WO2017040665A1

WO2017040665A1 - Piezoelectric-driven droplet impact printing with an interchangeable microfluidic cartridge

Info

Publication number: WO2017040665A1
Application number: PCT/US2016/049702
Authority: WO
Inventors: Tingrui Pan; Kit S. Lam; Jiannan LI; Baoqing Li; Jinzhen FAN
Original assignee: The Regents Of The University Of California
Priority date: 2015-08-31
Filing date: 2016-08-31
Publication date: 2017-03-09

Abstract

A droplet generation platform is disclosed that is based on the microfluidic impact printing technology, where low-cost piezoelectric actuators have been utilized as the impact forces. The modular microfluidic cartridge composed of all polymeric material provides a new, simple means for chemical loading and droplet-generation with interchangeability, low cost, non-contamination, and multiplexability.

Description

PIEZOELECTRIC-DRIVEN DROPLET IMPACT PRINTING WITH AN INTERCHANGEABLE MICROFLUIDIC CARTRIDGE

Inventors: Tingrui Pan, Kit S. Lam, Jiannan Li,

Baoqing Li, and Jinzhen Fan

BACKGROUND

Technical Field

[0001] This disclosure relates to droplet impact printing. More specifically, this disclosure relates to piezoelectric -driven droplet impact printing with an interchangeable microfluidic cartridge.

Related Art

[0002] Droplet generation has been recently adapted to numerous biological and biochemical applications in both academia and industry. These miniscule liquid carriers, often serving as microreactors or capsules, offer several distinct advantages over their conventional counterparts, including significantly high throughput, substantially lower reagent consumption, increased reaction efficiency due to reduced diffusion length, and massive multiplexability (i.e., the droplets can be generated simultaneously or sequentially through a physically multichannel system). Such advantages have led to a wide array of research and industrial applications, where the system throughput and reagent consumptions are two limiting factors. A number of droplet generation techniques have been previously investigated, among which microfluidic and inkjet printing are the most commonly used for their high throughput and high efficiency.

[0003] For the microfluidic approaches, flow-focusing methods and T-junction channels have been frequently adapted for high-throughput generation (>1 kHz) of picoliter- to nanoliter- sized droplets. The flow-focusing devices have been used for microencapsulations, ionic fluid emulsion generation, and double emulsions. T-junction configurations have been used for generating microreactors, synthesizing multifunctional particles, and forming droplets with alternating compositions. Both of the methods are primarily based on shear flow, and the isolated liquid contents carried by an immiscible fluid in individual droplets can be further processed and analyzed. For example, a research group has demonstrated the power of a flow- focusing method in determination of enzymatic kinetics on a millisecond timescale with nanoliter reagents (see e.g., "Millisecond Kinetics on a Microfluidic Chip Using Nanoliters of Reagents," Helen Song and Rustem F. Ismagilov, J. Am. Chem. Soc, 2003, 125 (47), pp 14613-14619). Another research group has demonstrated an alternative flow-focusing platform for continuous generation of monodispersed lipid vesicles of 20-110 μιη in diameter, and has demonstrated the cell-free, in vitro synthesis of proteins within lipid vesicles as an initial step towards the development of an artificial cell (see e.g., "Controlled Microfluidic Encapsulation of Cells, Proteins, and Microbeads in Lipid Vesicles," Yung-Chieh Tan , Kanaka Hettiarachchi, Maria Siu, Yen-Ru Pan, and Abraham Phillip Lee, J. Am. Chem. Soc, 2006, 128 (17), pp 5656-5658).

[0004] Inkjet printing provides an alternative to the microfluidic approaches. Inkjet printing is simple to implement and easy to scale up. The operating principle, functions, and applications of inkjet printing are well known in the art. For example, see (1) "Inkjet printing - the physics of manipulating liquid jets and drops," G. D. Martin, S. D. Hoath, and I. M.

Hutchings, J. Phys.: Conf. Ser. 105(1), 012001 (2008), (2) "Printing and Prototyping of Tissues and Scaffolds," B. Derby, Science 338(6109), 921 (2012), and (3) "Nonstandard Inkjets," O. A. Basaran, H. Gao, and P. P. Bhat, Annu. Rev. Fluid Mech. 45, 85 (2013).

[0005] Drop-on-demand (DOD) printing, which is typically categorized as a type of inkjet printing, is very popular for biomaterial and biological applications. A research-grade material deposition system, e.g., Dimatix (Fuji Film) or Jetlab (MicroFab) printer, has been frequently utilized to produce various biomaterial patterns for potential biological applications. In particular, the Andreescu group used the Dimatix DMP-2800 printer to fabricate enzymatic sensors with layer-by-layer disposition of chitosan, alginate, and enzyme onto a filter paper for colorimetric detection of phenolic compounds. More recently, by utilizing a Jetlab inkjet platform, the Yu group demonstrated quantitative analysis of polymerase chain reactions (PCR) in picoliter droplet-in-oil arrays with no crosstalk and minimal evaporation.

[0006] A variety of biomaterials have been deposited by these drop-on-demand printing systems, in which the piezoelectric actuation has been primarily utilized instead of the thermal expansion principle. Considering the high price tag of the dedicated materials printers, other groups have modified low-cost office printers to achieve similar functions. For example, the Jang group modified an office inkjet printer (Canon Pixma IP 1300) to deposit an ammonium solution into desired patterns on a PET film for biomolecule detection from live cells.

[0007] In general, microfluidic approaches offer high throughput (-kHz) and high uniformity (l%-3% difference in diameter) at a low unit cost. However, it requires a dedicated fabrication process for microchip development and also needs specialized external controls and drives (e.g., microvalves, pumps, and electric or laser controller) to spatially and temporally manipulate discrete droplets. Especially, these manipulations are highly suited for single-cell analysis of preselected cell subpopulations.

[0008] In comparison to microfluidic approaches, DOD printing is commercially available and easy to use. However, it is nearly impossible to configure existing DOD printing approaches for custom applications because of their fixed cartridge design with large loading and dead volumes and its difficulty in multiplexing. Additionally, existing DOD printing approaches have high equipment and cartridge costs.

[0009] U.S. Pub. No. 2014/0354734, entitled "Non-contact bio-printing," by inventors

Tingrui Pan, Yuzhe Ding, Eric Huang, and Kit Lam describes an interchangeable droplet printing approach, which is known as microfluidic impact printing. In this approach, a conventional dot- matrix printer head with a linear array of electromagnetic driven pins can be custom-modified to strike onto microfluidic cartridge membranes for multiplexed droplet generation. An important aspect of this approach is that all the printer components become modular and separable with no crosstalk, in particular, the microfluidic cartridge design becomes simple to fabricate and easy to standardize for various applications at an extremely low cost, as compared to the integrated cartridge design implemented in commercial inkjet printers. Moreover, the microfluidic cartridge has a low dead volume in a sub-microliter range, which is highly efficient for applications with precious or limited biochemical reagents/samples. However, there continues to be a strong need for improving approaches for droplet impact printing.

SUMMARY

[0010] In the approach described in U.S. Pub. No. 2014/0354734, the dot-matrix printer head has limited flexibility in the pin actuation design. For instance, both the actuation distance and magnitude are fixed by default, and therefore, control of the droplet generation becomes a challenging issue when different sized volumes of droplets are highly desired. This grows more problematic when precise mixing of more than two liquids is required, where each pin actuator has different tolerances on actuation distance and generates droplet volume with a certain variation.

[0011] The approach described in this disclosure overcomes the limitations of existing approaches by providing a microfluidic impact printing platform with a series of individually actuated piezoelectric actuators for high-throughput droplet generation. As compared to dot matrix printing, piezoelectric printing offers easy yet high-precision control over droplet generation. Moreover, the expandable design of the piezoelectric actuators allows for generation of complex combinatorial materials, which can be highly useful for building combinatorial libraries and designing multi-step biochemical reactions. Utilizing the high controllability in deformation of the piezoelectric actuator, the printer can precisely control the volume of the droplet by adjusting voltage amplitudes and waveform shapes.

[0012] In some embodiments described herein, the volume of each droplet can be regulated in a wide range for different purposes by combining microfluidic cartridges with nozzles of discrepant diameter. Some embodiments described herein have successfully printed a quantitative protein assay with 128-fold 100 concentration gradient profiles, with no crosstalk and minimal evaporation. The piezoelectric -driven droplet impact printing approach described in this disclosure can provide a generic platform to produce multiplexed pico-/nano-liter droplets for a variety of biological and biochemical applications in a high-throughput and high-precision manner.

[0013] Some embodiments described herein provide a customizable microfluidic piezoelectric impact printer used for dispensing pico- to nano- liter fluid. Some embodiments comprise an array of piezoelectric actuators, an interchangeable cartridge with multiple microfluidic channels, and a pin array on tips of piezoelectric actuators to apply force on the microfluidic cartridge. Control of droplet sizes can be enabled by manipulating input signals of piezoelectric actuator. In one embodiment, the device comprises a self-containing multi-channel piezoelectric printer head with a holder for a separable cartridge.

[0014] A piezoelectric actuator array for impact printing can be an array of piezoelectric actuators that is not directly in contact with the fluid to be dispensed, thus avoiding potential cross-contamination issues. Droplets are ejected from a nozzle under mechanical stroke from the separable piezoelectric actuator. The piezoelectric actuator described herein could be piezoelectric disk, beam, stack, or other customized shapes. Piezoelectric actuators can be single or multiple layers. Positioning of piezoelectric actuators can be in parallel, in opposite sides, or in an array format. In some embodiments, there could be only one piezoelectric actuator.

[0015] A microfluidic cartridge can have a three-layer stack of microfluidic structures, e.g., a top layer that is composed of deformable actuation membranes, a middle layer that contains connection channels, and a bottom layer that includes printing nozzles. A reservoir that holds the fluid can be either on the top layer or on the bottom layer. The droplets can be ejected toward any direction, i.e., the nozzle can be oriented in any direction. In some embodiments, printing performance is facilitated by a novel diffuser-type geometry design in the microfluidic cartridge. This diffuser-type structure makes an unequal dynamic flow resistance forward and backward. Specifically, the diffuser-type structure makes it easier for the fluid to flow from the reservoir to the nozzle which, in turn, helps to increase the printing frequency. In some embodiments, the angle of the corner of the diffuser-type geometry design can be from 3° to 30°. The nozzle diameter can influence the fluid resistance distribution in the micro channel of the cartridge, thus influencing the volume of the ejected droplet. In some embodiments, the cross- section of the channel fabricated by laser cutting here can be a rectangle, but it can also be circular if fabricated by other methods. The channel can be in the same side of the nozzle, or on another side, e.g., the opposite side.

[0016] In some embodiments, mechanical motion amplitude and speed of the actuator can be amplified by a displacement-amplification mechanism, such as a lever structure. The lever structure can amplify the strain of piezoelectric material, thereby ensuring that stroke generated is large enough for striking onto the cartridge's elastic membrane. With this volumetric

displacement, the liquid can be pushed out from nozzle to form droplets.

[0017] In some embodiments, the motion of piezoelectric actuators is used to strike the membrane of cartridge through pin structures attached to the body of piezoelectric actuators. The material of the pins can be metal, plastic, silicon, or ceramics. The tip of the pins can be round or sharp. The diameter of the pin can be from lOum to 2mm depending on the requirements. The position of pins can be on the tip, in the middle, or embedded on the body of pins. The nozzle's position could be directly beneath the pin or not.

[0018] Precise tuning of droplet volume can be enabled by manipulating the input signals of individual piezoelectric actuators. Manipulation of input signals can include change of voltage amplitude, voltage bias, pulse width, duty ratio, and frequency. In some embodiments, the amplitude and dwell time (which can be defined as the amount of time the signal remains above a threshold amplitude) of the driving signal on the piezoelectric actuator can be tuned to control the volume of ejected droplet. In some embodiments, the driving signal can be a pulse of a given amplitude, and the dwell time can be the pulse width of the driving signal.

[0019] Some embodiments can enable large range concentration gradient generation, or dilution, through generation of droplets in multiple sizes and fusion of droplets with different contents. For example, to generate 1: 1000 concentration gradient of a certain sample in a diluent, droplet sizes and numbers of samples can be manipulated to generate a series of merged sample drops with 1: 1000 size difference, and diluent can be added in a complementary way.

[0020] In some embodiments, fusion of droplets printed to the same spots in a sequence can be enhanced by hydrophilic anchors on the printed substrate. Hydrophilic anchors are hydrophilic pillars made by photolithography, or directly deposited by the dispenser. Material of the anchors can be gel, photo- sensitive polymers, temperature-responsive polymers, or other types of crosslinkable polymers. The height of hydrophilic pillars can be between Ιμιη to 500μιη. Position accuracy of deposited droplets can be increased through the use of hydrophilic anchors. In some embodiments, the hydrophilic anchors can be immersed in oil, and droplets penetrating through oil are anchored on the hydrophilic patterns on the substrates. In some embodiments, the hydrophilic anchors can be arranged in an array format. BRIEF DESCRIPTION OF THE FIGURES

[0021] FIGs. 1A-1B illustrate examples of drop-on-demand inkjet printing mechanisms in accordance with some embodiments described herein.

[0022] FIGs. 2A-2C illustrate additional examples of drop-on-demand inkjet printing mechanisms in accordance with some embodiments described herein.

[0023] FIG. 3 illustrates a top view of a drop-on-demand inkjet printing mechanism in accordance with some embodiments described herein.

[0024] FIG. 4 illustrates an impact printing system in accordance with some

embodiments described herein.

[0025] FIG. 5A illustrates a plot of the volume of droplets versus the diameter of the nozzle in accordance with some embodiments described herein.

[0026] FIG. 5B illustrates a plot of the volume of the droplet versus the driving voltage in accordance with some embodiments described herein.

[0027] FIG. 5C illustrates a plot of the volume of the droplet versus the dwell time of the actuation pulse in accordance with some embodiments described herein.

[0028] FIG. 6 demonstrates volumetric control of the droplet array in accordance with some embodiments described herein.

[0029] FIG. 7 illustrates photos of a color matrix printed 1mm apart with four solutions on a silanized glass in accordance with some embodiments described herein.

[0030] FIG. 8 summarizes the quantitative colorimetric readouts of the printed droplet array with a concentration gradient of BSA built inside in accordance with some embodiments described herein.

[0031] FIG. 9 illustrates a computer system in accordance with some embodiments described herein.

[0032] FIG. 10 illustrates a method for droplet impact printing in accordance with some embodiments described herein.

DETAILED DESCRIPTION

[0033] The following description is presented to enable any person skilled in the art to make and use the invention, and is provided in the context of a particular application and its requirements. Various modifications to the disclosed embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be applied to other embodiments and applications without departing from the spirit and scope of the present invention. Thus, the present invention is not limited to the embodiments shown, but is to be accorded the widest scope consistent with the principles and features disclosed herein.

Microfluidic impact printing

[0034] Microfluidic impact printing emphasizes the concept of designing a simplified microfluidic cartridge, which can be easily expanded for multiplexing and customized for different applications. Meanwhile, the actuation of the printer head is configured as plug-and- play without directly contacting the working fluid. In particular, the microfluidic cartridge has a three-layer stack of microfluidic structures, i.e., the top layer is composed of deformable actuation membranes and injection reservoirs, the middle layer contains connection channels, and in the bottom layer are printing nozzles, all made of flexible polymeric materials. As a piezoelectric-driven impact actuator strikes on the membrane, the fluid inside is accelerated bi- directionally, both towards the nozzle and away to the reservoir. The majority of the summative volume of liquid that is propelled towards the nozzle forms a droplet which is then ejected from the nozzle as it prints. The volume of the droplet can be predicted by the following equation:

where V, is the volumetric displacement caused by the membrane deformation under the impact actuator, while R_n and R_r represent the flow resistances of the microfluidic paths towards the nozzle and the reservoir, respectively. In addition, dj indicates the diameter of the impact chamber, and s is the stroke of the impact actuator, from which the overall volume displacement can be derived. It is worth noting that, except the stroke (s), the rest of the parameters are structurally related parameters to determine droplet size, which can be controlled through the microfluidic cartridge design.

[0035] FIGs. 1A-1B illustrate examples of drop-on-demand inkjet printing mechanisms in accordance with some embodiments described herein. Droplets are ejected from a nozzle under pressure waves exerted internally or externally, which can be attributed to a physical stroke from a separable actuator. For example, in FIG. 1A, piezoelectric actuator 102 (labeled "PZT 102" in FIG. 1 A) is a piezoelectric bender whose displacement 110 is controlled by electrical driving signal 104. Displacement 110 generated by piezoelectric actuator 102 causes pin 112 to impact microfluidic cartridge 106, thereby causing a droplet to be driven out of nozzle 108. In FIG. IB, piezoelectric actuator 122 (labeled "PZT 122" in FIG. IB) is a piezoelectric disk or stack whose displacement 130 is controlled by electrical driving signal 124. Displacement 130 generated by piezoelectric actuator 122 is amplified using a displacement amplification mechanism (e.g., lever 136) to generate amplified displacement 134. Amplified displacement 134 causes pin 132 to impact microfluidic cartridge 126, thereby causing a droplet to be driven out of nozzle 128.

[0036] FIGs. 2A-2C illustrate additional examples of drop-on-demand inkjet printing mechanisms in accordance with some embodiments described herein. In FIG. 2A, microfluidic cartridge 206 includes a fluid reservoir 210 and nozzle 208 that are coupled via channel 212. When lever 202 causes pin 204 to deform channel 212, a droplet of the fluid can be driven out of nozzle 208. FIG. 2B and FIG. 2C illustrate drop-on-demand inkjet printing mechanisms that include different configurations of levers 222 and 242, pins 224 and 244, microfluidic cartridges 226 and 246, nozzles 228 and 248, fluid reservoirs 230 and 250, and channels 232 and 252. In FIG. 2A, pin 204 is vertically aligned with nozzle 208. However, in FIG. 2B, pin 224 is shown slightly to the left of nozzle 228, i.e., pin 224 is located between fluid reservoir 230 and nozzle 228. In FIG. 2C, nozzle 248 is on the same side as fluid reservoir 250, whereas in FIG. 2A (and likewise in FIG. 2B), nozzle 208 is on the opposite side of fluid reservoir 210.

[0037] FIG. 3 illustrates a top view of a drop-on-demand inkjet printing mechanism in accordance with some embodiments described herein. Fluid reservoir 308 and nozzle 302 are coupled via channel 306. When pin 304 is pushed down in a direction that is normal to the plane of the drawing sheet (i.e., pushed down into the drawing sheet), a droplet of the fluid can be driven out of nozzle 302. Note that channel 306 can include diffuser-type geometry 310, which can cause channel 306 to have an unequal dynamic flow resistance forward (i.e., toward nozzle 302 and away from fluid reservoir 308) and backward (i.e., toward fluid reservoir 308 and away from nozzle 302). The unequal dynamic flow resistance can make it easier for the fluid to flow forward from reservoir 308 to nozzle 302, thereby helping to increase the printing frequency. The angle Θ (see inset in FIG. 3) of a corner of diffuser-type geometry 310 can be from 3° to 30°. As shown in FIG. 3, the diffuser-type geometry 310 refers to a segment of the channel that has a gradually increasing cross-sectional area.

[0038] Note that, in addition to the volume displacement, the fluid has to gain adequate kinetic energy to overcome the surface tension prior to breaking through the nozzle, which can be derived from the inertia of the liquid. Specifically, the minimum velocity of liquid

Umin — ~ I . d-n) required to exceed the surface tension limit and form a departed droplet can be estimated. In this equation, σ is the surface tension coefficient, and p is the fluid density. In order to provide the necessary fluidic inertia, the impact actuation needs to be accelerated to a critical speed (Ui), which can be estimated by the following equation: U,≥ 2U-

[0039] This equation can be derived as follows. The ejected flow volume is

^ = ^KrT⁺F^Kn ^ = (1 +F ^Kr)- (AD

[0040] The above equation shows that the ratio between the two flow resistances can be used to adjust the ejected volume. For the channel with rectangle section (wxh, h<w), the flow resistance is approximately,

12yL

X

wh³ 0.63ft (A2)

For the nozzle with diameter d„,

R_n =≡ , (A3) where L and / are the lengths of the channel and nozzle, respectively, and γ is the dynamic viscosity of the fluid.

[0041] Assuming the shape of the deformed membrane is approximately spherical when impacted by a pin with a relatively small diameter (-0.1mm), the volumetric displacement by the impact of the pin is

where dj indicates the diameter of the impact chamber, and s is the stroke of the impact actuator. Combining Equations A1-A4, we get

V_n = -sd l + f = -sd / [l + —₄ {! -—)[ (A5)

[0042] For R_n>10R_r, Equation A5 can be simplified to

[0043] The droplet diameter is

where Θ is the liquid contact angle on the substrate. The minimum velocity of fluid to overcome the surface tension and shrink into a droplet is min (A8) where σ is the surface tension coefficient, and p is the fluid density.

[0044] The ejected liquid from a nozzle extends as a cylinder in an unstable state, and eventually collapses into spherical drop/drops (main droplet and satellite drops). Assuming the shape of the ejected liquid is a liquid column, the flow volume is

where t is an equivalent time for each drop printed out.

[0045] The value "t" can also be estimated as the effective acting time of the pin to accelerate the fluid in chamber, i.e., the rising edge time of driving pulse. Combining Equation A5 with A9, we finally obtain the required impact velocity of the pin to be

Simplifying and substituting for £/_mi„, we get,

[0046] Note that there exists a minimum velocity of the impact actuator to generate a droplet. In other words, merely impacting the cartridge is not sufficient. The printer must be designed so that the impact velocity is greater than or equal to the minimum velocity. Otherwise, a droplet will not be generated even though the cartridge is being impacted. Another important point is that, in conventional inkjet printers, the ink flows through the cartridge with direct contact between the actuator and the ink. In contrast, in the microfluidic impact printers illustrated in FIGs. 1A-1B, the fluid does not touch the printing actuator or the pin (e.g., pins 112 and 132). This allows the cartridge (e.g., microfluidic cartridges 106 and 126) to be removable and interchangeable without causing any cross-contamination issues.

[0047] The following table compares the piezoelectric microfluidic impact printing with some typical droplet generation methods. Droplet

generation Advantages Disadvantages

technology

1. High throughput ( 1 k-87

1. Difficult to isolate single

kHz, 1-8 channels).

droplet, no position

Microfluidic 2. Large liquid viscosity range

control

method 3. Control of droplet volume

2. Dedicated fabrication of

4. Low dead volume

chip

5. Good biocompatibility

1. Low biocompatibility for

thermal inkjet printing

1. High throughput ( 1 k-20 k 2. High cost of cartridge,

Commercial

Hz, 3-6 channels) need of wash

DOD

2. Direct operation on single 3. Limited viscosity range

inkjet

droplet with (dynamic viscosity: 2-30 printing

position/composition control cp for DMP; less than 20

cp for Microfab)

4. Large dead volume

1. Multiple channels

expandability (4-12 channels)

2. Direct operation on single

1. Low frequency: less than

Piezoelectric droplet with

200 Hz

microfluidic position/composition control

2. Limited viscosity range

impact 3. Low-cost and disposable

(dynamic viscosity <14

printing cartridge

cp)

4. Control of droplet volume

5. Low dead volume

6. Good biocompatibility

An example implementation

[0048] FIG. 4 illustrates an impact printing system in accordance with some

embodiments described herein. System 400 includes a housing that can receive one or more interchangeable microfluidic cartridges (such as cartridge 402) and an impact printer head 404. Impact printer head 404 includes (1) pins, e.g., pin 406, (2) levers, e.g., lever 408, and piezoelectric actuators, e.g., PZT actuator 410. FIG. 4 also shows a picture of an actual cartridge (labeled 402-P), and a picture of an actual printer head (labeled 404-P).

[0049] System 400 also includes a positioning mechanism 412, e.g., a 3-axis travelling stage with external controller, and a software application 414 that can be used to control the impact printer. In one embodiment, the 3-axis traveling stage (Thorlabs) had a maximum motion speed of 300mm/s, and positioning repeatability of 0.25 μιη. Software application 414 can simultaneously coordinate the movement of the traveling stage and the actuation of each individual printer head. Specifically, software application 414 can generate a first control signal to select the printing channel through a custom-made, multi-channel, switching circuitry (shown as switch 420 in FIG. 4). A second control signal generated by software application 414 triggers a pulse through signal generator 416 (e.g., 33220, Agilent), which is amplified by a piezoelectric amplifier 418 (e.g., EPA- 104, Piezo System) to become the driving signal that is provided to the appropriate PZT actuator that is selected by switch 420. This occurs while the apparatus is moving accordingly under the control of the software. In one embodiment, low-cost

piezoelectric disks (AB2726B, Digi-key) were used as the PZT actuator attached with a steel lever of 38mm in length and 2mm in width, which drove a custom-made steel pin of 0.2mm in diameter mounted perpendicularly to the end of the steel lever. The displacement-amplification lever mechanism has been utilized to magnify the stroke and improve the kinetic velocity of the actuator by 10 fold which is confined by the limited deformation of the piezoelectric disks.

Moreover, this structure can help eliminate redundant spacing between adjacent pins for a more compact design of multiplexed printer heads. In this embodiment, a multichannel, microfluidic cartridge 402 can be clamped onto a support cube in contact with the pins. Under such an interchangeable design, the liquid can be pushed out from the microfluidic cartridge nozzle without coming into direct contact with the printer head, enabling the plug-and-play and non- contamination features of the printer. Then the ejected droplets, departed from the nozzle, travelled in air for about 2mm before landing onto the substrate.

[0050] Some embodiments described herein feature a droplet impact printer, comprising: (1) a housing to receive a removable cartridge; (2) the removable cartridge, comprising: (i) a fluid reservoir to hold a fluid, (ii) a channel coupled to the fluid reservoir, the channel comprising a deformable membrane, and (iii) a nozzle coupled to the channel, wherein deforming the deformable membrane compresses the channel, thereby driving droplets of the fluid out of the nozzle. Additionally, the droplet impact printer can include (1) a deforming mechanism to deform the deformable membrane, wherein the deforming mechanism comprises a piezoelectric actuator, and wherein displacement of the piezoelectric actuator is controlled by an electrical driving signal, and (2) a controller to (i) determine the electrical driving signal that would cause a droplet of a target droplet size (e.g., a droplet that contains a desired amount or volume of the fluid) to be driven out of the nozzle, (ii) generate the electrical driving signal, and (iii) provide the electrical driving signal to the piezoelectric actuator, thereby causing a droplet of the target droplet size (or volume) to be driven out of the nozzle.

[0051] In some embodiments, the controller determines the amplitude, the dwell time, or both the amplitude and the dwell time of the electrical driving signal that would cause a droplet of the target droplet size (or volume) to be driven out of the nozzle. In some embodiments, the deforming mechanism comprises: a pin to push the deformable membrane; and a displacement amplification mechanism coupled between the piezoelectric actuator and the pin, wherein the displacement amplification mechanism amplifies the displacement of the piezoelectric actuator. In some embodiments, the displacement amplification mechanism is a lever. In some embodiments, the deforming mechanism does not contact the fluid. Specifically, the deforming mechanism can be physically separate from the cartridge, and wherein removing the cartridge from the housing does not remove the deforming mechanism from the droplet impact printer. In some embodiments, the channel has a diffuser-type structure providing an unequal dynamic flow resistance that causes the fluid to flow more easily from the reservoir to the nozzle. In some embodiments, the piezoelectric actuator comprises one of: a piezoelectric bender, a piezoelectric disk, or a piezoelectric stack. Some embodiments can further comprise a positioning mechanism to position the nozzle relative to a substrate upon which droplets are to be printed.

[0052] Some embodiments described herein feature a multiplexed impact printing system, comprising: (1) a droplet impact printing mechanism having one or more piezoelectric actuators to drive a droplet of a fluid, selected from of a set of fluids, out of a nozzle

corresponding to the fluid based on an electrical driving signal; (2) a processor coupled to a storage medium storing instructions that, when executed by the processor, cause the processor to determine one or more characteristics of the electrical driving signal that would cause a droplet of a target fluid having a target droplet size (or volume) to be driven out of a nozzle

corresponding to the target fluid; and (3) a circuit coupled to the processor to (i) generate the electrical driving signal having the one or more determined characteristics, and (ii) provide the electrical driving signal to the droplet impact printing mechanism, thereby causing a droplet of the target fluid having the target droplet size (or volume) to be driven out of the nozzle corresponding to the target fluid.

[0053] In some embodiments, the droplet impact printing mechanism can comprise a set of cartridges, wherein each cartridge can comprise (1) a fluid reservoir to hold a fluid; (2) a channel coupled to the fluid reservoir, wherein the channel comprises a deformable membrane; (3) a nozzle coupled to the channel, wherein deforming the deformable membrane compresses the channel, thereby causing a droplet of the fluid to be driven out of the nozzle; and wherein the channel has a diffuser-type structure providing an unequal dynamic flow resistance that causes the fluid to flow more easily from the reservoir to the nozzle. In some embodiments, the droplet impact printing mechanism can comprise a set of sub-mechanisms, wherein each sub-mechanism can correspond to a distinct fluid in the set of fluids, and wherein each sub-mechanism can comprise: (1) a housing for receiving a removable cartridge; (2) the removable cartridge, comprising: (i) a fluid reservoir to hold the distinct fluid, (ii) a channel coupled to the fluid reservoir, the channel comprising a deformable membrane, and (iii) a nozzle coupled to the channel, wherein deforming the deformable membrane compresses the channel, thereby causing a droplet of the distinct fluid to be driven out of the nozzle; and (3) a deforming mechanism, comprising: (i) a piezoelectric actuator whose displacement is controlled by the electrical driving signal, (ii) a pin to push the deformable membrane, and (iii) a displacement amplification mechanism coupled between the piezoelectric actuator and the pin, wherein the displacement amplification mechanism amplifies the displacement of the piezoelectric actuator.

Microfabrication of the microfluidic cartridge and the microwell array

[0054] As an important component of the microfluidic impact printer, the interchangeable microfluidic cartridge is intended to be simple to fabricate and easy to customize with standard, modular designs. As previously described, some embodiments have three polymeric layers. A 100 μιη-thick Polydimethylsiloxane (PDMS) film used as bottom layer was prepared by mixing the silicone elastomer base and curing agent (SYLGARD 184, Dow Corning) at a ratio of 10: 1, and spinning on a glass slide. The film was then thermally cured at 120 °C for 15 minutes.

Afterwards, a C0₂ laser (Universal Laser Systems, VersaLaser 2.30) was used to drill the nozzle on the PDMS film. A commercial silicone film (Rogers Corporation Bisco™ HT-6240) with a 254μιη thickness was also cut by the laser to fabricate the middle channel layer and the top deformed layer. Eventually, these three layers were bonded together after oxygen plasma treatment (at 90 W for 30 s, Diener electronic). A microwell array was prepared as a substrate for protein droplet reaction. 66 microwells with 1mm diameter were fabricated on a 760μιη thick silicone sheet (Rogers Corporation) with the C0₂ laser, and bonded to a 25x75mm glass slide with the same oxygen plasma treatment.

Reagents

[0055] In one embodiment, silicon oil used in drop-size measurement was purchased from Scientific (Product No. S 159-500). Mineral oil was purchased from Sigma- Aldrich (M5904). Bicinchoninic acid (BCA) protein assay kit (Thermo Scientific Pierce, Product No.

23225) used in the protein assay contains two reagents: Reagent A, containing sodium carbonate, sodium bicarbonate, bicinchoninic acid and sodium tartrate in 0.1 M sodium hydroxide, and Reagent B, containing 4% cupric sulphate. Prior to assaying, a working reagent (WR) was prepared by mixing Reagent A and B in a 50: 1 ratio as a detection reagent. Bovine serum albumin (BSA, Sigma- Aldrich) was dissolved in DI water to a concentration of 2000μg/mL.

Soluble dyes (Jacquard iDye Natural Fabric Dye No. 451 Blue and No. 449 Red, No.447 yellow and No.454 black) were prepared in concentrations of 1.5g/L by dissolving dry powders in dimethyl sulfoxide (DMSO). Generation of concentration gradient

[0056] For ease of drop-number calculations, we adopted an evaporation-rehydration method to create a concentration gradient of BSA droplets, during which a series of ascending numbers of aqueous BSA protein droplets were dried first and then rehydrated with equal amounts of Phosphate-Buffered Saline (PBS) solution. This method was verified experimentally by assaying equal volumes of BSA solution created by both conventional manual dilution and the evaporation-rehydration dilution method, which contains the same amount of active BSA components. The two solutions were first printed into silicone oil to form droplets, and then measured under a microscope. The volume of a BSA droplet in comparison with that of a PBS and WR mixed droplet is 2.25nL + 18pL and 9.47nL + 97nL respectively. After measurements, BSA droplets were printed into a horizontal row of wells in a binary pattern, i.e., droplet number of 1, 2, 4, 8... 128, accordingly. After 5 minutes, the water content in all BSA droplets evaporated, and the dried protein contents remained in the wells, followed by which, the same volumes of PBS and WR (31 drops for each) were printed in a sequential pattern into each well. After that, mineral oil was manually dispensed on top of the well array to prevent further evaporation. The array was then covered by a glass slide and incubated at room temperature for 30 minutes before imaging.

Imaging and data analysis

[0057] An inverted microscope (EVOS, Life Technologies) was used to measure the size of droplets in oil and on a glass substrate. A desktop scanner (Onetouch 7300 USB, Visioneer) was used to scan the image of the protein assay in the microwell array on a glass slide at lOOOdpi. For colorimetric analysis of the BCA protein assay, the parameter of saturation intensity was selected to characterize the image results, as it was closely correlated with BSA concentrations. Specifically, scanned images were transformed into numerical color values and averaged over a freely selectable square area (3x3 pixels) using a color picker tool in a PC image processing software. Averaged saturation intensity of 3 freely selected square areas within the area of each individual microwell was plotted against the corresponding designed concentrations. Geometric control of droplet volume

[0058] As stated above, the structural parameters in the microfluidic cartridge can be designed and tuned for different sizes of droplet generation, for the fluid distribution under forced displacement is determined by them. As predicted by Poiseuille's equation, the fluidic resistance towards the printer nozzle (R_n) follows a 4th order relationship with the nozzle diameter, which can be adjusted during the microfabrication process. In order to minimize droplet evaporation and improve measurement accuracy, aqueous droplets were printed in some embodiments into an oil phase inside a petri dish.

[0059] FIG. 5A illustrates a plot of the volume of droplets versus the diameter of the nozzle in accordance with some embodiments described herein. The dwell time was 1ms and driving voltage was 120V. As shown in the plot, the volume of droplets increased from 23.4pL (35.3μιη) to 8.90nL (255. Ιμιη), as the nozzle opening changed from 25.7μιη to 91.5μιη. As expected, the nozzle size has strong influence on droplet volume through the change of flow resistance distribution in the microfluidic cartridge. The experimental data matches well against the 4th polynomial curve, as can be theoretically predicted by Equation (A6), which indicates a straightforward method to tune the droplet volume in a wide range by nozzle size variation.

Electrical control of the droplet volume

[0060] The piezoelectric actuators offer direct electrical control of droplet size (or volume) in the microfluidic impact printer. Notably, once the geometrical parameters of the microfluidic cartridge are completely set, the electrical control becomes a more convenient way to fine-tune the droplet volume.

[0061] FIG. 5B illustrates a plot of the volume of the droplet versus the driving voltage in accordance with some embodiments described herein. To obtain the data for the plot, aqueous droplets were printed on a silanized glass substrate using a lHz printing speed and a 1ms dwell time.

[0062] FIG. 5C illustrates a plot of the volume of the droplet versus the dwell time of the actuation pulse in accordance with some embodiments described herein. To obtain the data for the plot, aqueous droplets were printed on a silanized glass substrate using a lHz printing speed and an actuation voltage of 120V. In FIG. 5C, the inset is an enlarged view of the data in the circle.

[0063] In principle, the driving voltage of the piezoelectric actuators has a linear relationship with the stroke, which determines the overall volumetric displacement of the impact chamber. In our actuator setup, the linear response of the pin is measured at 11.7μιη/ν without a load. As shown in FIG. 5B, the droplet size (or volume) linearly increases with the amplitude of driving voltage, which is consistent with theory.

[0064] As shown in FIG. 5C, the variation of the droplet volume with respect to the dwell time shows a triphasic trend. In particular, with a short pulse dwell time (t < 2ms), the droplet dimension grows monotonically with the rising actuation time. This can be explained because as the piezoelectric actuator pushes and retracts during a short actuation period, the fluid inside the impact chamber has been squeezed, but not completely ejected, due to fluidic viscosity and channel compliance. Thus, part of the displaced fluid will be sucked back before merging into the departed droplet as soon as the actuator withdraws. For an intermediate dwell time (2ms < t < 996ms), the droplet size (or volume) presents independence from the pulse duration with a limited range of fluctuation (less than 2%), as the majority of the displaced volume has been ejected as a departed droplet from the nozzle. Finally, as the dwell time continues increasing (t is above 997ms in 1 Hz printing), there is not enough time for the impact chamber to refill completely, and therefore, the refilling process becomes the limiting factor, restricting the amount of ejected volume. As the dwell time is set to greater than 999ms, a second droplet cannot be produced due to insufficient refilling time. In brief, for droplet generation stability, a duty cycle of 2 - 99% is preferred as the droplet size (or volume) becomes independent of the dwell time. Moreover, the ejection and the refilling time become limiting factors of the printing frequency.

[0065] FIG. 6 demonstrates volumetric control of the droplet array in accordance with some embodiments described herein. In the x-axis of the array, the number of ejections are varied from 2 to 10, while in the y-axis, the voltage is varied from 88V to 126V (the bar below the first two droplets on the top row is 1mm long; this provides the scale of the illustration). Based on the above electrical characterization results, some embodiments use the following volumetric control strategy: vary the driving voltage and the number of ejections, while keeping the dwell time constant (e.g., 2ms). In the droplet array shown in FIG. 6, the volume variation is from 2.7nL (in the top left corner) to 47.6nL (in the bottom right corner). Specifically, as mentioned above, in the x-axis, the number of ejections is varied from 2 to 10, while in the y- axis, the voltage is increased from 88V to 126V.

Multiplexed printing

[0066] One of the important features of the microfluidic cartridge in impact printing is the simple scalability in multiplexing. It can be highly beneficial to biological and biochemical applications where complex reagents and media are frequently encountered, e.g., proteins, cells, extracellular matrices, and signaling molecules. To illustrate the applicability of microfluidic impact printing, a 4-channel printer prototype was built to deposit arbitrary microdroplet patterns and combinations on solid substrates at a printing frequency of 100Hz. The 4 different channels in the microfluidic cartridge can be individually loaded with the desired chemicals using a standard pipetting procedure. In the prototye, DMSO solutions with 4 color dyes were used for their low evaporation rates. It is well known that the smaller droplets experience faster evaporation rates as their surface-area-to-volume ratio is larger. To alleviate the evaporation issue of a minute droplet volume, the substrate can either by immersed in oil after printing, or the droplets can be directly printed into an oil film. A printing program was used to automatically produce arrayed micropatterns, and to command the four printing channels to generate drops upon the request sequence. As a result, a matrix pattern can be generated by software and built on a silanized glass substrate by microfluidic impact printing.

[0067] Specifically, FIG. 7 illustrates photos of a color matrix printed 1mm apart with four solutions on a silanized glass in accordance with some embodiments described herein. The solutions are red (top left), blue (top right), yellow (bottom left), and black (bottom right) dye dissolved in DMSO (scale bar is 1mm - the scale bar is shown below the two bottom right droplets in the red matrix). The colors are not shown in FIG. 7 because the figures have to be in black and white as per the patent law rules.

Concentration gradient generation

[0068] Furthermore, with the high- stability and high-precision control of droplet printing, the microfluidic impact printer can be utilized for the generation of arbitrary chemical gradients with high efficiency. As compared to conventional preparation protocols, the printing method consumes significantly less reagent and can be adapted to any substrates, without involving any additional steps. In particular, for many biological and biochemical assays, concentration gradient generation has been a routine practice and a critical preparation step where samples are required to be diluted into a wide range of concentrations. A demonstration implementation was built on droplet generation of a discrete logarithmic concentration gradient of BSA, and concentration of BSA was analyzed in the droplet arrays with a BCA protein assay. A binary gradient of BSA concentrations was designed and deposited in a droplet array format, followed by adding a second WR to report in a colorimetric way. Total volume of 1.8μί of the BSA solution is consumed for the entire droplet array, at least an order of magnitude less than that of the conventional microtiter plates (on the order of ΙΟΟμί) and conventional microfluidic approaches (on the order of ΙΟμί).

[0069] FIG. 8 summarizes the quantitative colorimetric readouts of the printed droplet array with a concentration gradient of BSA built inside in accordance with some embodiments described herein. In FIG. 8, the concentration profiles range from 16μg/mL to 2,000μg/mL. The measurement results are based on the average of triplicate experiments over each droplet, and the standard 16 derivations have also been calculated accordingly. As can be seen, BSA

concentration and reflectance intensity follow a natural logarithm relationship, which shows consistency compared with the measurement for reflectance detection when the array is generated using conventional approaches. Aside from the substantially reduced chemical consumption, the reaction time within the miniature droplets (in a nL range) is considerably reduced from 2 hours to 30 minutes at room temperature due to the short diffusion length (on the order of ΙΟΟμιη).

[0070] Specifically, FIG. 8 illustrates the quantitative colorimetric readouts of the printed droplet array with a concentration gradient of BS A built inside. The inset is a photo of a BCA sample. The plotted results are averaged measurements graphed with standard derivations from triplicate experiments.

[0071] The foregoing description provides a droplet generation platform based on the microfluidic impact printing technology, where low-cost piezoelectric actuators have been utilized as the impact forces. The modular microfluidic cartridge composed of all polymeric material provides a new, simple means for chemical loading and droplet generation with interchangeability, low cost, non-contamination, and multiplexability. The driving voltage, dwell time, and nozzle size can be controlled, resulting in user-friendly manipulation of high-precision droplet sizes, varying from picoliter to nanoliter. Generation of a large concentration gradient (16-2,000 μg/mL) has been demonstrated using this microfluidic printing platform, and a protein assay has been implemented and measured colorimetrically. Compared with the conventional and microfluidic quantitative assay platforms, this novel droplet generation system can create arbitrary dilution ratios and reagent combinations by a simple matrix design using custom-made software. In summary, the piezoelectric-driven droplet impact printing system, with a low-cost, plug-and-play microfluidic cartridge, is capable of performing high-precision, high-throughput droplet-generation for quantitative molecular analysis with minimal reagent costs.

[0072] FIG. 9 illustrates a computer system in accordance with some embodiments described herein. Computer system 902 can include processor 904, memory 906, and storage device 908. Computer system 902 can be coupled to display device 914, keyboard 910, and pointing device 912. Storage device 908 can store operating system 918, application 916, and data 920. Data 920 can include input required by application 916 and/or output generated by application 916.

[0073] Computer system 902 may automatically (or with user intervention) perform one or more operations that are implicitly or explicitly described in this disclosure. Specifically, during operation, computer system 902 can load application 916 into memory 906. Application 916 can then be used to control an impact printing system.

[0074] FIG. 10 illustrates a method for droplet impact printing in accordance with some embodiments described herein. The method can begin by determining one or more

characteristics of an electrical driving signal that would cause a droplet having a target droplet size (or volume) of a fluid to be driven out of a nozzle of a removable cartridge (operation 1002). Next, the electrical driving signal having the determined one or more characteristics can be generated (operation 1004). The electrical driving signal can then be provided to a piezoelectric actuator, thereby causing the piezoelectric actuator to produce a displacement (operation 1006). Next, the displacement can be amplified using a displacement amplification mechanism to obtain an amplified displacement (operation 1008). Finally, the amplified displacement can be provided to a pin to push a deformable membrane in the removable cartridge, thereby causing a droplet of a target droplet size (or volume) to be driven out of a nozzle of the removable cartridge

(operation 1010).

[0075] The foregoing description has been presented to enable any person skilled in the art to make and use the embodiments. The described embodiments are not intended to be exhaustive or to limit the present invention. Various modifications to the disclosed embodiments will be readily apparent to those skilled in the art, and the general principles defined herein are applicable to other embodiments and applications without departing from the spirit and scope of the present disclosure. Thus, the present invention is to be accorded the widest scope consistent with the principles and features disclosed herein. The scope of the present invention is defined by the appended claims.

Claims

What Is Claimed Is:

1. A droplet impact printer, comprising:

a housing to receive a removable cartridge;

the removable cartridge, comprising:

a fluid reservoir to hold a fluid,

a channel coupled to the fluid reservoir, the channel comprising a deformable membrane, and

a nozzle coupled to the channel, wherein deforming the deformable membrane compresses the channel, thereby driving droplets of the fluid out of the nozzle;

a deforming mechanism to deform the deformable membrane, wherein the deforming mechanism comprises a piezoelectric actuator, and wherein displacement of the piezoelectric actuator is controlled by an electrical driving signal; and

a controller to (1) determine the electrical driving signal that would cause a droplet of a target droplet size to be driven out of the nozzle, (2) generate the electrical driving signal, and (3) provide the electrical driving signal to the piezoelectric actuator, thereby causing a droplet of the target droplet size to be driven out of the nozzle.

2. The droplet impact printer of claim 1, wherein the controller determines the amplitude, the dwell time, or both the amplitude and the dwell time of the electrical driving signal that would cause a droplet of the target droplet size to be driven out of the nozzle.

3. The droplet impact printer of claim 2, wherein the deforming mechanism comprises:

a pin to push the deformable membrane; and

a displacement amplification mechanism coupled between the piezoelectric actuator and the pin, wherein the displacement amplification mechanism amplifies the displacement of the piezoelectric actuator.

4. The droplet impact printer of claim 3, wherein the displacement amplification mechanism is a lever.

5. The droplet impact printer of claim 1, wherein the deforming mechanism does not contact the fluid.

6. The droplet impact printer of claim 5, wherein the deforming mechanism is physically separate from the cartridge, and wherein removing the cartridge from the housing does not remove the deforming mechanism from the droplet impact printer.

7. The droplet impact printer of claim 1, wherein the channel has a diffuser-type structure providing an unequal dynamic flow resistance that causes the fluid to flow more easily from the reservoir to the nozzle.

8. The droplet impact printer of claim 1, wherein the piezoelectric actuator comprises one of: a piezoelectric bender, a piezoelectric disk, or a piezoelectric stack.

9. The droplet impact printer of claim 1, further comprising a positioning mechanism to position the nozzle relative to a substrate upon which droplets are to be printed.

10. A multiplexed impact printing system, comprising:

a droplet impact printing mechanism having one or more piezoelectric actuators to drive a droplet of a fluid, selected from of a set of fluids, out of a nozzle corresponding to the fluid based on an electrical driving signal;

a processor coupled to a storage medium storing instructions that, when executed by the processor, cause the processor to determine one or more characteristics of the electrical driving signal that would cause a droplet of a target fluid having a target droplet size to be driven out of a nozzle corresponding to the target fluid; and

a circuit coupled to the processor to (1) generate the electrical driving signal having the one or more determined characteristics, and (2) provide the electrical driving signal to the droplet impact printing mechanism, thereby causing a droplet of the target fluid having the target droplet size to be driven out of the nozzle corresponding to the target fluid.

11. The multiplexed impact printing system of claim 10, wherein the one or more characteristics include an amplitude and a dwell time of the electrical driving signal.

12. The multiplexed impact printing system of claim 10, wherein the droplet impact printing mechanism comprises a set of cartridges, and wherein each cartridge comprises:

a fluid reservoir to hold a fluid;

a channel coupled to the fluid reservoir, wherein the channel comprises a deformable membrane; a nozzle coupled to the channel, wherein deforming the deformable membrane compresses the channel, thereby causing a droplet of the fluid to be driven out of the nozzle; and wherein the channel has a diffuser-type structure providing an unequal dynamic flow resistance that causes the fluid to flow more easily from the reservoir to the nozzle.

13. The multiplexed impact printing system of claim 12, further comprising a deforming mechanism, wherein the deforming mechanism comprises:

a piezoelectric actuator whose displacement is controlled by the electrical driving signal; a pin to push the deformable membrane; and

14. The multiplexed impact printing system of claim 13, wherein the deforming mechanism does not contact the fluid.

15. The multiplexed impact printing system of claim 14, wherein the deforming mechanism is physically separate from the set of cartridges, and wherein removing the set of cartridges from the multiplexed impact printing system does not remove the deforming mechanism from the multiplexed impact printing system.

16. The multiplexed impact printing system of claim 13, wherein the piezoelectric actuator comprises one of: a piezoelectric bender, a piezoelectric disk, or a piezoelectric stack.

17. The multiplexed impact printing system of claim 10, comprising:

a substrate upon which droplets are to be printed; and

a positioning mechanism to position the droplet impact printing mechanism relative to the substrate.

18. The multiplexed impact printing system of claim 17, wherein the substrate comprises hydrophilic anchors having a height between Ιμιη and 500μιη.

19. The multiplexed impact printing system of claim 18, wherein the hydrophilic anchors are immersed in oil, and the droplets are anchored on the hydrophilic anchors.

20. A method for droplet impact printing using a droplet impact printer that comprises (1) a housing to receive a removable cartridge, wherein the removable cartridge comprises a fluid reservoir to hold a fluid, a channel coupled to the fluid reservoir, and a nozzle coupled to the channel, wherein the channel comprises a deformable membrane, wherein deforming the deformable membrane compresses the channel, thereby driving droplets of the fluid out of the nozzle, and wherein the channel has a diffuser-type structure providing an unequal dynamic flow resistance that causes the fluid to flow more easily from the fluid reservoir to the nozzle, and (2) a deforming mechanism to deform the deformable membrane, wherein the deforming mechanism comprises a piezoelectric actuator, wherein displacement of the piezoelectric actuator is controlled by an electrical driving signal, wherein the deforming mechanism does not contact the fluid, wherein the deforming mechanism is physically separate from the removable cartridge, and wherein removing the removable cartridge from the housing does not remove the deforming mechanism from the droplet impact printer, the method comprising:

determining one or more characteristics of the electrical driving signal that would cause a droplet having a target droplet size of a fluid to be driven out of the nozzle of the removable cartridge;

generating the electrical driving signal having the determined characteristics;

providing the electrical driving signal to the piezoelectric actuator, thereby causing the piezoelectric actuator to produce a displacement;

amplifying the displacement using a lever in the deforming mechanism to obtain an amplified displacement; and

providing the amplified displacement to a pin in the deforming mechanism to push the deformable membrane, thereby causing a droplet of the target droplet size to be driven out of the nozzle.