuous body, whether moving or stationary) is described as being "on", "at", or "over" an electrode, array, matrix or surface, such liquid could be either in direct contact with the electrode/array/matrix/surface, or could 19 be in contact with one or more layers or films that are interposed between the liquid and the electrode/array/matrix/surface. When a droplet is described as being "on"or "loaded on"a droplet actuator, it should be understood that the droplet is arranged on the droplet actuator in a manner which 5 facilitates using the droplet actuator to conduct one or more droplet operations on the droplet, the droplet is arranged on the droplet actuator in a manner which facilitates sensing of a property of or a signal from the droplet, and/or the droplet has been subjected to a droplet operation on the droplet actuator. It is to be understood that, if any prior art information is referred to herein, such 0 reference does not constitute an admission that the information forms a part of the common general knowledge in the art, in Australia or any other country. Brief Description of the Figures 5 Figures 1A, 1 B, 1C, 1D, and 1 E illustrate top views of an electrode configuration and process of dispensing droplets having a predetermined volume; Figures 2A, 2B, and 2C illustrate top views of an electrode configuration and process of dispensing droplets having more accurate and/or precise volumes by controlling the drainage of the droplet during the droplet formation process; 0 Figures 3A and 3B illustrates top views of electrode configurations that include an intermediate electrode or electrode configuration for controllably dispensing droplets having more accurate and/or precise volumes; Figures 4A and 4B illustrate a top and side view, respectively, of a droplet actuator electrode configuration and its use in a process of staged droplet dispensing; 25 Figure 5 illustrates a top view of an electrode configuration that uses a physical structure for assisting with a droplet splitting operation in a droplet actuator; Figures 6A and 6B illustrate a top and side views of an electrode configuration that for improved dispensing of droplets in a droplet actuator; Figures 7A and 7B illustrates side views of a droplet actuator configured for 30 providing improved droplet dispensing by reconfiguring gap topology at a designated target electrode; Figures 8A and 8B illustrate another embodiment of the invention for controlling necking-and-splitting during a droplet splitting or dispensing process, in which the necking-and-splitting electrode includes a wire trace; 35 Figure 9 illustrates an electrode configuration that includes an intermediate necking-and-splitting electrode configuration flanked by droplet operations electrodes; 20 Figure 10 illustrates an electrode configuration that includes an intermediate necking-and-splitting electrode configuration flanked by droplet operations electrodes; Figures 11 A and 11 B illustrate a side view and top view, respectively, of a section of a droplet actuator configured to include a reservoir associated with top substrate for 5 loading/unloading operations fluid; Figures 12A, 12B, 12C, and 12D illustrate a side view of another droplet actuator configuration including a reservoir for input/output of operations fluid; Figure 13 illustrates a side view of another droplet actuator configuration including a reservoir for input/output of operations fluid; 0 Figures 14A and 14B illustrate a side view of another droplet actuator configuration including a reservoir for input/output of operations fluid; and Figure 15 illustrates a side view of another droplet actuator configuration including a reservoir for input/output of operations fluid. 5 Description The invention provides droplet actuators and methods for conducting droplet operations on a droplet actuator. For example, the invention provides droplet actuator configurations and techniques for improved droplet loading, splitting and/or dispensing in a o droplet actuator. The droplet actuators of the invention may in some cases include various modified electrode configurations. In some embodiments, the droplet actuators and methods of the invention are useful for dispensing droplets having a varied volume (e.g. analog metering of droplets). In some embodiments, the droplet actuators of the invention are useful for dispensing droplets having more accurate and/or precise volumes by controlling the 25 drainage of the droplet during the droplet formation process. In some embodiments, the droplet actuator and methods of the invention a useful for facilitating staged droplet dispensing. Certain embodiments make use of an electrode configuration that employs one or more physical structures for assisting with the droplet splitting operation. Priming operations are also provided. The invention also provides a droplet actuator that uses a 30 reservoir associated with the top substrate for operations fluid input/output (1/O). Examples of embodiments of the operations fluid 1/O mechanisms of the invention may include a droplet actuator that has a reservoir electrode feeding an arrangement of electrodes (e.g. electrowetting electrodes), a top substrate that has an opening positioned in relation to the reservoir electrode, and a reservoir substrate that has a reservoir that is positioned in 35 relation to the opening in the top substrate. Other embodiments of the invention will be apparent from the ensuing discussion in light of the definitions provided above. 21 Electrode Configurations for Analog Metering of Droplets Figures 1A and 1 B illustrate top views of an electrode configuration 100 and process of dispensing droplets having a predetermined volume. The volume of the dispensed 5 droplets may be selected in an analog or digital fashion. Electrode configuration 100 is configured relative to a droplet operations surface such that electrodes in electrode configuration 100 may be used to conduct droplet operations on the droplet operations surface. Electrode configuration 100 includes a reservoir electrode 110, which serves as a liquid source for droplet dispensing operations, positioned in proximity to a configuration of 0 dispensing electrodes 114, 118, 122. Dispensing electrodes 114, 118, 122 may be configured for dispensing a droplet within a certain range of droplet volumes. In the embodiment illustrated, the dispensing electrodes include electrode 114 that has a standard droplet operations electrode geometry, an electrode 118 that has a standard droplet operations geometry with a notch or indention 5 therein, and a generally triangular-shaped electrode 122. The narrow end of triangular-shaped electrode 122 is oriented toward reservoir electrode 110 and situated within the notch or indentation of electrode 118. The wide end of triangular-shaped electrode 122 is in proximity with a path of droplet operations electrodes (e.g. dielectrophoresis or electrowetting electrodes), such as electrodes 126 and 130. The electrode configuration is 0 aligned along an axis which passes through a center of each of the electrodes in the configuration, though it will be appreciated that a straight, linear axis is helpful but not required for the operation of the invention. Figure 1A shows a volume of liquid 134 positioned atop reservoir electrode 110. When electrode 114, electrode 118, and triangular-shaped electrode 122 are activated, a 25 droplet extension 138 is flows out of the volume of liquid 134 at reservoir electrode 110 and onto the activated electrodes. Droplet extension 138 generally conforms to the shape of the activated droplet operations electrodes. The length of the droplet extension 138 depends on the voltage applied to triangular-shaped electrode 122. Increasing the voltage applied increases the length of the 30 droplet extension 138. For example, when a voltage V1 is applied to triangular-shaped electrode 122, the droplet extension 138 extends a certain distance. When a voltage V2, which is greater than voltage V1, is applied to triangular-shaped electrode 122, the droplet extension 138 extends a certain greater distance. When a voltage V3, which is greater than voltage V2, is applied to triangular-shaped electrode 122, the droplet extension 138 extends 35 a certain greater distance still. Voltage may be varied in discrete steps and/or in an analog fashion. 22 Referring to Figure 1 B, once the droplet extension 138 extends to a desired distance on the droplet operations surface, one or both of electrodes 114 and 118 may be deactivated, while triangular-shaped electrode 122 remains activated. The deactivation of the intermediate electrodes causes a droplet 138 to be formed atop triangular-shaped electrode 5 122. The volume of droplet 138 depends on the voltage applied at triangular-shaped electrode 122. For example, when voltage V1 is applied to triangular-shaped electrode 122, droplet 138 is a certain volume. When voltage V2, which is greater than voltage V1, is applied to triangular-shaped electrode 122, droplet 138 has a certain greater volume. When a voltage V3, which is greater than voltage V2, is applied to triangular-shaped electrode 122, 0 droplet 138 is a certain greater volume still. The aspect of the invention that is illustrated in Figures 1A and 1B provides a method to vary the volume of dispensed droplets on the droplet actuator. The volume may be varied in an analog fashion or a digital fashion. The method makes use of a set of droplet dispensing electrodes, including one or more intermediate electrodes and an elongated 5 terminal electrode. By varying the voltage applied to the elongated terminal electrode, the volume of dispensed droplets may be controllably varied. The elongated terminal electrode may be configured in any manner which permits the length of the droplet extension to be controlled atop the elongated electrode. For example, the control may be effected by controlling voltage supplied to the elongated electrode. In alternative embodiments, the 0 terminal electrode may be laterally elongated or both laterally and axially (relative to the axis of the electrode path) elongated. The elongated electrode may be generally triangular, having an apex pointed towards the region in which the droplet splits away from the parent droplet during dispensing. Other tapering electrode shapes, such as trapezoids (e.g. an isosceles trapezoid), 25 trapeziums, elongated pentagons, elongated hexagons, and other elongated polygonal (e.g. elongated polygons that are generally symmetrical with respect to a centrally located axis extending along the length of the elongated polygon) shapes, may be used. In the triangular embodiment illustrated, increasing the voltage applied to the triangular-shaped electrode causes the droplet extension to extend away from the apex towards the wide end 30 of the triangle. Thus, by simply controlling the voltage on that dispensing electrode, a longer or shorter droplet extension may be formed, and the volume of the dispensed droplet may be controlled. Figure 1C illustrates an alternative in which the tapering electrode is replaced with a series of electrode bars. Electrode configuration 101 includes a dispensing electrode, droplet 35 operations electrodes 114 and 118 and bar configuration 123, which is composed of a series of electrode bars 124. Electrode bars 124 may be oriented in any manner in which sequential activation of electrode bars beginning with the bar that is proximal with respect to electrode 23 118 and continuing in the direction of the electrode bar 124 that is distal with respect to electrode 118 will incrementally expand the volume atop electrode configuration 123. Once a predetermined volume atop electrode configuration 123 is achieved, the droplet may be formed by deactivating an intermediate droplet operations electrode, such as electrode 118 5 or electrode 114. In one embodiment, electrode bars 124 have a dimension lateral to an axis which is similar to the lateral dimension of the adjacent droplet operations electrode 118. In one embodiment, electrode bars 124 have a dimension lateral to an axis which is approximately the same as the lateral dimension of the adjacent droplet operations electrode 118. In one embodiment, the axial dimension of the electrode bars ranges from about 0.75 to 0 about 0.01 % of the axial dimension of the adjacent droplet operations electrode 118. In another embodiment, the axial dimension of the electrode bars ranges from about 0.5 to about 0.1 % of the axial dimension of the adjacent droplet operations electrode 118. In another embodiment, the axial dimension of the electrode bars ranges from about 0.25 to about 0.1 % of the axial dimension of the adjacent droplet operations electrode 118. 5 The control may in some cases be effected by a field gradient produced across the electrode. For example, the field gradient may cause a lengthening in the droplet extension as voltage is increased. Examples of other techniques for establishing a field gradient across the electrode are gradients in the dielectric constant of the dielectric material atop the electrode caused by doping or thickness of the dielectric material, using various electrode 0 patterns or shapes. Examples are discussed below. The terminal electrode may be provided in any configuration or include any structure or shape which causes the length of the droplet extension to depend on the characteristics of the terminal electrode, such as the voltage applied to the terminal electrode. For example, the electrode may be vertically thicker at one terminus then at the other terminus. Further, various embodiments may be provided in which 25 one or more counter electrodes are also utilized to control the length of the droplet extension across the terminal electrode. The volume control facilitated by the novel dispensing techniques described herein has a wide variety of uses. In one example, droplet volume control facilitates variable-ratio mixing. Instead of executing multiple complex droplet operations in a binary mixing tree to 30 produce droplets having the desired mixing ratio, droplets having the desired volume may simply be dispensed and combined. For example, if a mixing ratio of 1.7-to-I is desired, a droplet having a volume of 1.7 units may be dispensed and combined with a droplet having volume of 1 unit. In some embodiments, the extension of the droplet extension along the elongated 35 electrode may be further controlled by detecting the extent of the droplet extension and effecting droplet formation when the droplet extension has achieved a certain predetermined length. Examples of such detection modalities include visual detection, detection based on 24 imaging, and various detection techniques based on electrical properties of the droplet extension (e.g. electrical properties of the droplet extension relative to the surrounding filler fluid). For example, capacitance detection techniques may be used in some embodiments for determining or monitoring the droplet extension length. 5 Feedback mechanisms may be used to control the formation of droplets, such as splitting or dispensing of droplets. For example, feedback mechanisms may be used in a droplet formation process to control the volume of a sub-droplet. Formation of new droplets requires the formation and breaking of a meniscus connecting the two liquid bodies, generally referred to herein as "necking" and "splitting", respectively. A feedback mechanism 0 can be used to monitor the shape and position of the droplet and/or meniscus to determine whether breaking would result in unequal or out of specification droplet volumes. Adjustments can then be made to voltage and/or timing of adjustments to voltage. For example, impedance sensing may be used to monitor the capacitive loading of the electrowetting electrode to infer droplet overlap and by inference, the volume supported by 5 each electrode in the electrode splitting process. Other feedback mechanisms, such as image analysis are also suitable for use in the present invention. Feedback may be used to dynamically alter the applied voltage in magnitude, frequency and/or shape to result in more controlled droplet formation. In one embodiment, capacitance at the elongated terminal electrode may be 0 monitored to determine the volume of the droplet extension, and the one or more intermediate electrodes may be deactivated when the extension has reached a predetermined length sufficient to create a droplet having a desired droplet volume. For examples of suitable capacitance detection techniques, see Sturmer et al., International Patent Publication No. WO/2008/101194, entitled "Capacitance Detection in a Droplet 25 Actuator", published on August 21, 2008; and Kale et al., International Patent Publication No. WO/2002/080822, entitled "System and Method for Dispensing Liquids", published on October 17, 2002; the entire disclosures of which are incorporated herein by reference. In another embodiment, impedance of the advancing contact line can be monitored by using electrodes that are separate from the electrodes used for manipulation of droplets. For 30 example, elongated electrodes along the sides of electrodes 114, 118, 122, and 126 can be utilized to monitor the impedance of the advancing droplet. These elongated impedance measurement electrodes may be dedicated for measurement of impedance and they can be either strictly coplanar with the droplet operations electrodes or substantially coplanar or in another plane such as on the top plate. 35 In some embodiments, variability in droplet volume is established using an intermediate electrode or electrode assembly rather than the terminal electrode. For example, referring to Figures 1 D and 1 E, dispensing configuration 150 or 151 includes a 25 dispensing electrode 155, an intermediate electrode 160 for causing the droplet to split (which may in other embodiments, have any of the other intermediate or droplet splitting electrode configurations described herein), a laterally extended electrode 167 or electrode configuration 165, and a terminal electrode 170. Electrode 167 or electrode configuration 165 5 is laterally extended relative to the other electrodes in dispensing configuration 150 or 151. Dispensing configuration 150 may be associated with one or more additional droplet operations electrodes 175. In an alternative embodiment, the orientation of electrode 122 may be reversed, i.e. with the apex oriented distally with respect reservoir electrode 110 and the wide end oriented proximally with respect to reservoir electrode 110. 0 In the embodiment illustrated, the electrodes in the set are activated to cause the droplet to extend along the electrodes of dispensing configuration 150 and onto terminal electrode 170. In dispensing configuration 150, droplet volume may be controlled by selectively applying voltage to one or more sub-electrodes 166 of electrode configuration 165. In dispensing configuration 151, droplet volume may be controlled by varying the 5 voltage applied to electrode 167; increasing the voltage increases the area of the laterally extended electrode that is covered by the droplet. When a predetermined volume has been reached, e.g. as observed or as calculated, intermediate electrode 160 is deactivated, causing the droplet to be formed on the laterally extended electrode 167 or electrode configuration 165 and terminal electrode 170. The laterally extended electrode may have any 0 variety of shapes. For example, it may be circular, ovular, rectangular, diamond shaped, star shaped, hourglass shaped, etc. Any of the various techniques for creating a field gradient described herein with respect to the terminal electrode may also be used with respect to the laterally extended intermediate electrode. The various techniques may also be combined in a single electrode configuration and/or with respect to a single electrode. For example, the 25 electric field may be controlled with dielectric doping, dielectric thickness, electrode doping, electrode thickness and/or electrode shape. The laterally extended intermediate electrode may be extended in one or both directions relative to an axis of the electrode set. Additional electrodes may be inserted between the electrodes described in the specifically illustrated examples without departing from the invention. 30 In another alternative embodiment, rather than changing the voltage at an electrode in order to create an electric field gradient, the gradient is produced by applying a predetermined voltage for predetermined period of time. Of course, combinations of the two approaches are also within the scope of the invention. This approach is suitable for the terminal elongated electrode technique, as well as the intermediate laterally extended 35 electrode technique. The timing of the applied voltage may establish a particular droplet extension length prior to droplet formation. In this manner, a droplet having a predetermined volume may be dispensed. Because the transport time of the droplet extension may be 26 predetermined, timing may be used to dispense a droplet having a predetermined volume. As an example, the timing of the applied voltage at the elongated or laterally extended electrode may be used for determining the droplet extension volume, which determines the droplet volume. Because the transport time of the droplet extension from one end of the 5 elongated electrode to the other end may be predetermined, timing may be used to dispense a droplet having a predetermined volume. Similarly, because the time it takes the droplet to cover the laterally extended electrode varies with time, the volume can be predicted based on the duration of electrode activation. In various other embodiments, timing of voltage applied may be combined with changes in voltage in order to determine the length of the o droplet extension and thereby determine the volume of the droplet dispensed. The invention provides related embodiments in which the electric field gradient is established by electrode shape and/or means other than electrode shape. In addition to shape, a patterned field gradient may be mediated by the electrical characteristics of the electrode and/or electrical characteristics of materials associated with the electrode, such as 5 dielectric and/or other coatings atop the electrode. The electrode itself may be patterned, e.g. as illustrated by electrode 805 in Figure 8. The electrode may be composed of different conductive materials patterned to provide a desired patterned field gradient. Conductive and/or non-conductive materials with differing electrical conductivity may be patterned to form a single electrode which produces a patterned field gradient. Similarly, conductive 0 materials with differing electrical conductivity may be patterned to form a single electrode which produces a patterned field gradient. Materials associated with an electrode may be patterned in a manner which produces a patterned field gradient. The dielectric material situated atop the electrode may be patterned to establish a dielectric topography in which various regions atop an electrode 25 have different dielectric constants. The dielectric topography may thus produce a patterned field gradient. Patterning of dielectric materials atop the electrode may be based on thickness patterns established in the dielectric material. Materials with different dielectric constants may be patterned atop the electrode to establish the dielectric topography. Among other things, the techniques for establishing patterned field gradients may be 30 used to mimic the effects of droplet operations conducted on groups of electrodes or droplet operations produced by specially shaped electrodes. The patterned field gradient may exhibit characteristics which mimic the electric field produced by electrodes having certain shapes, non-limiting examples of which include electrode 122 of Figure 1A, electrode configuration 123 of Figure 1C, electrode 166 of Figure 1D, electrode 167 of Figure 1E, electrode 805 of 35 Figure 8. The patterned field gradient may exhibit characteristics which mimic electrode configurations, such as electrode configuration 165 of Figure 1C, electrode configuration 214 of Figure 2A, electrode configuration 314 of Figure 3A, electrode configuration 356 of 27 Figure 3B, electrode configuration 165 of Figure 3C, and various combinations of electrodes 614a, 614b, 614c, and 618 of Figure 6A. Similarly, various standard electrode configurations for conducting droplet operations described here and known in the art may be replaced or supplemented with techniques that effect a patterned field gradient, such as those 5 techniques described here. For example, field gradients may be produced which effect loading of a droplet into the droplet actuator; dispensing of one or more droplets from a source droplet; splitting, separating or dividing a droplet into two or more droplets; transporting a droplet from one location to another in any direction; merging or combining two or more droplets into a single droplet; diluting a droplet; mixing a droplet; agitating a droplet; 0 deforming a droplet; retaining a droplet in a specific position; incubating a droplet; heating a droplet; vaporizing a droplet; cooling a droplet; disposing of a droplet; transporting a droplet out of a droplet actuator; and various combinations of the foregoing. As an example, in a droplet splitting operation, a field gradient across three electrodes may be established such that at a first, higher voltage, an elongated droplet will form along the elongated electrode, 5 and at a second, lower, voltage the droplet will split, yielding two daughter droplets. In one embodiment, the field gradient is patterned to effect controllable droplet extension over time or with changes in voltage applied to the electrode, e.g. as described with respect to electrode 122 of Figures 1A and 1B. For example, a field gradient at a terminal electrode may vary in a manner which effects controllable droplet extension over 0 time or with changes in voltage applied to the electrode. In another example, a terminal electrode may be configured using a trace technique, such as that described with respect to electrode 805 of Figure 8, which effects controllable droplet extension over time or with changes in voltage applied to the electrode. Figures 2A. 2B. and 2C illustrate top views of an electrode configuration 200 and 25 process of dispensing droplets having more accurate and/or precise volumes by controlling the drainage of the droplet during the droplet formation process. Electrode configuration 200 includes electrodes 210a and 210b (e.g. electrowetting electrodes) having an intermediate droplet splitting electrode configuration 214 arranged therebetween. In the embodiment illustrated, intermediate electrode configuration 214 is formed of two lateral electrodes 218 30 (e.g. lateral electrodes 218a and 218b having a semicircle geometry) and a necking electrode 222 (e.g. having an hourglass type geometry) arranged between the two lateral electrodes, e.g. as shown in Figures 2A, 2B, and 2C. Figures 2A, 2B, and 2C illustrate a sequence of steps for performing a droplet splitting operation using electrode configuration 200. First, as shown in Figure 2A, an 35 elongated droplet 230 is formed across electrode configuration 200 by activating electrode 210a, all parts of electrode configuration 214, and electrode 210b. Second, as shown in Figure 2B, electrodes 218a and 218b are deactivated, while all other electrodes in electrode 28 configuration 200 remain activated. Deactivation of electrodes 218a and 218b initiates a necking process in which an intermediate region of droplet 230 atop intermediate electrode configuration 214 is reduced in width. Droplet 230 still spans electrode configuration 200 from electrode 218a to electrode 218b; however, the width of neck 234 of slug 230 is 5 controllably reduced, generally conforming to the shape of necking electrode 222. Third, as shown in Figure 2C, necking electrode 222 is deactivated, while electrodes 218a and 218b remain activated. At this point in the process, the entire intermediate electrode to 14 has been deactivated, causing the neck 234 to break, yielding two daughter droplets 230a and 230b. Either of electrodes 210a and 210b may be replaced with a larger reservoir electrode. 0 Additional electrodes may be inserted between the electrodes described in the specifically illustrated examples without departing from the invention. The embodiment shown in Figure 2 is illustrative of a variety of embodiments in which necking is controlled during droplet dispensing in order to produce one or more daughter droplets having a predetermined volume. In these embodiments, a path of droplet 5 operations electrodes is provided. The path includes one or more intermediate electrode configurations. Droplet splitting occurs at the intermediate electrode configurations. The intermediate electrode configurations are configured to permit a multi-step droplet necking-and-splitting operation. Generally speaking, the controlled necking-and-splitting is effected by sequentially deactivating electrodes beginning with electrodes adjacent to an 0 edge of the droplet, such as electrodes 218a and 218b and continuing to centrally positioned electrodes, such as electrode 222. The invention provides related embodiments, in which the electric field is controllably manipulated to reduce the electric field from an outer edge of the region of the neck of the droplet towards a central region of the neck of the droplet, thereby yielding a 25 similarly controlled necking-and-splitting process. For example, in some embodiments a single intermediate electrode may be provided, and the dielectric material atop the intermediate electrode may establish a dielectric topography which effects controllable necking-and-splitting as voltage at the intermediate electrode is reduced. In another embodiment, a single intermediate electrode may be provided, and the electrode itself may 30 be doped, patterned, shaped, and/or spatially oriented in a manner which effects controllable necking-and-splitting as voltage at the intermediate electrode is reduced. In yet another technique, the splitting electrode may be configured using a trace technique, such as that described with respect to Figure 8, to provide controllable necking as voltage is reduced on the electrode. 35 The patterned field gradient techniques described herein may be used to effect a stepwise controlled necking-and-splitting process similar to the process effected by electrode configuration 214. For example, electrode 214 may be replaced with a standard droplet 29 operations electrode such as electrode 210a. The patterned field gradient techniques may produce an electric field which at a first, higher, voltage causes the droplet to elongate across the three electrodes as illustrated in Figure 2A. At a second, reduced, voltage, the droplet conforms to a second electrowetting pattern which is similar to the pattern illustrated 5 in Figure 2B. At a third voltage, reduced still further or deactivated, the neck breaks, forming 2 daughter droplets on the flanking electrodes, as illustrated in Figure 2C. Similarly, the patterned field gradient techniques may be used to effect an analog or substantially analog necking and splitting process, in which the droplet neck gradually narrows and then breaks as voltage to the electrode is reduced in an analog or substantially analog fashion. 0 Figure 3A illustrates a top view of an electrode configuration 300 that includes an intermediate electrode configuration 314 for controllably dispensing droplets having more accurate and/or precise volumes. Intermediate electrode configuration 314 enhances accuracy and/or precision of droplet volume by controlling the drainage of liquid from the neck region of an elongated droplet during the droplet formation process. Electrode 5 configuration 300 includes electrodes 310a and 310b (e.g. electrowetting electrodes) and an intermediate droplet splitting electrode configuration 314 that is arranged therebetween. Intermediate electrode configuration 314 includes a set of necking electrodes 322. Necking electrodes 322 are generally shaped in a manner which permits them to mimic the curve of the edge of the neck of a droplet during a splitting operation. In the 0 embodiment illustrated, three necking electrodes 322A, 322B, and 322C are provided on either side of a central necking electrode 318. Necking electrodes 322 are generally convex in the direction of the edge of the neck of the droplet. Where a central necking electrode 318 is present, necking electrodes 322 may be generally convex in a direction which is away from necking electrode 318. Where a central necking electrode 318 is not present, necking 25 electrodes 322 may be generally convex away from a central axis extending from a centrally located point on electrode 310A to a centrally located point on electrode 310B. Central necking electrode 318 is generally symmetrical and centrally located relative to necking electrodes 322. In the embodiment illustrated, central necking electrode 318 is generally linear; however, it will be appreciated that other geometries are possible within the scope of 30 the invention. For example, central necking electrode 318 may have an hourglass shape similar to electrode 322 in Figure 2. Central necking electrode 318 may also be I-shaped, e.g. as illustrated in Figure 9 below. Compared with intermediate electrode configuration 214 of Figure 2, intermediate electrode configuration 314 of Figure 3A shows a finer pattern of electrodes (i.e. finer 35 gradient). Each electrode segment of intermediate electrode configuration 314 is independently controlled or alternatively matching sets may be independently controlled together. For example, electrodes 322A on either side of intermediate electrode 318 may be 30 controlled together; electrodes 322B may be controlled together; and electrode 322C may be controlled together. As a result, the deactivation of each electrode pair during the droplet formation may be effected in a deactivation sequence selected to control the neck volume (i.e. drainage) of the elongated droplet (not shown). 5 In operation, all of electrodes 310A, 310B and some or all of intermediate electrodes 314 may be activated to elongate a droplet across electrode configuration 300. Intermediate electrodes may be sequentially deactivated to controllably cause a neck-and-split droplet formation operation. For example, electrodes 322A may be deactivated, followed by electrodes 322B, followed by electrodes 322C, followed by central necking electrode 318. As 0 each set of electrodes is sequentially deactivated, the diameter of the neck of the elongated droplet gradually narrows and is broken. Controlling the drainage of liquid from the neck of the droplet during the droplet splitting operation may enhance the accuracy and/or precision of dispensed droplet volumes. Either of electrodes 310a and 310b may be replaced with a larger reservoir electrode. Additional electrodes may be inserted between the electrodes 5 described in the specifically illustrated example without departing from the invention. Figure 3B illustrates a top view of an electrode configuration 350 that includes an intermediate electrode configuration 354 configured for dispensing droplets. Droplets dispensed using electrode configuration 350 may have more accurate and/or precise volumes due to control on the necking process exerted by intermediate electrodes 354 0 during droplet formation. Electrode configuration 350 includes electrodes 310A and 310B (e.g. electrowetting electrodes). An intermediate electrode configuration 354 is arranged between electrodes 310A and 310B. Intermediate electrode configuration 354 includes a set of geometrically similar triangular-shaped electrodes 354. Electrodes 354 are arranged to form a square. It 25 will be appreciated that various alternative arrangements are possible. More than four triangular electrodes may be used. The triangular electrodes may be elongated or shortened relative to the triangular electrodes shown in Figure 3B, e.g. an elongated configuration 356 is shown in Figure 3C. As illustrated, intermediate electrode configuration 354 includes electrodes 354A 30 and electrodes 354B. Electrodes 354A are configured to help control the necking of the elongated droplet during a droplet splitting operation. Electrodes 354A include outer edges that are generally parallel with each other and generally parallel with and contiguous with the outer edge of the elongated droplet. Electrodes 354A each have an apex which is pointed towards a generally central point within intermediate electrode configuration 354. Electrodes 35 354B at a configuration which is generally identical to the configuration of electrodes 354A, except that electrodes 354B are arranged at a right angle relative to electrodes 354A. Together, electrodes 354A and electrodes 354B form an intermediate electrode configuration 31 354, which is generally square shaped. In an alternative embodiment, the overall shape of the configuration may be hourglass shaped (e.g. similar to electrode 222 in Figure 2A), or H-shaped (e.g. similar to electrode 905a in Figure 9). Each electrode of intermediate electrode configuration 354 may be independently 5 controlled. Alternatively, electrodes 354A may be controlled together, while electrodes 354B may be controlled together. Deactivation of electrodes 354A during droplet formation assists in the control of droplet necking-and-splitting. In a splitting operation, electrodes 310A, 310B and electrode configuration 354 may be activated to cause an elongated droplet to extend across electrode configuration 350. Electrodes 354A may be deactivated to initiate necking. 0 Electrodes 354B may be deactivated to effect droplet splitting, yielding two daughter droplets. Similar embodiments with a greater number of triangular electrodes can readily be envisioned by one of skill in the art in light of the instant disclosure. Figure 3C illustrates an electrode configuration which is substantially similar to the configuration illustrated in Figure 3A, except that the intermediate electrode configuration 354 5 is elongated along the direction of the droplet path. As with other examples, the lateral draining and droplet formation may be further controlled by detecting the volume of the droplet being formed, extent of necking, or other parameters, and effecting droplet formation in a manner which precisely controls the volume of the resulting droplet. Examples of such detection modalities include visual detection, 0 detection based on imaging, and various detection techniques based on electrical properties of the droplet extension (e.g. electrical properties of the droplet extension relative to the surrounding filler fluid). For example, capacitance detection techniques may be used in some embodiments for determining or monitoring the lateral draining and/or droplet formation. Voltage to the necking electrode or electrode configuration may, for example, be controlled 25 based on the detected volume of the droplet being dispensed. Although the configurations illustrated in Figure 3 are described with respect to droplet splitting operations in which two daughter droplets are formed having substantially similar volumes, similar configurations may be used for droplet dispensing operations. Generally speaking, and in droplet dispensing operations, the lateral electrodes (e.g. 310A 30 and 31 OB) will have different sizes. For example, one outer electrode may have the size and shape of a reservoir electrode, while the other may be a standard droplet operations electrode. Further, while the examples are shown having a single intermediate electrode configuration, multiple intermediate electrode configurations are possible. For example, in 35 one embodiment, an electrode path includes multiple droplet operations electrodes interspersed with one or more intermediate electrode configurations. All electrodes within the group may be activated to cause a droplet to extend along the electrode path. Intermediate 32 electrode configurations, such as those described with reference to Figure 3, may then be deactivated in a stepwise manner to controllably cause the formation of multiple droplets. As with other configurations, alternative techniques, such as electrode doping, dielectric doping, electrode thickness, dielectric thickness, trace electrodes, counter electrodes, and other 5 techniques may be used to mimic the controllable splitting effected by the described electrode configurations. Figures 4A and 4B illustrate a top and side view, respectively, of a droplet actuator electrode configuration 400. Electrode configuration 400 provides a process of "staged" droplet dispensing. Droplet actuator 400 includes a bottom substrate 410 and a top substrate 0 414. Substrates 410 and 414 are arranged in a generally parallel fashion and are separated to provide a gap 416 therebetween. A first droplet dispensing configuration 418 that includes a reservoir electrode 422 that is in proximity with a set of dispensing electrodes 426 (e.g. electrowetting electrodes) is associated with bottom substrate 410. Electrodes 426 5 of first droplet dispensing configuration 418 are arranged in proximity with a second droplet dispensing configuration 430, such that droplets dispensed by first droplet dispensing configuration 418 may be transported using droplet operations into second droplet dispensing configuration 430. Additional droplet operations electrodes (not shown) may be inserted at position B. 0 In one embodiment, second droplet dispensing configuration 430 has one or more features which differ from the features of first droplet dispensing configuration 418. For example, second droplet dispensing configuration 430 may include a reservoir electrode which has a size that is different relative to the size of the reservoir electrode of first droplet dispensing configuration 418. Similarly, second droplet dispensing configuration 430 may 25 include droplet operations electrodes which have a size that is different from the size of droplet operations electrodes of first droplet dispensing configuration 418. As another example, second droplet dispensing configuration 430 may include a gap 417 having a height which is different than the height of the gap of first droplet dispensing configuration 418. In various embodiments, some or all of these size differences are present. 30 Similarly, in certain embodiment, second droplet dispensing configuration 430 has one or more features which are smaller the corresponding features of first droplet dispensing configuration 418. For example, second droplet dispensing configuration 430 may include a reservoir electrode which has a size that is smaller relative to the size of the reservoir electrode of first droplet dispensing configuration 418. Similarly, second droplet dispensing 35 configuration 430 may include droplet operations electrodes which have a size that is smaller relative to the size of droplet operations electrodes of first droplet dispensing configuration 418. As another example, second droplet dispensing configuration 430 may include a gap 33 417 having a height which is smaller relative to the height of the gap of first droplet dispensing configuration 418. In various embodiments, some or all of these size differences are present. In another embodiment, second droplet dispensing configuration 430 has features 5 which are substantially identical to the features of first droplet dispensing configuration 418. Where the gap height of second droplet dispensing configuration 430 differ from the gap height of first droplet dispensing configuration 418, the difference in height may be effected using a variety of means. In one example, the topology of gap 416 may vary by varying the topology of top substrate 414. For example, the thickness of top substrate 414 0 may vary at a transition point 442 (e.g. a step), such that top substrate 414 has a certain thickness in the region of first droplet dispensing configuration 418 and a different thickness in the region of second droplet dispensing configuration 430. In this example, the height of gap 416 may be inversely proportional to the thickness of top substrate 414. Consequently, gap 416 has a certain height in the region of first droplet dispensing configuration 418 and a 5 different height in the region of second droplet dispensing configuration 430. Because the volume of droplets that are dispensed within droplet actuator 400 is proportional to the features of the droplet dispensing configurations, such as droplet operations electrode size and or gap height, droplets having different volumes may be dispensed from the differently sized droplet dispensing configurations. For example, in one 0 embodiment, first droplet dispensing configuration 418 is configured to dispense droplets having a larger volume than droplets dispensed from second droplet dispensing configuration 430. In this manner, large droplets may be dispensed from first droplet dispensing configuration 418 and transported onto reservoir electrode 434 of second droplet dispensing configuration 430. Relatively smaller droplets may be dispensed from second droplet 25 dispensing configuration 430. In this way, droplet actuator 400 provides a mechanism for "staged" droplet dispensing, where, in this example, each successive stage produces a smaller droplet than the previous stage. Droplet actuator 400 is not limited to two droplet dispensing stages only. Droplet actuator 400 may include any number of droplet dispensing stages and, thereby, 30 provide multiple stages for progressing to smaller and smaller droplets. In this manner, scaling from larger fluid volume and larger droplets to smaller fluid volume and smaller droplets may be achieved in the same droplet actuator. Further, the volume of a droplet dispensed may depend on the volume of liquid atop the dispensing electrode. The staged dispensing approach of the invention may be used to 35 maintain the volume of liquid volume atop the second dispensing electrode within a predetermined range in order to maintain the droplets dispensed from the second dispensing electrode within a predetermined droplet volume. Maintaining the droplets dispensed from 34 the second dispensing electrode within a predetermined droplet volume may result in greater accuracy and/or precision of droplets dispensed using the second dispensing configuration 430. In operation, electrodes 422 and 426 may be used to dispense daughter droplets 5 having a first volume from droplet 450. Various techniques for dispensing daughter droplets from a parent droplet using a reservoir electrode and droplet dispensing electrodes may be used. In one such technique, electrodes 422 and 426 are activated to extend the parent droplet along the path of electrodes 426. An intermediate one or more of electrodes 426 may be deactivated to yield a daughter droplet on the path of electrodes 426. Intermediate 0 electrodes designed for controllable necking-and-splitting may be used in this embodiment as well. Terminal electrodes designed for controlling dispensed volume may also be included. The daughter droplet may be transported using droplet operations onto reservoir electrode 434. In this manner, reservoir electrode 434 maybe controllably supplied with liquid. The 5 volume of droplet 454 may thus be established within a predetermined range in order to improve the precision and/or accuracy of droplet dispensing from droplet dispensing configuration 438. Similarly, in embodiments in which gap 416 and/or droplet operations electrodes 438 are smaller along second droplet dispensing configuration 430 relative to droplet operations electrodes 426 along droplet dispensing configuration 418, a smaller 0 volume droplet may be dispensed from droplet dispensing configuration 430. In one example, the droplets that are formed along first droplet dispensing configuration 418 may have microliter volumes and the droplets that are formed along second droplet dispensing configuration 430 may have nanoliter volumes. Figure 5 illustrates a top view of an electrode configuration 500 that uses a physical 25 structure for assisting with a droplet splitting operation in a droplet actuator. Electrode configuration 500 may include a configuration of electrodes 510 (e.g. electrowetting electrodes), such as an array or grid. As illustrated, electrode configuration 500 includes a lane 1 , lane 2, and lane 3 of electrodes 510. Additionally physical obstacle 514 is integrated into electrode configuration 500 at lane 2, in place of electrodes 510 in lane 2. In one 30 example, obstacle 514 may be formed of gasket material, e.g. dry film solder mask. In operation, when an elongated droplet 518 is transported along the grid of electrodes 510, obstacle 514 intersects elongated droplet 518, causing elongated droplet 518 to split into two droplets 522. More specifically, in a first step elongated droplet 518, is formed across three electrodes 510. In a second step elongated droplet 518, is transported 35 via electrowetting operations along electrodes 510 and toward obstacle 514. In a third step, obstacle 514 intersects the elongated droplet 518. In a fourth step, the transport of elongated droplet 518 along electrodes 510 continues until a split occurs due to the action of obstacle 35 514, which results in the formation of two daughter droplets 522. Obstacle 514 produces a reproducible splitting action that results in daughter droplets each having an approximately identical volume. In an alternative embodiment, elongated droplet 518 may span any number of 5 electrodes 510 and/or electrodes may have any of a variety of sizes, so that the elongated droplet may be split via obstacle 514 at any of a range of points along elongated droplet 518. In other words, the point at which the droplet splits may be varied to yield daughter droplets, e.g. a 2:1 split ratio, a 3:1 split ratio, a 4:1 split ratio, etc. The physical barrier may be an elongated barrier, such as the one illustrated in Figure 5, or a shorter barrier, such as a 0 column extending from the bottom substrate to the top substrate of the droplet actuator. The physical barrier may extend from the bottom substrate to the top substrate of the physical barrier or may fill any sufficient space therebetween to cause droplet splitting. Electrodes may be omitted from the region of the physical barrier as illustrated in Figure 5; in other cases, electrodes may underlie the physical barrier. 5 Figure 6A illustrates a top view of an electrode configuration 600 that uses a priming operation in combination with dispensing droplets in a droplet actuator. Figure 6A shows a priming inlet 606 that is positioned for loading liquid 608 at a reservoir electrode 610, which is in proximity with a path of electrodes 614 (e.g. electrowetting electrodes). Additionally, arranged along the path of electrodes 614 are two lateral electrodes 618, as shown in 0 Figure 6A. The two lateral electrodes 618 are used (1) to assist the 'pulling" back of liquid during the droplet splitting operation and (2) to enhance drainage during the droplet necking-and-splitting operation. Alternatively, it will be appreciated that electrodes 618 may be used to control volume of the dispensed droplet, while electrode 614a is used split the droplet. 25 In operation, initially the path of electrodes 614 (e.g. electrodes 614a, 614b, 614c, and 614d) are all activated, and a droplet extension 608 flows from reservoir electrode 610 along electrodes 614a, 614b, 614c, and 614d. Lateral electrodes 618 are initially deactivated. Once the droplet extension is formed, a droplet may be dispensed at electrode 614d by the activating intermediate electrode 614c, which is the intermediate electrode, and activating the 30 two lateral electrodes 618. A variety of activation sequences of possible. Lateral electrodes 618 may be activated followed by deactivation of intermediate electrode 614c. Lateral electrodes 618 may be activated substantially simultaneously with the deactivation of intermediate electrodes 614c. Any activation sequence which reliably yields a droplet at electrode 630 may be used in accordance with the invention. 35 Lateral electrodes 618 may provide 'pulling" action which assists the droplet formation at electrode 614c. Lateral electrodes 618 may provide locations to which liquid may drain, also assisting with the droplet splitting operation. Controlling the drainage of liquid 36 from the neck of the droplet during the droplet splitting operation may enhance the accuracy and/or precision of dispensed droplet volumes. In an alternative configuration, electrodes 618 may be joined with electrode 614b as a single lateral draining electrode. As with other examples, the control of draining may be effected by a field gradient 5 produced across the lateral draining electrode. For example, the field gradient may cause a lengthening in the droplet extension across the lateral draining electrode as voltage is increased. Examples of other techniques for establishing a field gradient across the lateral electrode are gradients in the dielectric constant of the dielectric material atop the electrode caused by doping or thickness of the dielectric material, using various electrode patterns or 0 shapes. The lateral draining electrode may be provided in any configuration or include any structure or shape which causes the length of the droplet extension to depend on the characteristics of the terminal electrode, such as the voltage applied to the terminal electrode. For example, the electrode may be vertically thicker centrally and thinner towards the lateral extensions. Further, various embodiments may be provided in which one or more 5 counter electrodes are also utilized to control the length of the droplet extension across the terminal electrode. As with other examples, the lateral draining and droplet formation may be further controlled by detecting the extent of the droplet extension and effecting droplet formation when the droplet extension has achieved a certain predetermined length. Examples of such 0 detection modalities include visual detection, detection based on imaging, and various detection techniques based on electrical properties of the droplet extension (e.g. electrical properties of the droplet extension relative to the surrounding filler fluid). For example, capacitance detection techniques may be used in some embodiments for determining or monitoring the lateral draining and/or droplet formation. Voltage to the lateral draining 25 electrode or electrodes may, for example, be controlled based on the detected volume of the droplet being dispensed. Figure 6B illustrates a top view of an electrode configuration 640. Figure 6B shows a priming inlet 646 that is configured for loading liquid 648 at a reservoir electrode 650. The priming inlet may, for example, the provided in a top substrate of the droplet actuator. 30 Reservoir electrode 650 is in proximity with a second reservoir electrode 654 in order to form a reservoir electrode pair. In some embodiments, reservoir electrodes 650 and 654 may have an interlocking tongue(656)-and-notch(657) geometry or interdigitations along their common border. Reservoir electrode 654 is in proximity with a path of electrodes 658 (e.g. electrowetting electrodes) arranged for dispensing droplets from reservoir electrode 35 645. In operation, electrodes 658 (e.g. electrodes 658a, 658b, and 658c) are activated to form droplet extension 648, as liquid from reservoir electrode 650 and reservoir electrode 37 654 flows along electrodes 658a, 658b, and 658c. Upon formation of the droplet extension, a droplet may be dispensed at electrode 658b by deactivating intermediate electrode 658a. Electrode 658c may remain activated to provide a 'pulling" action which assists the droplet splitting operation. Consequently, a droplet (not shown) may be formed at electrodes 658b 5 and 658c. Figure 7A illustrates a side view of a droplet actuator 700 configured for providing improved droplet dispensing by modifying gap topology at a designated target electrode. Droplet actuator 700 includes a top substrate 710 and a bottom substrate 722. Top substrate 710 is separated from bottom substrate 722 by a gap 723. Top substrate 710 is associated 0 with a ground electrode 714 configured to serve as a ground for a droplet provided in the gap. Bottom substrate 722 includes droplet operations electrodes 726, configured in a manner appropriate for conducting one more droplet operations in the gap. Both substrates include a dielectric layer 718 facing the gap, and as is typical for droplet actuators, the dielectric layer may be hydrophobic or may be coated with a hydrophobic coating (not 5 shown). A droplet 740 (in Figure 7B) situated in gap 723 may be subjected to droplet operations on droplet operations surface 719. The invention provides a recessed region 734, such as a divot, in the droplet operations surface 719 and/or in the top surface 720. Recessed region 734 may be situated atop one of more of the droplet operations electrodes. For example, as illustrated, recessed 0 region 734 is situated atop electrode 726d. Recessed region 734 may be configured in a manner which stabilizes a droplet atop the electrode. For example, recessed region 734 may be configured in a manner which stabilizes a droplet atop the electrode during a droplet splitting operation. Recessed region 734 may be any variation in the physical topology at the surface of 25 the substrate generally atop an electrode in a manner which enhances stability of a droplet at the electrode relative to a corresponding configuration which lacks the recessed region. Any configuration which provides a recessed region sufficient to enhance stability of a droplet at the electrode will suffice. The size and shape of the recessed region may vary. The recessed region may correspond generally with the shape and size of the associated electrode; 30 however, it is not necessary for the shape and size of the recessed region to exactly correspond with the shape and size of the associated electrode. Sufficient overlap to provide enhanced stability of the droplet that the electrode will suffice. The size and shape of the recessed region may be selected to enhance the accuracy and/or precision of dispensed droplet volumes. 35 Figure 7B illustrates a side view of droplet actuator 700 when in use during a droplet dispensing operation. In operation, electrodes adjacent to the electrode which is associated with the recessed region may be activated, and an intermediate electrode may be 38 deactivated to cause the formation of a droplet situated in the recessed region. As illustrated, electrodes 726a, 726b, 726c, and 726d are activated to cause a droplet extension to flow across the active in electrodes. Electrode 726c is deactivated to cause formation of a droplet in recessed region 734 atop electrode 726d. Because of the larger gap at indent 734, the 5 liquid inherently tends to stay in indent 734. Also a pressure difference at indent 734 tends to pull the droplet or cause the droplet to flow into indent 734. Multiple recessed regions may be provided. For example, a recessed region may be provided atop electrodes 726b (not shown) and 726d (as shown). A droplet may be provided atop activated electrodes 726b, 726c and 726d. Electrode 726c may be deactivated to cause 0 splitting of the droplet, yielding to daughter droplets, one in recessed region 734 atop electrode 726d, and another in the recessed region (not shown) atop electrode 726b. The size and shape of the recessed regions may be selected to enhance the accuracy and/or precision of the daughter droplet volumes. A variety of alternative configurations will be apparent to one of skill in the art on 5 consideration of the disclosure provided herein. For example, the recessed region may in some embodiments be associated with multiple electrodes. A recessed region may be associated with 2, 3, 4 or more electrodes. A droplet splitting operation may produce a droplet which lies atop 2, 3, 4 or more electrodes within such an extended recessed region. In another embodiment, a single droplet actuator may include a variety of recessed regions 0 having different sizes and/or associated with different numbers of electrodes. The recessed region may be provided as an indentation in the dielectric layer. The region may be provided as an indentation in the dielectric layer and the electrode. The region may be provided as an indentation in the dielectric layer the electrode, and the substrate material. The region may be provided as an indentation in the dielectric layer and the substrate material. A recessed 25 region may be provided in the bottom substrate, the top substrate, or both top and bottom substrates. Figure 8 illustrates another embodiment for controlling necking-and-splitting during a droplet splitting or dispensing process. In this embodiment, the necking-and-splitting electrode includes a wire trace in which the wires are more densely spaced in the central 30 region and more sparsely spaced in the outer region. As voltage applied to the necking-and-splitting electrode is reduced, the diameter of the neck is controllably reduced, thereby enhancing the accuracy and/or precision of the daughter droplet volumes. The figure also illustrates alternative configurations for arranging the intermediate necking-and-splitting electrode, which may be used with any of the other embodiments described herein. Voltage 35 may be applied at any point along the trace. In one embodiment, the contact for applying voltage to the trace is generally centrally located. 39 Figure 8A illustrates an arrangement suitable for droplet splitting. Electrode configuration 800 includes droplet operations electrodes 810a and 810b flank necking-and-splitting electrode 805. In operation, all three electrodes may be activated to cause a droplet to extend across the electrode configuration 800. Voltage applied to 5 electrode 805 may be gradually reduced to control necking-and-splitting of the droplet, yielding two daughter droplets atop electrodes 81 0a and 81 Ob. Figure 8B illustrates an arrangement suitable for droplet dispensing. Electrode configuration 840 includes reservoir electrode 816, inset droplet operations electrode 810a, necking-and-splitting electrode 805 and couple operations electrode 810b. Reservoir 0 electrode 816 is adjacent to droplet operations electrode 810a, which is adjacent to necking-and-splitting electrode 805, which is adjacent to droplet operations electrode 810b. In operation, a droplet may be supplied atop reservoir electrode 816. All the electrodes in configuration 840 may be activated, causing a droplet extension to extend from reservoir electrode 816, flowing across electrodes 805 and 810b. Voltage applied to electrode 805 5 may be gradually reduced to control necking-and-splitting of the droplet, yielding a droplet atop electrode 81 Ob. It will be appreciated that the trace electrode in these configurations may be replaced with other electrodes described herein for controlling necking and splitting. Other techniques described herein for creating a field gradient may be used to replace the trace 0 electrode. Further, as with other embodiments, droplet formation and related parameters may be monitored, and voltage applied to the splitting electrode may be controlled to enhance precision and/or accuracy of dispensed droplet volume. Figure 9 illustrates an electrode configuration 900 that is similar to electrode configuration 200 illustrated in Figure 2. Configuration 900 includes an intermediate 25 necking-and-splitting electrode configuration 905 flanked by two droplet operations electrodes 910. The necking-and-splitting electrode configuration 905 includes inner I-shaped electrode 905a and outer electrodes 905b. In operation, all electrodes of electrode configuration 900 may be activated to form an elongated droplet across the top of the electrode configuration. Electrodes 905b may be deactivated to initiate necking of the 30 elongated droplet. Electrode 905a may be deactivated to initiate splitting of the elongated droplet, yielding two daughter droplets atop electrodes 910. Controlling the drainage of liquid from the neck of the droplet during the droplet splitting operation may enhance droplet volume accuracy and/or precision. Figure 10 illustrates an electrode configuration 1000 that is similar to electrode 35 configuration 300 illustrated in Figure 3. Configuration 1000 includes an intermediate necking-and-splitting electrode configuration 1005 flanked by two droplet operations electrodes 1010. The necking-and-splitting electrode configuration includes a series of 40 generally linear or elongated electrodes, including central electrode 1005a, intermediate flanking electrodes 1005b, and outer flanking electrodes 1005c. In operation, all electrodes of electrode configuration 1000 may be activated to form an elongated droplet across the top of the electrode configuration. Outer flanking electrodes 1005c may be deactivated to initiate 5 the necking process. Intermediate flanking electrodes 1005b may be deactivated to continue the necking process. Central electrode 1005a may be initiated to complete the splitting process, yielding two droplets atop electrodes 1010. Controlling the drainage of liquid from the neck of the droplet during the droplet splitting operation may enhance droplet volume accuracy and/or precision. 0 Figures 11 A and 11 B illustrate a side view and top view, respectively, of a section of droplet actuator 1100. Droplet actuator 1100 includes a reservoir substrate 1130 associated with top substrate 1122 for operations fluid 1/O. Reservoir substrate 1130 may be integral with or coupled to top substrate 1122. Droplet actuator 1100 includes a bottom substrate 1110 that includes a reservoir electrode 1114. Reservoir electrode 1114 feeds an 5 arrangement of electrodes 1118 (e.g. electrowetting electrodes 1118a and 1118b). Top substrate 1122 includes an opening 1126 that provides a path suitable for transferring fluid from reservoir 1134 into proximity with or contact with electrode 1114. Reservoir substrate 1130 includes a reservoir 1134 (which may be enclosed, partially enclosed or open). A quantity of sample fluid 1138 operations fluid 1138 may be held in reservoir 1134. 0 Various parameters in the configuration may be adjusted to control dispensing results. Examples of such parameters include: the gap h between bottom substrate 110 and top substrate 122; the width w of reservoir electrode 114; the diameter DI of opening 126 in top substrate 122; the diameter D2 of reservoir 134 and the general geometry of reservoir; the height H of operations fluid 138 in the reservoir 134; the surface tension yo of filler fluid; 25 the surface tension Fl of operations fluid 138; the interfacial tension yLO of operations fluid 138 with filler fluid; the critical surface tension ysolid of droplet actuator surfaces; the liquid contact angle Bs on droplet actuator surface; the critical surface tension well of reservoir substrate wall; the liquid contact angle Ow on the reservoir substrate wall; the applied voltage V; the contact angle 8V at the applied voltage; the applied voltage type i.e. AC or DC; the oil 30 meniscus level; the position of the opening in the top substrate in relation to the reservoir electrode; and the electrode switching sequence. Depending on the function of the reservoir (i.e. input or output) it may be beneficial to adjust the opening in the top substrate (and the reservoir) relative to the reservoir electrode. For example, in order to act as a waste reservoir, the opening is preferably 35 positioned overlapping the first electrode that is adjacent to the reservoir electrode, e.g. as illustrated in Figure 12. A combination of this opening position and the electrode switching 41 sequence used in the "disposal" operation prevents any inadvertent dispensing from this reservoir. The waste reservoir may be made as large as possible to accommodate a large volume of waste. Making the reservoir large lowers the pressure at the reservoir, which 5 allows the discarded liquids to easily flow into the reservoir and prevents inadvertent dispensing from the waste reservoir. More details of one example reservoir position are described with reference to Figures 2A, 2B, 2C, and 2D. Figures 12A, 12B, 12C and 12D illustrate a side view of a droplet actuator 1200. Droplet actuator 1200 includes a reservoir substrate over the top substrate for operations 0 fluid 1/O. Droplet actuator 1200 is substantially the same as droplet actuator 1100 of Figures 1A and 1B, except that droplet actuator 1200 has a certain reservoir(1 134)-to-opening(1 126) position that is suited for disposing of droplets (e.g. droplet 1210) by use of certain electrode switching sequences. It is preferable for the waste droplet to be unit sized (diameter nominally the size of unit electrode) or two times the unit size (2x). 5 The waste droplet may in some embodiments be several times the unit size. For disposing a 2x droplet the switching sequence is changed such that two electrodes are kept ON at a time: OFF ON ON; ON ON OFF; ON OFF OFF; OFF OFF OFF. In a simpler embodiment the opening in the top substrate substantially overlaps the first electrode and the reservoir electrode is not necessary. In this case the switching 0 sequence for 1x droplets is OFF ON; ON OFF; OFF OFF; and the switching sequence for a 2x droplet is ON ON; ON OFF; OFF OFF. Alternatively, the 1x or 2x droplet switching sequence may be used for larger droplets. This embodiment may also be used with a fourth electrode (not shown) for dispensing droplets, e.g. using a switching sequence: ON ON OFF OFF; ON ON ON OFF; ON OFF OFF ON. 25 Figure 12A shows a first step of the sequence, wherein reservoir electrode 114 is turned OFF, electrode 1118a is turned OFF, and electrode 1118b is turned OFF. In this step, the quantity of operations fluid 1138 is retained in reservoir 1134. Figure 2B shows a second step of the sequence, wherein reservoir electrode 1114 is turned ON, electrode 1118a is turned OFF, and electrode 1118b is turned OFF. In this step, a quantity of operations fluid 30 1138 is pulled from reservoir 1134, through opening 1126, and onto reservoir electrode 1114. Figure 2C shows a third step of the sequence, wherein reservoir electrode 1114 is turned OFF, electrode 1118a is turned ON, and electrode 1118b is turned OFF. In this step, droplet 1210 is dispensed from reservoir electrode 1114 and onto electrode 118a due to the pulling action of electrode 118a. Figure 2D shows a fourth step of the sequence, wherein reservoir 35 electrode 1114 is turned OFF, electrode 1118a is turned OFF, and electrode 11 8b is turned ON. In this step, droplet 1210 is transported from electrode 11 8a to electrode 11 8b due to the pulling action of electrode 1118b. 42 Another example switching sequence is: ON ON OFF OFF; ON ON ON OFF; OFF ON ON ON; ON OFF OFF ON. The third state "OFF ON ON ON"with the reservoir electrode OFF allows for the finger to be extended easily up to the 4 th electrode. In typical operation, this state is maintained for only a fraction of a second (e.g. about 1/4 or about 1/8 sec). 5 In order to enter the waste well 1134, the droplet must first overcome the pressure difference between the reservoir and the top substrate opening and then overcome the pressure difference between the opening and the inside of the droplet actuator. These pressure differences may be overcome by the hydrostatic head created by the droplet. The invention also provides embodiments in which the reservoir diameter is large 0 enough to accept small, medium, and large volume pipette tips, without having to use specialized small diameter gel loading tips. In some embodiments the reservoir diameter should be larger than about 1 millimeter (mm). In order to further avoid wetting of the top surface of the reservoir substrate, the diameter of the reservoir may be larger, depending for example, on the volume of liquid to be loaded. A reservoir diameter that is greater than or 5 equal to about 2 mm is sufficient a large range of input volumes, e.g. from about 5 pL to about 5000 pL, or from about 10 pL to about 2000 pL, or from about 50 pL to about 1500 pL. In one configuration, the reservoir is cylindrical. The reservoir may be centered around the opening in the top substrate, as shown in droplet actuator 1100 of Figures 11 A and 11 B. The diameter of the opening in the top substrate is typically between about 1 mm 0 and about 2 mm. The reservoir substrate diameter is typically greater than or equal to about 1.5 mm. The hydrostatic head that is required increases with the diameter, but asymptotically approaches a constant value that is a function of the liquid-oil interfacial tension, liquid-solid contact angle, applied voltage, and gap between the top substrate and the bottom substrate. There is also a hydrostatic head which, when exceeded, may cause the liquid to 25 spontaneously flow into the gap between the bottom and top substrate. It is preferable to keep the head below this value. The graph shown in Figure 16 shows typical behavior of the hydrostatic head requirement while varying the diameter of the reservoir well. The head required asymptotically approaches a constant value with increasing diameter. The region between 30 the two curves (with and without voltage) is the preferred region for dispensing. A head less than the lower curve may interfere with loading of liquid into the droplet actuator, and a head greater than the upper curve may cause causes liquid to flow in spontaneously. The dead volume increases with diameter; however, the number of droplets per additional mm of liquid also increases correspondingly. For a given reservoir substrate height this means that the 35 number of droplets increases. Table 1 below shows experimental data for two different opening diameters for an immunoassay wash buffer (e.g. for conducting bead washing operations). The opening in the 43 top substrate was about 2 mm. The gap between the top substrate and the bottom substrate was about 200 um. The oil was about 0.1% Triton X-15 in 2cSt silicone oil and was added in excess. The reservoir substrate was about 0.250 inches (in) thick. Xwevoir diamotw Ladod. vv1wrno Dmd volwne :Nuimbm of roplos 5 Figure 13 illustrates a side view of a droplet actuator 1300. Droplet actuator 300 is substantially the same as droplet actuator 1100 of Figures 1A and 1B, except that reservoir substrate 1130 of droplet actuator 1100 is replaced with a reservoir substrate 1310. 0 Reservoir substrate 1310 includes reservoir 1318 which includes a larger diameter region having a diameter DI and a restricted diameter region having a restricted diameter DI. Reservoir 1318 also includes a tapering transition region 1319, in which the reservoir diameter tapers from diameter D3 to diameter D2. The height (Hi) of restricted region 1314 may be larger than the "dead height"that 5 corresponds to the dead volume for a reservoir that has diameter D2. The height (H3) of the reservoir substrate 1310 may be larger than the "dead height" (H2) for a reservoir that has diameter D3. Because D2 is smaller than D3, the overall dead volume is small. Because D3 is large, the number of droplets generated may be large. For example, using H1=O.125 in, H3=0.250 in, D1=1.5 mm, and D3=4 mm the final dead volume is from about 5 pL to about 20 10 pL, while being able to dispense about 100 droplets from an initial operations fluid volume of about 40 pL. Though the final dead volume is from about 5 pL to about 10 pL, an initial "activation" volume of liquid may be needed to overcome the pressure difference between D3 and D2. For the case where D3=4 mm and D1=1.5 mm, this "activation" volume was found to 25 be from about 15 pL to about 20 pL. This "activation volume"may be reduced by decreasing D3 or increasing D2. Referring again to Figure 13, as a specific embodiment of this design, HI is about equal to the "dead height" H2 that is required for larger diameter reservoir 1318. The entire capacity of larger diameter reservoir 1318 is then available for dispensing droplets. In 30 another embodiment HI is equal to the asymptotic value of "dead height" as illustrated above. Figures 14A and 14B illustrate a side view and top view, respectively, of a droplet actuator 400. Droplet actuator 400 is substantially the same as droplet actuator 1300 of 44 Figure 13, except that reservoir substrate 1310 of droplet actuator 1300 is replaced with a reservoir substrate 1410, which a constricted opening 1414 providing fluid communication between reservoir main volume 1138 and opening 1126. Opening 1414 may in some embodiments be cylindrical with a diameter D2. Reservoir 1418 may in some embodiments 5 be elongated (e.g. elliptical) with a first dimension D3a and a second dimension D3b, as shown in Figures 4A and 4B. This configuration may increase the capacity of the wells further and the resulting number of available droplets without significantly increasing the dead volume. As compared with droplet actuator 1300 of Figure 13, the dimension of the larger reservoir is increased in one dimension (e.g. D3b) while keeping the other dimension 0 (e.g. D3a) substantially the same as D3 of droplet actuator 1300. Figure 15 illustrates a top view of a droplet actuator 1500. Droplet actuator 500 is substantially the same as droplet actuator 1400 of Figures 14A and 14B, except that reservoir substrate 1410 of droplet actuator 1400 is replaced with a reservoir substrate 1510. Reservoir substrate 1510 includes restricted volume region 1514 and a main volume region 5 which is elongated such that a cross-section of the volume tapers in a direction which is distal with respect to the restricted volume region 1514. Restricted volume region 1514 provides a fluid path from reservoir 1518 through opening 1514 and into the gap of the droplet actuator. Referring to Figures 1A through 15, the use of a spacer may be used in order to 0 prevent liquid from spontaneously flowing into the droplet actuator. For example, a spacer pattern around the reservoir, which narrows down to an approximately one-electrode opening, reduces the chances of liquid from spontaneously flowing into the droplet actuator in an uncontrolled manner. The top substrate and reservoir substrate may be fabricated separately or as one piece of material. Alternative embodiments of the invention may be 25 implemented using a "hybrid"top substrate in which the liquid is loaded around the edge of the glass. Increasing the gap h reduces "dead height" and correspondingly the dead volume. However increasing the gap may adversely affect other processes, such as splitting, and causes an increase in droplet volume. The width w of the reservoir is preferably larger than 30 the unit electrode. The gap height should not be so great as to cause undue interference with droplet operations, such as droplet dispensing and droplet splitting, for which the droplet actuator is intended. Lowering the surface tension Yo of the filler fluid may improve the loading process significantly by lowering the interfacial tension of the liquid with the filler fluid. This is the most 35 effective way of reducing dead volume because it improves the loading of all operations fluids. However extremely low values of surface tension may result in emulsification of the droplets in the filler fluid. The surface tension of the filler fluid should not be lowered to the 45 extent that any resulting emulsification of droplets in the filler fluid is sufficient to cause undue interference with the droplet operations for which the droplet actuator is intended. Lowering the surface tension yL of the droplet improves the loading process significantly by lowering the interfacial tension of the liquid with the oil. However lower 5 surface tension may also causes the liquid to wet the solid surface more. The surface tension of the droplet should not be sufficiently reduced to cause undue interference with the droplet operations for which the droplet actuator is intended. A higher contact angle 8, on the reservoir substrate wall enhances loading. A lower contact angle is preferred for disposal. Higher applied voltage 8v causes a larger contact 0 angle change and aids loading. Contact angle hysteresis is reduced using AC voltage and loading is enhanced. The oil meniscus level has a significant effect on the loading process. Reducing the oil level in the wells to a point at which the liquid in the reservoir has an interface with air significantly improves loading. This is because a liquid-air interface has a higher interfacial 5 tension and a correspondingly higher Laplace pressure than a liquid-oil interface. A higher Laplace pressure at the reservoir reduces the pressure difference that needs to be overcome. Concluding Remarks 0 The foregoing detailed description of embodiments refers to the accompanying drawings, which illustrate specific embodiments of the invention. Other embodiments having different structures and operations do not depart from the scope of the present invention. This specification is divided into sections for the convenience of the reader only. Headings 25 should not be construed as limiting of the scope of the invention. The definitions are intended as a part of the description of the invention. It will be understood that various details of the present invention may be changed without departing from the scope of the present invention. Furthermore, the foregoing description is for the purpose of illustration only, and not for the purpose of limitation, as the present invention is defined by the claims as set forth 30 hereinafter. Variations and Modifications It will be appreciated by persons skilled in the art that numerous variations and/or 35 modifications may be made to the invention as shown in the specific embodiments without departing from the spirit or scope of the invention as broadly described. The present embodiments are, therefore, to be considered in all respects as illustrative and not restrictive. 46 In the claims which follow and in the preceding description of the invention, except where the context requires otherwise due to express language or necessary implication, the word "comprise" or variations such as "comprises" or "comprising" is used in an inclusive sense, i.e. to specify the presence of stated features but not to preclude the presence or 5 addition of further features in various embodiments of the invention. 47

Claims (184)

1. A droplet actuator comprising: (a) a top substrate assembly comprising reservoir; 5 (b) a bottom substrate assembly separated from the top substrate to form a gap; (c) electrodes associated with the top substrate assembly and/or the bottom substrate assembly and configured to conduct one or more droplet operations; 0 (d) a fluid path configured for: (i) flowing fluid from the reservoir into the gap, where the droplet is subjected to one or more droplet operations mediated by one or more of the electrodes; and/or (ii) transporting fluid using the electrodes into contact with the opening 5 and causing the fluid to substantially exit the gap and enter the reservoir.

2. The droplet actuator of Claim 1, wherein the top substrate assembly comprises: (a) a top substrate; and 0 (b) a reservoir substrate associated with the top substrate and comprising the reservoir formed therein.

3. The droplet actuator of Claim 1 or Claim 2, comprising a reservoir electrode associated with the bottom substrate. 25

4. The droplet actuator of Claim 3, wherein the opening overlaps an edge of the reservoir electrode.

5. The droplet actuator of Claim 3 or Claim 4, further comprising a first droplet 30 operations electrode associated with the bottom substrate and adjacent to the reservoir electrode, wherein the opening overlaps an edge of the first electrode and an edge of the droplet operations electrode.

6. The droplet actuator of Claim 3 or Claim 4, further comprising a first droplet 35 operations electrode associated with the bottom substrate and at least partially inset into the reservoir electrode, wherein the opening overlaps an edge of the first electrode and an edge of the droplet operations electrode. 48

7. The droplet actuator of any one of the preceding claims, configured to facilitate flow of droplets from the gap into the reservoir. 5

8. The droplet actuator of any one of the preceding claims, wherein the reservoir has a diameter which is greater than about 1 mm.

9. The droplet actuator of any one of Claims 1 to 7, wherein the reservoir has a diameter which is greater than about 2 mm. 0

10. The droplet actuator of any one of Claims 1 to 7, wherein the reservoir has a volume sufficient to hold a volume of liquid ranging from about 100 to about 300mL.

11. The droplet actuator of any one of Claims 1 to 7, wherein the reservoir has a volume 5 sufficient to hold a volume of liquid ranging from about 5 pL to about 5000 pL.

12. The droplet actuator of any one of Claims 1 to 7, wherein the reservoir has a volume sufficient to hold a volume of liquid ranging from about 10 pL to about 2000 pL. 0

13. The droplet actuator of any one of Claims 1 to 7, wherein the reservoir has a volume sufficient to hold a volume of liquid ranging from about 50 pL to about 1500 pL.

14. The droplet actuator of any of the preceding claims, wherein the reservoir has dimensions which are substantially cylindrical. 25

15. The droplet actuator of Claim 14, wherein the opening is substantially aligned about an axis of the cylindrical dimensions of the reservoir.

16. The droplet actuator of any one of the preceding claims, wherein the gap comprises 30 a filler fluid.

17. The droplet actuator of Claim 16, wherein the filler fluid comprises an oil.

18. The droplet actuator of any one of the preceding claims, wherein the reservoir 35 comprises a region having a reduced diameter relative to a main volume of the reservoir, the region having a reduced diameter providing a fluid path between the main volume of the reservoir and the opening. 49

19. The droplet actuator of Claim 18, wherein the restricted region of the reservoir has a height above the bottom substrate that exceeds the dead height corresponding to the dead volume of the restricted region of the reservoir. 5

20. The droplet actuator of Claim 18, wherein the main volume of the reservoir has a height above the bottom substrate that exceeds the dead height corresponding to the dead volume of the main volume of the reservoir. 0

21. The droplet actuator of Claim 18, wherein: (a) the restricted region of the reservoir has a first diameter and a first height above the bottom substrate; (b) the main volume of the reservoir has a second diameter, a second height above the bottom substrate; and 5 (c) the first diameter, first height, second diameter, and second height are selected such that a liquid volume equal to substantially all of the volume of the main volume of the reservoir is available for dispensing.

22. The droplet actuator of any one of the preceding claims, wherein the main volume of 0 the reservoir is elongated relative to a cylindrical main volume without substantially increasing dead volume relative to the corresponding cylindrical main volume.

23. A method of transporting a droplet out of a droplet actuator gap, the method comprising: 25 (a) providing a droplet actuator comprising: (i) a top substrate assembly comprising reservoir; (ii) a bottom substrate assembly separated from the top substrate to form a gap; (iii) electrodes associated with the top substrate assembly and/or the 30 bottom substrate assembly and configured to conduct one or more droplet operations; (iv) a fluid path configured for flowing fluid from the gap into the reservoir; (v) transporting fluid using the electrodes into contact with the opening 35 and causing the fluid to substantially exit the gap and enter the reservoir. 50

24. The method of Claim 23, wherein the top substrate assembly comprises: (a) a top substrate; and (b) a reservoir substrate associated with the top substrate and comprising the reservoir formed therein. 5

25. The method of Claim 23, comprising a reservoir electrode associated with the bottom substrate.

26. The method of Claim 25, wherein the opening overlaps an edge of the reservoir 0 electrode.

27. The method of Claim 26, further comprising a first droplet operations electrode associated with the bottom substrate and adjacent to the reservoir electrode, wherein the opening overlaps an edge of the first electrode and an edge of the droplet operations 5 electrode.

28. The method of Claim 26, further comprising a first droplet operations electrode associated with the bottom substrate and at least partially inset into the reservoir electrode, wherein the opening overlaps an edge of the first electrode and an edge of the droplet 0 operations electrode.

29. A droplet actuator comprising a droplet formation electrode configuration associated with a droplet operations surface, wherein the electrode configuration comprises one or more electrodes configured to control a position of an edge of a droplet during formation of a 25 sub-droplet on the droplet operations surface.

30. The droplet actuator of Claim 29, wherein the edge of the droplet controlled during droplet formation comprises an edge of a necking region of the droplet. 30

31. The droplet actuator of Claim 29, wherein the edge of the droplet controlled during droplet formation comprises an edge of the sub-droplet being formed.

32. The droplet actuator of Claim 31, wherein the control of the position of the edge of the droplet controls the volume of the sub-droplet. 35

33. The droplet actuator of any one of Claims 29 to 32, wherein the control is exerted by controlling voltage applied to the electrode. 51

34. The droplet actuator of Claim 29, wherein: (a) the electrode configuration comprises: (i) an intermediate electrode configuration comprising: 5 (1) one or more inner electrodes; and (2) two or more outer electrodes arranged laterally with respect to the inner electrode; and (ii) electrodes flanking the intermediate electrode configuration; and (b) the intermediate electrode configuration and electrodes flanking the 0 intermediate electrode configuration are arranged such that activation of the intermediate electrode configuration and the electrodes flanking the intermediate electrode configuration in the presence of the droplet causes the droplet to elongate across the droplet forming electrode configuration. 5

35. The droplet actuator of Claim 34, wherein a reduction in voltage applied to two or more of the outer electrodes in the presence the elongated droplet initiates necking of the elongated droplet.

36. The droplet actuator of Claim 35, wherein reduction in voltage applied to the one or 0 more inner electrodes following a reduction in voltage applied to the two or more outer electrodes breaks the elongated droplet, forming one or more sub-droplets.

37. The droplet actuator of Claim 34, wherein deactivation of the two or more outer electrodes in the presence the elongated droplet initiates necking of the elongated droplet. 25

38. The droplet actuator of Claim 35, wherein deactivation of the one or more inner electrodes following deactivation of all outer electrodes breaks the elongated droplet, forming one or more sub-droplets. 30

39. The droplet actuator of Claim 34, wherein two or more outer electrodes arranged laterally with respect to the inner electrode are electrically coupled and function as a single electrode.

40. The droplet actuator of any one of Claims 29 to 39, comprising a reservoir electrode 35 adjacent to the droplet formation electrode configuration. 52

41. The droplet actuator of any one of Claims 29 to 40, comprising a droplet operations electrode adjacent to the droplet formation electrode configuration.

42. The droplet actuator of Claim 30, wherein: 5 (a) the electrode configuration comprises: (i) one or more centrally located electrodes; and (ii) one or more necking electrodes adjacent to an edge of the droplet forming electrode configuration; (b) the centrally located electrodes and necking electrodes are configured to 0 control droplet necking and splitting in a droplet splitting process effected by sequential deactivation of sets of electrodes beginning with the necking electrodes and continuing to the centrally located electrodes.

43. The droplet actuator of any one of Claims 29 to 42, wherein the electrode 5 configuration comprises a centrally located electrode that is generally I-shaped and/or hourglass shaped.

44. The droplet actuator of any one of Claims 29 to 43, wherein: (a) the electrode configuration is interposed in a path of electrodes; 0 (b) the electrode configuration and the path of electrodes are arranged along a common axis; (c) the electrode configuration comprises: (i) a central electrode arranged symmetrically about the common axis; and 25 (ii) necking electrodes flanking the central electrode.

45. The droplet actuator of Claim 44, further comprising a second set of necking electrodes flanking the first set of necking electrodes. 30

46. The droplet actuator of Claim 44, wherein the necking electrodes have a shape which is convex away from the axis.

47. The droplet actuator of Claim 44, wherein the necking electrodes comprise electrode bars oriented in a substantially parallel orientation relative to the central electrode. 35 53

48. The droplet actuator of any one of Claims 44 to 47, wherein the electrode configuration has a size which is approximately equal to the size of one or more adjacent electrodes in the path of electrodes. 5

49. The droplet actuator of any one of Claims 29 to 48, wherein the electrode configuration comprises four triangles arranged to form a square or rectangle.

50. The droplet actuator of Claim 29, wherein the electrode configuration comprises an electrode that produces an electrical field gradient that controls a position of an edge of the o droplet during formation of the sub-droplet.

51. The droplet actuator of Claim 50, wherein the electrode that produces the electrical field gradient controls a position of an edge of a necking region of the droplet during formation of a sub-droplet. 5

52. The droplet actuator of Claim 51, wherein the electrode produces: (a) an electrical field gradient at a first voltage that induces droplet necking; and (b) an electrical field gradient at a second voltage that induces droplet splitting. 0

53. The droplet actuator of Claim 51, wherein the electrode produces: (a) an electrical field gradient at a first voltage that induces droplet extension; (b) an electrical field gradient at a second voltage that induces droplet necking; and 25 (c) an electrical field gradient at a third voltage that induces droplet splitting.

54. The droplet actuator of any of Claims 50 to 53, wherein the field gradient is established by a composition atop the electrode. 30

55. The droplet actuator of Claim 54, wherein the composition comprises a dielectric composition.

56. The droplet actuator of Claim 54, wherein the composition comprises a patterned material comprising regions having different thicknesses. 35

57. The droplet actuator of Claim 54, wherein the composition comprises a patterned material comprising regions having different relative static permittivity or dielectric constant. 54

58. The droplet actuator of Claim 54, wherein the composition comprises two or more patterned materials, each patterned material having a different relative static permittivity or dielectric constant. 5

59. The droplet actuator of Claim 54, wherein the composition comprises: (a) a dielectric material having a first dielectric constant; and (b) a dielectric material having a second dielectric constant which is different from the first dielectric constant. 0

60. The droplet actuator of Claim 54, wherein the composition comprises dielectric material doped in a patterned fashion with one or more substances that modify the dielectric constant of the dielectric material. 5

61. The droplet actuator of any one of the preceding claims, wherein the field gradient is established by means comprising shape of the electrode that produces the electrical field gradient.

62. The droplet actuator of any one of Claims 50 to 61, wherein the field gradient is 0 established by means comprising variations in electrode thickness in the electrode that produces the electrical field gradient.

63. The droplet actuator of any one of Claims 50 to 62, wherein the field gradient is established by means comprising spatial orientation of the electrode in a z direction relative 25 to a droplet operations surface of the droplet actuator.

64. The droplet actuator of any one of Claims 50 to 63, wherein the electrode that produces the electrical field gradient comprises conductivity patterns established within the electrode. 30

65. The droplet actuator of Claim 64, wherein the electrode that produces the electrical field gradient comprises two or more different conductive materials patterned to produce a predetermined field gradient. 35

66. The droplet actuator of any one of Claims 50 to 65, wherein the electrode that produces the electrical field gradient comprises a wire trace in which different regions the 55 electrode that produces the electrical field gradient comprise different densities of wire spacing.

67. A system comprising the droplet actuator of any one of Claims 29 to 66, and a 5 processor programmed to control the supply of voltage to the one or more electrodes configured to control a position of an edge of the droplet during formation of the sub-droplet.

68. The system of Claim 67, further comprising a sensor for monitoring an edge of the droplet during formation of the sub-droplet. 0

69. The system of Claim 68, wherein the processor is further configured to adjust voltage of one or more of the electrodes configured to control the position of the edge of the droplet during formation of the sub-droplet. 5

70. The system of Claim 67, further comprising a sensor for monitoring a parameter associated with volume of the sub-droplet.

71. The system of Claim 70, wherein the processor is further configured to adjust voltage of one or more of the electrodes configured to control a position of an edge of the o droplet during formation of the sub-droplet.

72. The system of any one of Claims 68 to 71, wherein the sensor is selected to detect one or more electrical, chemical and/or physical properties of the droplet. 25

73. The system of any one of Claims 68 to 72, wherein the sensor comprises an imaging device configured to image the droplet.

74. A droplet actuator comprising substrate comprising a path or array of electrodes, the path or array comprising one or more electrodes formed using a wire trace. 30

75. The droplet actuator of Claim 74, wherein the wire trace configuration includes wires in a meandering path, wherein each turn in the meandering path is substantially equal to other turns in the path. 35

76. The droplet actuator of Claim 74, wherein the wire trace configuration comprises regions of differing wire density. 56

77. The droplet actuator of Claim 74, wherein the wire trace configuration comprises a central axial region that has greater wire density than an outer region.

78. The droplet actuator of Claim 74, wherein: 5 (a) the wire trace configuration comprises an elongated electrode having a first end region and a second end region; and (b) the first end region has greater wire density than the second end region.

79. The droplet actuator of Claim 78, wherein wire density gradually increases along the 0 length of the elongated from the second end region to the first end region.

80. A droplet actuator comprising an droplet formation electrode configuration for forming a droplet, wherein: (a) the droplet forming electrode configuration comprises: 5 (i) a droplet source; (ii) an intermediate electrode; and (iii) a terminal electrode; (b) when a liquid is present at the droplet source, activation of the intermediate electrode, and the terminal electrode causes a droplet extension to flow 0 across the intermediate electrode and onto the terminal electrode; (c) increasing voltage applied to the terminal electrode increases length of the droplet extension; and (d) deactivation of the intermediate electrode breaks the droplet into two sub-droplets. 25

81. The droplet actuator of Claim 80, wherein the droplet source comprises a droplet source electrode.

82. The droplet actuator of Claim 80, wherein the droplet source electrode comprises a 30 reservoir electrode.

83. The droplet actuator of Claim 80, wherein the droplet source electrode comprises a droplet operations electrode. 35

84. The droplet actuator of any of Claims 80, and following, wherein the terminal electrode is elongated relative to the intermediate electrode. 57

85. The droplet actuator of any of Claims 80, and following, wherein the terminal electrode has a substantially tapering shape.

86. The droplet actuator of Claim 84, wherein the terminal electrode tapers away from 5 the droplet source electrode.

87. The droplet actuator of Claim 84, wherein the terminal electrode tapers towards the droplet source electrode. 0

88. The droplet actuator of any of Claims 80, and following, wherein the terminal electrode is substantially triangular in shape.

89. The droplet actuator of Claim 88, wherein an apex of the terminal electrode is inset into a notch in the intermediate electrode. 5

90. The droplet actuator of any one of Claims 80 to 89, wherein the terminal electrode tapers from a widest region which is oriented distally with respect to the intermediate electrode to a narrow region which is oriented proximally with respect to the intermediate electrode. 0

91. The droplet actuator of any one of Claims 80 to 90, wherein the terminal electrode tapers from a widest region which is oriented proximally with respect to the intermediate electrode to a narrow region which is oriented distally with respect to the intermediate electrode. 25

92. The droplet actuator of Claim 90 or 91, wherein the widest region is approximately equal in width to the diameter of the intermediate electrode taken along an axis of the electrode configuration. 30

93. The droplet actuator of Claim 90 or 91, wherein the narrow region is narrower than the diameter of the intermediate electrode taken along an axis of the electrode configuration.

94. The droplet actuator of any one of Claims 90 to 93, wherein the droplet actuator is provided as a component of a system comprising: 35 (a) the droplet actuator; and (b) a processor programmed to: (i) control voltage applied to electrodes of the electrode configuration; 58 (ii) control droplet volume by adjusting voltage applied to the terminal electrode.

95. A droplet actuator comprising an electrode configured to conduct a droplet 5 operation, wherein the electrode is configured to produce an electric field gradient that effects a droplet operation by effecting a change in voltage applied to the electrode.

96. The droplet actuator of Claim 95, comprising a dielectric material atop the electrode configured to establish a dielectric topography that controls the droplet operation upon 0 effecting the change in voltage applied to the electrode.

97. The droplet actuator of any one of Claims 95 to 96, wherein the field gradient is established by means comprising a patterned material atop the electrode. 5

98. The droplet actuator of Claim 97, wherein the patterned material atop the electrode comprises a dielectric material comprising regions having different thicknesses.

99. The droplet actuator of Claim 97, wherein the patterned material atop the electrode comprises a dielectric material comprising regions having different dielectric constants. 0

100. The droplet actuator of Claim 97, wherein the patterned material atop the electrode comprises a dielectric material comprising two or more patterned materials, each patterned material having a different dielectric constant. 25

101. The droplet actuator of Claim 97, wherein the patterned material atop the electrode comprises a dielectric material having a composition which is varied to produce the electric field gradient.

102. The droplet actuator of any one of the Claims 97 to 101, wherein the patterned 30 material atop the electrode comprises: (a) a first dielectric material of a first dielectric constant patterned on the electrode; and (b) a second dielectric material of a second dielectric constant layered on the first dielectric material. 35 59

103. The droplet actuator of any one of Claims 97 to 102, wherein the field gradient is configured to control the droplet necking and splitting upon reduction of voltage applied to the electrode. 5

104. The droplet actuator of Claim 103, wherein necking is induced by a first reduction in voltage applied to the electrode configuration and breaking is induced by a second reduction in voltage applied to the electrode configuration.

105. The droplet actuator of any one of Claims 97 to 104, wherein the field gradient is 0 established by means comprising electrode shape.

106. The droplet actuator of any one of Claims 97 to 105, wherein the field gradient is established by means comprising electrode thickness. 5

107. The droplet actuator of any one of Claims 97 to 106, wherein the field gradient is established by means comprising conductivity patterns established within the electrode.

108. The droplet actuator of Claim 107, wherein the electrode comprises two or more different conductive materials patterned to produce a predetermined field gradient. 0

109. The droplet actuator of any one of Claims 97 to 108, wherein the field gradient is established by means comprising a wire trace in which different regions of the electrode configuration have different densities of wire spacing. 25

110. The droplet actuator of any one of Claims 97 to 109, wherein the field gradient is established by a means comprising a pattern of conductive material within the electrode.

111. The droplet actuator of any one of Claims 97 to 110, wherein the field gradient is established by a means comprising a pattern of nonconductive material within the electrode. 30

112. The droplet actuator of any one of Claims 97 to 111, wherein the field gradient is established by a means comprising a pattern of differently conductive material within the electrode. 35

113. The droplet actuator of any one of Claims 97 to 112, wherein the electrode produces a patterned field gradient that effects a droplet operation upon activation, deactivation or an adjustment in voltage. 60

114. The droplet actuator of any one of Claims 97 to 113, wherein a reduction in voltage effects a droplet operation. 5

115. The droplet actuator of any one of Claims 97 to 114, wherein an increase in voltage effects extension of a droplet.

116. The droplet actuator of any one of Claims 97 to 115, wherein an increase in voltage in the presence of a droplet on the electrode effects extension of the droplet. 0

117. A method of controlling a position of an edge of a droplet during formation of a sub-droplet, the method comprising: (a) providing droplet actuator comprising a droplet formation electrode configuration associated with a droplet operations surface, wherein the 5 electrode configuration comprises one or more electrodes configured to control a position of an edge of the droplet during formation of the sub-droplet on the droplet operations surface; and (b) forming the sub-droplet while using the electrode configuration to control the edge of the droplet. 0

118. The method of Claim 117, comprising controlling an edge of a necking region of the droplet while forming the sub-droplet.

119. The method of Claim 117, comprising controlling an edge of the sub-droplet while 25 forming the sub-droplet.

120. The method of Claim 117, comprising controlling the volume of the sub-droplet while forming the sub-droplet. 30

121. The method of any one of Claims 117 to 120, wherein forming the sub-droplet comprises voltage applied to the electrode configuration.

122. The method of Claim 117, wherein: (a) the electrode configuration comprises: 35 (i) an intermediate electrode configuration comprising: (1) one or more inner electrodes; and 61 (2) two or more outer electrodes arranged laterally with respect to the inner electrode; and (ii) electrodes flanking the intermediate electrode configuration; and (b) the intermediate electrode configuration and electrodes flanking the 5 intermediate electrode configuration are arranged such that activation of the intermediate electrode configuration and the electrodes flanking the intermediate electrode configuration in the presence of the droplet causes the droplet to elongate across the droplet forming electrode configuration. 0

123. The method of Claim 122, wherein a reduction in voltage applied to two or more of the outer electrodes in the presence the elongated droplet initiates necking of the elongated droplet.

124. The method of Claim 123, wherein reduction in voltage applied to the one or more 5 inner electrodes following a reduction in voltage applied to the two or more outer electrodes breaks the elongated droplet, forming one or more sub-droplets.

125. The method of Claim 122, wherein deactivation of the two or more outer electrodes in the presence the elongated droplet initiates necking of the elongated droplet. 0

126. The method of Claim 125, wherein deactivation of the one or more inner electrodes following deactivation of all outer electrodes breaks the elongated droplet, forming one or more sub-droplets. 25

127. The method of Claim 122, wherein two or more outer electrodes arranged laterally with respect to the inner electrode are electrically coupled and function as a single electrode.

128. The method of any one of Claims 117 to 127, wherein: (a) the electrode configuration comprises a reservoir electrode adjacent to the 30 droplet formation electrode configuration; and (b) forming the sub-droplet comprises dispensing a smaller volume droplet from a larger volume droplet.

129. The method of any one of Claims 117 to 128, comprising a droplet operations 35 electrode adjacent to the droplet formation electrode configuration.

130. The method of Claim 117, wherein: 62 (a) the electrode configuration comprises: (i) one or more centrally located electrodes; and (ii) one or more necking electrodes adjacent to an edge of the droplet forming electrode configuration; and 5 (b) forming the sub-droplet comprises sequentially deactivating sets of electrodes beginning with the necking electrodes and continuing to the centrally located electrodes.

131. The method of any one of Claims 117 to 130, wherein the electrode configuration 0 comprises a centrally located electrode that is generally I-shaped and/or hourglass shaped.

132. The method of any one of the Claims 117 to 131, wherein: (a) the electrode configuration is interposed in a path of electrodes; (b) the electrode configuration and the path of electrodes are arranged along a 5 common axis; (c) the electrode configuration comprises: (i) a central electrode arranged symmetrically about the common axis; and (ii) necking electrodes flanking the central electrode. 0

133. The method of Claim 132, further comprising a second set of necking electrodes flanking the first set of necking electrodes.

134. The method of Claim 132, wherein the necking electrodes have a shape which is 25 convex away from the axis.

135. The method of Claim 132, wherein the necking electrodes comprise electrode bars oriented in a substantially parallel orientation relative to the central electrode. 30

136. The method of any one of Claims 132 to 135, wherein the electrode configuration has a size which is approximately equal to the size of one or more adjacent electrodes in the path of electrodes.

137. The method of any one of Claims 117 to 136, wherein the electrode configuration 35 comprises four triangles arranged to form a square or rectangle. 63

138. The method of Claim 117, wherein the electrode configuration comprises an electrode that produces an electrical field gradient that controls a position of an edge of the droplet during formation of the sub-droplet. 5

139. The method of Claim 138, comprising controlling the position of an edge of the droplet by using the electrode configuration to establish an electrical field gradient that controls the position of an edge of a necking region of the droplet during formation of a sub-droplet. 0

140. The method of Claim 139, comprising controlling voltage applied to the electrode configuration to establish: (a) an electrical field gradient at a first voltage that induces droplet necking; and (b) an electrical field gradient at a second voltage that induces droplet splitting. 5

141. The method of Claim 139, comprising controlling voltage applied to the electrode configuration to establish: (a) an electrical field gradient at a first voltage that induces droplet extension; (b) an electrical field gradient at a second voltage that induces droplet necking; 0 and (c) an electrical field gradient at a third voltage that induces droplet splitting.

142. The method of any one of Claims 138 to 141, wherein the field gradient is established by a composition atop the electrode. 25

143. The method of Claim 142, wherein the composition comprises a dielectric composition.

144. The method of Claim 142, wherein the composition comprises a patterned material 30 comprising regions having different thicknesses.

145. The method of Claim 142, wherein the composition comprises a patterned material comprising regions having different relative static permittivity or dielectric constant. 35

146. The method of Claim 142, wherein the composition comprises two or more patterned materials, each patterned material having a different relative static permittivity or dielectric constant. 64

147. The method of Claim 142, wherein the composition comprises: (a) a dielectric material having a first dielectric constant; and (b) a dielectric material having a second dielectric constant which is different 5 from the first dielectric constant.

148. The method of Claim 142, wherein the composition comprises dielectric material doped in a patterned fashion with one or more substances that modify the dielectric constant of the dielectric material. 0

149. The method of any one of Claims 138 to 148, wherein the field gradient is established by means comprising shape of the electrode that produces the electrical field gradient. 5

150. The method of any one of Claims 138 to 149, wherein the field gradient is established by means comprising variations in electrode thickness in the electrode that produces the electrical field gradient.

151. The method of any one of Claims 138 to 150, wherein the field gradient is 0 established by means comprising spatial orientation of the electrode in a z direction relative to a droplet operations surface of the droplet actuator.

152. The method of any one of Claims 138 to 151, wherein the electrode that produces the electrical field gradient comprises conductivity patterns established within the electrode. 25

153. The method of Claim 152, wherein the electrode that produces the electrical field gradient comprises two or more different conductive materials patterned to produce a predetermined field gradient. 30

154. The method of any one of Claims 138 to 153, wherein the electrode that produces the electrical field gradient comprises a wire trace in which different regions the electrode that produces the electrical field gradient comprise different densities of wire spacing.

155. The method of any one of Claims 117 to 154, comprising using a system to control 35 forming the sub-droplet and using the electrode configuration to control the edge of the droplet. 65

156. The method of Claim 155, wherein the system comprises a processor programmed to control the supply of voltage to the one or more electrodes of the electrode configuration.

157. The method of Claim 156, comprising using a sensor coupled to the processor for 5 monitoring an edge of the droplet during formation of the sub-droplet.

158. The method of Claim 157, wherein the processor is configured to control the volume of the dispensed sub-droplet by adjusting voltage of one or more electrodes of the electrode configuration in response to a sensed position of the edge of the droplet while forming of the 0 sub-droplet in order to locate the edge of the droplet at a predetermined position indicative of a desired sub-droplet volume.

159. A method of forming a sub-droplet from a droplet, the method comprising controllably reducing the diameter of a necking region of a droplet in a necking-and-splitting 5 process.

160. The method of Claim 159, wherein the sub-droplet has a predetermined volume.

161. A method forming a sub-droplet from a droplet, the method comprising controllably 0 expanding the volume of the droplet atop a terminal electrode and initiating a droplet splitting process at an intermediate electrode upon reaching a predetermined volume atop the terminal electrode.

162. The method of Claim 161, wherein the sub-droplet has a predetermined volume. 25

163. A method of forming a sub-droplet, the method comprising: (a) providing an elongated droplet spanning an electrode configuration comprising a first electrode and a second electrode, the elongated droplet comprising a volume of liquid atop the first electrode and a volume of liquid 30 atop the second electrode; (b) controllably expanding the volume of the elongated droplet atop the second electrode; and (c) splitting the droplet at the first electrode to yield the sub-droplet. 35

164. The method of Claim 163, wherein the sub-droplet has a predetermined volume.

165. A method of forming a sub-droplet, the method comprising: 66 (a) providing an elongated droplet spanning an electrode configured to produce a field gradient comprising an intermediate region in which a relatively higher voltage is required to effect electrowetting atop the intermediate region; 5 (b) applying a voltage to the electrode sufficient to cause a droplet to expand across the intermediate region; (c) sufficiently reducing the voltage to cause the droplet to break at the intermediate region. 0

166. The method of Claim 165, wherein the field gradient is established by means comprising electrode shape.

167. The droplet actuator of any one of Claims 165 to 166, wherein the field gradient is established by means comprising electrode thickness. 5

168. The droplet actuator of any one of Claims 165 to 167, wherein the field gradient is established by means comprising conductivity patterns established within the electrode.

169. The droplet actuator of Claim 168, wherein the electrode comprises two or more o different conductive materials patterned to produce a predetermined field gradient.

170. The droplet actuator of any one of Claims 165 to 169, wherein the field gradient is established by means comprising a wire trace in which different regions of the electrode configuration have different densities of wire spacing. 25

171. The droplet actuator of any one of Claims 165 to 170, wherein the field gradient is established by a means comprising a pattern of conductive material within the electrode.

172. The droplet actuator of any one of Claims 165 to 171, wherein the field gradient is 30 established by a means comprising a pattern of nonconductive material within the electrode.

173. The droplet actuator of any one of Claims 165 to 172, wherein the field gradient is established by a means comprising a pattern of differently conductive material within the electrode. 35 67

174. The droplet actuator of any one of Claims 165 to 173, wherein the electrode produces a patterned field gradient that effects a droplet operation upon activation, deactivation or an adjustment in voltage. 5

175. A method of forming a sub-droplet, the method comprising: (a) providing an elongated droplet spanning an electrode configuration comprising a terminal electrode region configured to produce a field gradient, wherein droplet volume atop the terminal region is incrementally increased by increasing voltage applied to the terminal region; 0 (b) applying a voltage to the electrode sufficient to cause a droplet to expand to a predetermined volume atop the terminal region; (c) causing the droplet to break, thereby forming a sub-droplet atop the terminal region. 5

176. The method of Claim 175, wherein the terminal region is configured to permit increasing droplet volume atop the terminal region to a volume which is greater than the volume of an adjacent unit sized droplet operations electrode.

177. The droplet actuator of any one of Claims 175 to 176, wherein the field gradient is 0 established by means comprising electrode shape.

178. The droplet actuator of any one of Claims 175 to 177, wherein the field gradient is established by means comprising electrode thickness. 25

179. The droplet actuator of any one of Claims 175 to 178, wherein the field gradient is established by means comprising conductivity patterns established within the electrode.

180. The droplet actuator of Claim 179, wherein the electrode comprises two or more different conductive materials patterned to produce a predetermined field gradient. 30

181. The droplet actuator of any one of Claims 175 to 180, wherein the field gradient is established by means comprising a wire trace in which different regions of the electrode configuration have different densities of wire spacing. 35

182. The droplet actuator of any one of Claims 175 to 181, wherein the field gradient is established by a means comprising a pattern of conductive material within the electrode. 68

183. The droplet actuator of any one of Claims 175 to 182, wherein the field gradient is established by a means comprising a pattern of nonconductive material within the electrode.

184. The droplet actuator of any one of Claims 175 to 183, wherein the field gradient is 5 established by a means comprising a pattern of differently conductive material within the electrode. 69