WO2005018082A1 - Apparatus and method for producing electrical energy from fluid energy - Google Patents

Abstract

An apparatus and a method for producing electrical energy from fluid energy using electrokinetic and hydrodynamic principles. In an apparatus form the invention is an energy conversion apparatus including a channel assembly, where the channel assembly includes a channel, a first terminal located at a first axial position and in communication with the channel, and a second terminal located at a second axial position and in communication with the channel. In a method form, the invention involves the steps of providing the energy conversion apparatus and passing a fluid through the channel in order to produce the electrical energy. In a preferred embodiment the energy conversion apparatus includes a plurality of channel assemblies which are electrically connected together in a parallel configuration in order to increase the amount of electrical energy which can be produced by the apparatus

Description

APPARATUS AND METHOD FOR PRODUCING ELECTRICAL ENERGY FROM FLUID ENERGY

TECHNICAL FIELD

An apparatus and a method for producing electrical energy from fluid energy using electrokinetic and hydrodynamic principles.

BACKGROUND OF THE INVENTION

The conversion of energy from one form to another and the production of useful work from energy sources are both topics for engineering and scientific research which have had and continue to have important implications for society. Chemical energy, for example, is readily converted into mechanical work by classical devices such as internal combustion engines and steam engines. Similarly, the potential energy of dammed water, and its associated hydrostatic pressure, can be exploited by turbines to be another source of mechanical work. If necessary, electric generators can be employed to convert any produced mechanical work into electrical work. Batteries and fuel cells are devices that avoid the creation of mechanical work and directly convert chemical energy into electrical energy.

Electricity has become the most versatile means of powering our modern world. Some of the reasons for the popularity of electricity include: its relatively high energy density, ease of use, widespread distribution and from the end users' perspective, environmental cleanliness. The modern end user of electrical energy seldom considers the origins of electricity or the nature of the primary energy source before its conversion into electrical energy. When the origins of electrical energy are considered, it is apparent that one common element is that useful electrical energy is typically obtained through the conversion of other energy sources.

The key element in creating electrical energy is to tap into a physical phenomena or property that allows for charge separation over a physical distance to create an electrical potential difference over the physical distance. This electrical potential difference or voltage enables the creation of an electrical current and the production of useful electrical work. The work required to cause the charge separation is typically provided by a primary energy source and may involve several processes or steps and intermediate conversions of energy.

The most famous and commonly used method of creating a usable charge separation is through the phenomenon of electromagnetic induction; which was first observed in 1831 by Michael Faraday as a result of moving a magnet in and out of the center of an electrically conductive coil. A more modern application of this phenomenon is the rotation of a conductor relative to a magnetic field so that the mechanical energy of a rotating shaft is converted into electricity. There has been considerable research undertaken to maximize the efficiency of this conversion of mechanical energy into electrical energy, which research has resulted in the modern electric generator. The mechanical energy of the rotating shaft in an electric generator is typically provided by devices such as a turbine (steam, water, or air) or an internal combustion engine. These devices derive their energy from other more primary energy sources (e.g., chemical energy associated with the burning of fuels, potential energy of damned water, wind, etc .) .

Other phenomena or properties that have been used to produce an electrical charge separation or potential difference include the photovoltaic effect first described by Edmond Becquerel in 1839, electrostatic generators first developed by Robert Van de Graaff in 1931, thermoelectric generators (eg., thermocouples and thermopiles) based upon the Seebeck Effect which is named after Thomas Seebeck' s work of 1821, fuel cells that use proton exchange membranes as first developed by Sir William Grove in 1839, and the ubiquitous chemical battery originating with Alessandro Volta in about 1800. The electromagnetic induction phenomenon observed by Faraday was also applied in a different geometry by Boris Karlovitz in the 1930's in attempts to construct a magnetohydrodynarnic generator.

Each of these methods of converting some form of energy to electrical power comes with its own characteristics in terms of potential voltage or current ranges, conversion efficiencies, and environmental effects.

An additional physical phenomenon which has been observed over the past 100 years is an electrokinetic phenomenon in which an electrical double layer (EDL) is created at any phase boundary, which is most commonly observed at an interface between a solid surface and a fluid or liquid. In the typical case, the EDL includes an "immobile layer" of ions in the fluid directly adjacent to the solid surface and a "mobile layer" of ions which is adjacent to the immobile layer.

The EDL is caused by an excess charge at the solid surface, which excess charge is under various theories believed to be due to some dissociation of the material of the solid surface at the phase boundary, preferential absorption of fluid ions into the solid surface, an ionization process resulting from interaction of the solid surface and the fluid, or a combination of these and perhaps other effects. The excess charge at the solid surface electrostatically attracts oppositely charged ions in the fluid (referred to as "counter-ions") and electrostatically repels similarly charged ions in the fluid (referred to as "co-ions"). The redistribution of ions in the fluid caused by the excess charge at the solid surface results in the fluid in close proximity to the solid surface having a localized excess of counter-ions and the fluid farther away from the solid surface having a localized excess of co-ions. The various charges (i.e., the excess charge at the solid surface, the counter-ions and the co-ions) may be either positive or negative depending upon the properties of the solid surface and the fluid.

Under static conditions, where the fluid is not moving relative to the solid surface, the redistribution of ions creates a potential difference in a transverse direction relative to the solid surface. This potential difference is commonly referred to as a "zeta potential".

Under flow conditions, where the fluid is moving relative to the solid surface (such as, for example, within a channel such as a conduit), it has been found that an additional potential difference referred to as a "streaming potential" is created in a direction which is parallel to the fluid flow. This streaming potential is caused by the combined effects of electrokinetics (the creation of the EDL and the redistribution of ions) and hydrodynamics (i.e., fluid mechanics) at the microfluidic level. According to hydrodynamics, fluid flow within a conduit exhibits a varying velocity profile in the transverse direction in which the velocity of flow is relatively lower adjacent to the solid surface and relatively higher towards the centerline of the conduit. Under fully developed laminar flow conditions, the velocity profile is typically "parabolic" in shape, varying with a relatively high velocity gradient from essentially zero velocity at the conduit surface to a maximum velocity at the centerline of the conduit. Under fully developed turbulent flow conditions, the velocity profile is somewhat less predictable, but typically varies from essentially zero velocity at the conduit surface to a maximum velocity at or near the centerline of the conduit. The combination of the electrokinetic phenomenon of the EDL and the hydrodynamic phenomenon of a varying velocity profile facilitates preferential movement of ions in the direction parallel to the fluid flow. More specifically, co-ions which are repelled from the conduit surface and accumulate towards the centerline of the conduit are transported downstream in the conduit at a higher average velocity than are counter-ions which are attracted to the conduit surface. This preferential movement of co-ions represents a net flow of charge downstream in the conduit which is described as a "convection current" or a "streaming current". It is this streaming current which gives rise to the streaming potential.

As a related phenomenon, it has been observed that the streaming potential created in the conduit induces in the fluid a conduction current which is in a direction which is opposite to the streaming current. This conduction current is the result of co-ions at the downstream end of the conduit seeking to move upstream to a location of reduced concentration of co-ions. This conduction current essentially impedes the flow of the fluid toward the downstream end of the conduit and results in an electro-viscous effect, in which the viscosity of the fluid apparently increases due to the increased resistance to flow of the fluid in the downstream direction. In addition, depending upon the conductivity of the conduit surface, a surface current may be induced in the conduit surface in the direction opposite to the streaming current as a result of the streaming potential, which surface current is typically considered as a component of the conduction current.

Some of the effects of the electrokinetic phenomenon on the flow of fluid through a conduit have been studied and considered.

U.S. Patent No. 4,274,937 (Findl et al) describes a sensor apparatus and a method for measuring electrokinetic effects across a double layer formed at a boundary between a solid wall and an ionic fluid flowing through a channel formed by the wall. In particular, Findl et al is directed at measuring a "K-effect potential", where the K-effect potential is defined as the change in zeta potential which occurs between static (zero flow) conditions and flow conditions. It is described in Findl et al that the measurement of the K- effect potential may be useful for sensing surface charge effects on mineral particles which are suspended in an ionic fluid.

Dongqing Li, "Electro- Viscous Effects on Pressure-Driven Liquid Flow in Microchannels", Colloids and Surfaces A: Physiochemical and Engineering Aspects 195 (2001) 35-57 investigates the extent to which electro-viscous effects caused by the EDL phenomenon affect pressure driven flow in microchannels, and concludes that the pressure drop effects are significant and potentially important to the design and process control of micro- electro-mechanical systems (MEMS) and other microtechnology or nanotechnology apparatus and systems.

L.M. Fu, J.Y. Lin and R. J. Yang, "Analysis of Electroosmotic Flow with Step

Change in Zeta Potential", Journal of Colloid and Interface Science 258 (2003) 266-275 investigates the effects of a change in zeta potential upon the velocity profile and pressure distribution of an electrolytic solution during electroosmotic flow (EOF) and concludes that a nonuniform zeta potential may seriously reduce the efficiency of electrophoresis.

None of the references referred to above describe or suggest the utilization of the streaming potential as a source of useful electrical energy.

SUMMARY OF THE INVENTION

The present invention is an apparatus and method for producing electrical energy from fluid energy. The invention is based upon a combination of the phenomena of electrokinetics and hydrodynamics. The invention involves the use of a streaming potential which is created by passing an electrolytic fluid through one or more channels.

More particularly, the invention involves providing a means or mechanism for exploiting the streaming potential so that the streaming potential can be used to provide a useful source of electrical energy. The means or mechanism for exploiting the streaming potential may include terminals which are exposed to the streaming potential and to which an electrical load may be connected either directly or indirectly. hi a first particular aspect, the invention is an energy conversion apparatus for producing electrical energy from fluid energy, the energy conversion apparatus comprising a channel assembly, the channel assembly comprising: (a) a channel;

(b) a first terminal located at a first axial position and in communication with the channel; and (c) a second terminal located at a second axial position and in communication with the channel. hi a second particular aspect, the invention is a method for producing electrical energy from fluid energy comprising the following steps:

(a) providing an energy conversion apparatus, wherein the energy conversion apparatus is comprised of a channel assembly, wherein the channel assembly is comprised of: (i) a channel;

(ii) a first terminal located at a first axial position and in communication with the channel; (iii) a second terminal located at a second axial position and in communication with the channel; and

(b) passing an electrolytic fluid through the channel. The fluid energy may be provided by a fluid energy source which provides pressure, kinetic energy, hydrostatic head, or any combination of fluid energy components. For example, the fluid energy could be provided by a pump as a fluid energy source which delivers the fluid to the channel at a desired pressure and flowrate. Preferably, however, the fluid energy is provided primarily or exclusively by a hydrostatic head or pressure. For example, the channel may be associated with a fluid reservoir as a fluid energy source which provides a desired hydrostatic pressure to cause the fluid to pass through the channel.

The amount of fluid energy may be any amount which is sufficient to pass the fluid through the channel. Although the fluid may be passed through the channel under any flow conditions which provide for some velocity gradient in the transverse direction across the channel, the amount of fluid energy preferably causes the fluid to pass through the channel under substantially laminar flow conditions in order to provide a well defined velocity gradient for the fluid in the transverse direction across the channel.

The electrical energy which is produced by the invention is manifested as a potential difference between the first terminal and the second terminal. The open circuit voltage of this potential difference is substantially equivalent to the streaming potential. The streaming potential and the resulting potential difference between the first terminal and the second terminal may be exploited by completing an electrically conducting path between the first terminal and the second terminal, which electrically conducting path may then carry an external load current. When the electrically conducting path is completed between the first terminal and the second terminal, the potential difference between the first terminal and the second terminal may decrease, depending upon the external load current which is carried by the electrically conducting path.

The channel may be comprised of any shape. For example, the channel may be circular in cross-section or may be some other shape. Furthermore, the channel may be closed or open. Preferably, subject to considerations relating to management of the phenomenon of hydro-viscosity in the channel, the shape of the channel is selected to maximize the surface area of an interior surface of the channel, since the interior surface of the channel produces the electrokinetic phenomenon. In a preferred embodiment, the channel is a generally circular closed conduit so that an interior surface of the channel completely surrounds the channel. The channel may be comprised of any cross-sectional area which will enable the combined effects of the EDL and the velocity profile of the fluid through the channel to produce a noticeable preferential transport of ions through the channel. For example, if the diameter or width of the channel is very large relative to the thickness of the EDL, the velocity flow profile may not provide a significant velocity gradient through the localized regions of excess ions to produce an appreciable streaming potential. Preferably the size of the channel is selected so that the effects of the EDL are noticeable throughout substantially the entire cross- sectional area of the channel. As a result, selection of the size of the channel is dependent upon the properties of both the channel and the fluid, since the effects of the EDL phenomenon are also dependent upon these properties. hi a preferred embodiment, the channel has a finite cross-sectional area which is less than about 300 square millimeters. More preferably, in a preferred embodiment the channel has a finite cross-sectional area which is less than about 3 square millimeters. Even more preferably, in a preferred embodiment the channel has a finite cross-sectional area which is less than about 0.03 square millimeters. Most preferably, in a preferred embodiment the cross-sectional area of the channel ranges from between about 3 x 10^"4 square microns and about 0.03 square millimeters, or from between about 0.03 square microns and about 300 square microns, depending upon the properties of the fluid and the channel and upon the desired electrical energy output and efficiency of the apparatus.

The channel has an interior surface which provides an interface between the channel and the fluid. The interior surface of the channel is preferably constructed of a channel material which is relatively electrically non-conductive so that any surface current induced by the streaming potential in the interior surface of the channel is relatively small and thus does not dissipate the streaming potential. The interior surface of the channel may be comprised of the same material as the remainder of the channel or may be comprised of a different material.

The channel material may be comprised of any material which will exhibit an excess charge at the interior surface of the channel in the presence of the fluid, since it is this excess charge which is responsible for the EDL phenomenon. The remainder of the channel may be comprised of virtually any material.

Preferably the extent of the excess charge at the interior surface of the channel is maximized in order to maximize the effects of the EDL. It is believed that the development of excess charge at the interior surface of the channel may be due to some dissociation of the interior surface in the presence of the fluid, preferential absorption of fluid ions into the solid surface, an ionization process resulting from interaction of the interior surface and the fluid, or a combination of these and perhaps other effects. The interior surface of the channel should preferably be comprised of a channel material which will significantly exhibit the development of this excess charge at the interior surface regardless of which effect or effects is responsible for the development of the excess charge.

In a preferred embodiment, the channel is constructed entirely of glass so that the channel material is comprised of glass, which has been observed to result in the production of measurable electrical energy. Many other materials may however be potentially suitable or preferred for use as the channel material, including ceramics, plastics and naturally occurring materials such as rock and soil.

The channel has a finite length. The length of the channel is preferably minimized in order to minimize fluid energy losses through the channel. Preferably the length of the channel is less than about 10 centimeters. More preferably the length of the channel is less than about 2 centimeters. Even more preferably the length of the channel is less than about 1 centimeter. The length of the channel may be greater than, equal to, or less than the distance between the first axial position and the second axial position.

The electrolytic fluid which is passed through the channel may be comprised of any fluid which will exhibit some dissociation into ions. The electrolytic fluid may be comprised of a liquid or a gas or a combination of liquids and gases. Preferably the electrolytic fluid is a liquid.

Generally, strong electrolytic fluids will exhibit strong EDL effects and weak electrolytic fluids will exhibit weak EDL effects. It has been generally observed that the thickness of the EDL decreases as the electrolytic strength of the fluid increases. As a result, the properties of the electrolytic fluid are preferably considered in the selection of the channel material and the size and shape of the channel. In a preferred embodiment, measurable electrical energy has been produced with the use of deionized water (a weak electrolyte) as the electrolytic fluid, but more electrical energy has been produced with the invention by using tap water (a stronger electrolyte than deionized water) as the fluid.

The amount of electrical energy produced by the invention and the efficiency of the apparatus and method of the invention are dependent upon the thickness of the EDL and upon the zeta potential in the channel, which in turn are dependent upon the properties of the channel (in particular the channel material) and the properties of the electrolytic fluid which is passed through the channel. The thickness of the EDL and a quantity defined as the reciprocal of the EDL thickness can both be defined mathematically. It has been observed that both the amount of electrical energy produced by the invention and the efficiency of the apparatus and method of the invention generally increase up to a plateau value as the reciprocal of the EDL thickness increases (i.e., as the thickness of the EDL decreases). In a preferred embodiment, where the electrolytic fluid is deionized water and the channel material is glass, it has been observed that it is preferable that the reciprocal of the EDL thickness be greater than about 1 x 10⁵/m and that further beneficial effects are negligible after the reciprocal of the EDL thickness exceeds about 1 x 107m. As a result, in a preferred embodiment, the reciprocal of the EDL thickness is preferably between about 1 x lOVm and about 1 x 107m and more preferably between about 1 x 10⁶/m and about 1 x 107m. The first terminal and the second terminal are separated by a finite axial distance so that the streaming potential can be established between the first terminal and the second terminal. As a result, the first terminal is located at the first axial position in the channel and the second terminal is located at the second axial position in the channel. Since the streaming potential is dependent upon the streaming current, the amount of electrical energy produced by the invention is believed not to be strongly dependent upon the axial distance between the first axial position and the second axial position.

As a result, the locations of the first terminal and the second terminal are preferably selected having regard to the overall design of the channel assembly, hi a preferred embodiment, the first axial position is located adjacent to a first end of the channel and the second axial position is located adjacent to a second end of the channel so that the axial distance between the first terminal and the second terminal is approximately equal to the length of the channel. Specifically, in a preferred embodiment the first axial position and the second axial position are located at some small distance outside the ends of the channel in order to simplify the construction of the channel assembly, but the first axial position and the second axial position could alternatively be located at some distance within the ends of the channel, which configuration may serve to minimize entry and exit effects which may affect the operation and efficiency of the invention. The first terminal and the second terminal are in communication with the fluid as it passes through the channel such that the streaming potential is exhibited between the first terminal and the second terminal. In other words, the first terminal and the second terminal are comprised of an electrically conductive material which is in electrical communication with the fluid.

Preferably the first terminal and the second terminal extend outside the channel and are electrically insulated from any electrically conductive portions of the channel. Alternatively, the first terminal and the second terminal may be connected to a suitably insulated electrical conductor which extends outside of the channel.

The invention may be practiced with a single channel assembly if the amount of electrical energy which is required to be produced by the invention is very small (in the order of about 1 nano-ampere or less per kilopascal (kPa) of fluid pressure drop). Where larger amounts of electrical energy are required to be produced, the invention is preferably practiced using a plurality of electrically connected channel assemblies. In a preferred embodiment the apparatus of the invention is comprised of at least about 1 x 10⁵ electrically connected channel assemblies, and more preferably at least about 450,000 electrically connected channel assemblies. Essentially, the invention may be scaled to include any number of channel assemblies.

If the invention includes a plurality of channel assemblies, each of the channel assemblies may be identical or may be different. For example, each of the channel assemblies may include a separate first terminal and second terminal, or two or more of the channel assemblies may share terminals.

The plurality of channel assemblies may be electrically connected in a parallel configuration so that the first terminals of the channel assemblies are electrically connected, a series configuration so that the first terminal of one of a pair of channel assemblies and the second terminal of the other of the pair of channel assemblies are electrically connected, or some combination of parallel and series configurations. Configuring the channel assemblies in parallel provides additive currents while configuring the channel assemblies in series provides additive potential differences, i a preferred embodiment, the plurality of channel assemblies is configured in parallel and the first terminals and the second terminals of each of the channel assemblies are shared.

If the first terminals and the second terminals are shared in a parallel configuration of channel assemblies, the first terminals may be comprised of a first electrode and the second terminals may be comprised of a second electrode. Where the invention includes a first electrode and a second electrode, the first electrode preferably comprises a first connection point and the second electrode preferably comprises a second connection point which are adapted to provide connections for the electrically conducting path between the first electrode and the second electrode so that an external load current can be carried between the first electrode and the second electrode. The electrode connection points may be comprised of the electrodes themselves, or they may be electrically connected with the electrodes.

If the invention includes a plurality of channel assemblies, the channel assemblies may be comprised of discrete channels or the apparatus of the invention may be comprised of a bulk material which includes a plurality of channels. The bulk material may be fabricated or may be naturally occurring. The plurality of channels may be defined by pores in the bulk material if the pores facilitate passage of the fluid from the first axial position to the second axial position in the pores. As a result, the bulk material should include pores which provide permeability to the bulk material. If the channels are defined by pores in a bulk material, at least the interior surface of the pores is preferably constructed of a relatively non- conductive channel material. In a preferred embodiment the channels are defined by pores in a porous glass filter material. The electrically conducting path may be provided between terminals, between electrodes, or between electrode connection points. The electrically conducting path preferably includes an electrical load. The electrical load preferably utilizes the electrical energy produced by the invention to perform useful work. The electrical load may be any type of electrical load including a resistive, capacitive or inductive load or a combination of such loads.

The electrical load may be selected so that the conduction current between the first terminals and the second terminals is minimized, hi other words, the electrical load may be selected to function as a shunt load in order to minimize electro-viscous effects in the channels. The use of the invention to minimize electro-viscous effects in the channels may provide beneficial effects by minimizing the amount of energy that is required to pass fluids through the channels and by minimizing energy losses which are experienced as fluids pass through the channels. These beneficial effects may in turn be applied towards improving the performance of apparatus which rely upon the passage of fluids through channels, particularly very small channels or "microchannels". For example, the operation and efficiency of cooling apparatus which rely upon passing a cooling fluid through microchannels to cool mechanical parts or electrical components such as integrated circuits and computer chips may be enhanced by application of the invention in a manner which minimizes electro-viscous effects in the microchannels.

Preferably, however, the electrical load is selected to optimize the amount of electrical work which is produced by the invention. For example, if the electrical load is very small, the external load current through the electrical load will be very large, which may have the effect of reducing significantly the potential difference between the first terminal and the second terminal due to high demands on the amount of charge which must be carried between the first terminal and the second terminal. Conversely, if the electrical load is very large, the external load current through the electrical load will be very small, which will have the effect of reducing the electrical power output between the first terminal and the second terminal, since electrical power output will vary according to the square of the external load current.

In a preferred embodiment comprising an estimated 450,000 channel assemblies, it has been observed that the electrical load is preferably a resistive load of between about 1 ohm and about 1 x 10^s ohms (or a load which is equivalent to resistive load of between about 1 ohm and about 1 x 10^s ohms), or is more preferably a resistive load of between about 100 ohms and about 1 x 10⁶ ohms (or a load which is equivalent to resistive load of between about 100 ohms and about 1 x 10⁶ ohms).

Selection of the electrical load to optimize the work produced by the invention will be dependent upon the properties of the channels, the properties of the electrolytic fluid and the number of channel assemblies which are utilized in the invention.

The invention may be used in a steady state manner in which the fluid is passed in a single direction through the channels either toward the first axial position or toward the second axial position. The invention may also be used in an alternating manner in which the fluid is passed alternately through the channels in a direction toward the second axial position or in a direction toward the first axial position to provide an alternating potential difference between the first terminal and the second terminal of the channel assemblies. Where the invention is used in the alternating manner, preferably the fluid is passed through the channels so that the potential difference between the first terminal and the second terminal of the channel assemblies alternates sinusoidally. The frequency of the alternating potential difference may be any frequency which can be produced through the movement of the fluid through the channels, and will depend upon the properties of the fluid, the properties of the channel material and the size of the channels.

The apparatus of the invention may include an alternating means such as an alternating mechanism for causing the fluid to pass through the channels in an alternating manner. The alternating mechanism may be comprised of any mechanism or mechanisms for causing the fluid to pass through the channels in an alternating manner, and may or may not be associated with the fluid energy source.

As one non-limiting example of an alternating mechanism, the alternating mechanism may be comprised of a valve mechanism which alternately directs the fluid in different directions from the fluid energy source.

As a second non-limiting example, the alternating mechanism may be comprised of a movable mount associated with the apparatus by which the positions of the first axial position and the second axial position relative to the fluid energy are alternately varied as the movable mount is actuated, such as for example by reciprocation or rotation.

As a third non-limiting example, the fluid energy source may be comprised of a fluid reservoir positioned at each end of the channels and the relative hydrostatic heads of the fluid reservoirs may be alternately varied to create an alternating pressure gradient in the different directions, either by varying the fluid levels in the reservoirs or by changing the relative elevations of the fluid reservoirs. The second and third examples may also be combined to provide an alternating mechanism which comprises a movable mount which moves the channel assemblies and the reservoirs together to create alternating pressure gradients.

As a fourth non-limiting example, the fluid energy source may be comprised of a reciprocating apparatus including a piston in a cylinder which may be used to alternately apply pressure and suction to the fluid to cause the fluid to pass in opposite directions through the channels. The fourth non-limiting example may be utilized in conjunction with a fluid reservoir which provides a source of fluid to be acted upon by the reciprocating apparatus.

In a preferred embodiment where the fluid is deionized water and the channel material is glass, it has been observed that oxygen gas is produced at one of the terminals due to oxidation of hydroxyl groups and that hydrogen gas is produced at the other of the terminals due to reduction of hydrogen ions. The invention may therefore provide an ancillary function as an electrochemical cell in which the electrolytic fluid is converted into nonionic constituents, which nonionic constituents may be withdrawn from the terminals either to increase the efficiency of the apparatus of the invention or to produce the nonionic constituents. As a result, the invention may include one or both of withdrawing a reduced product from one of the first terminal or the second terminal or withdrawing an oxidized product from the other of the first terminal or the second terminal of one or more of the channel assemblies.

BRIEF DESCRIPTION OF DRAWINGS

Embodiments of the invention will now be described with reference to the accompanying drawings, in which:

Figure 1 is a schematic representation of a charge distribution within an EDL.

Figure 2 is a schematic representation of a charge distribution in a channel containing a liquid under static conditions.

Figure 3 is a schematic representation of a typical parabolic velocity profile for fluid flow through a channel under laminar flow conditions. Figure 4 is a schematic representation of an apparatus according to the invention including a single channel circuit and depicting a charge distribution under flow conditions.

Figure 5 is a schematic representation of a single channel circuit including streaming current and conducting current without an electrically conducting path and without an electrical load as contemplated by the invention.

Figure 6 is a schematic representation of a circuit according to the invention including a plurality of channel assemblies configured in parallel, an electrically conducting path and an electrical load.

Figure 7 is a schematic representation of a circuit according to the invention including a plurality of channel assemblies configured in series, an electrically conducting path and an electrical load.

Figure 8 is a graph which depicts a theoretical relationship between zeta potential and external load current produced by the invention.

Figure 9 is a graph which depicts a theoretical relationship between the reciprocal of EDL thickness and external load current produced by the invention.

Figure 10 is a graph which depicts a theoretical relationship between channel length and external load current produced by the invention. Figure 11 is a graph which depicts a theoretical relationship between the radius of a circular channel and the efficiency of the invention.

Figure 12 is a graph which depicts a theoretical relationship between the reciprocal of EDL thickness and the efficiency of the invention.

Figure 13 is a graph which depicts a theoretical relationship between channel length and the efficiency of the invention.

Figure 14 is a graph which depicts a theoretical relationship between an external electrical load and the efficiency of the invention. Figure 15 is a schematic representation of a preferred embodiment of an experimental apparatus according to the invention. Figure 16 is a schematic representation of one embodiment of an alternating mechanism according to the invention.

Figure 17 is a schematic representation of an alternate embodiment of an alternating mechanism according to the invention.

DETAILED DESCRIPTION

Referring to Figure 1, an electric double layer (EDL) (20) is created at an interface between a solid surface (22) and an electrolytic fluid such as a liquid (24). The EDL (20) is created as a result of a localized charge (26) at the solid surface (22). It is believed that the localized charge (26) may be caused by some dissociation of the material of the solid surface (22), preferential absorption of liquid (24) ions into the solid surface (22), an ionization process resulting from interaction of the solid surface (22) and the liquid (24), or a combination of these and perhaps other effects.

The EDL (20) includes an immobile layer (28) of liquid (24) ions adjacent to the solid surface (22) and a mobile layer (30) of liquid (24) ions adjacent to the immobile layer (28). The creation of the EDL (20) results in a zeta potential (31) between the solid surface (22) and the liquid (24).

The immobile layer (28) of the EDL (20) consists essentially of counter-ions (33) which have a charge opposite to the localized charge (26) at the solid surface (22) and which are therefore attracted to the localized charge (26). The mobile layer (30) includes both counter-ions (33) and co-ions (35) having the same charge as the localized charge (26), but the mobile layer (30) contains a relative excess of co-ions (35), due to electrostatic repulsion of the co-ions (35) from the localized charge (26) and due to the relative shortage of counter-ions (33) in the mobile layer (30). i Figure 1, the localized charge (26) at the solid surface (22) is negative, the counter-ions (33) in the immobile layer (28) are positive, and the co-ions (35) in the mobile layer (30) are positive. These charges are exemplary only, and the respective charges may be reversed in a particular EDL (20) system, depending upon the properties of the solid surface (22) and the liquid (24).

The magnitude of the EDL (20) effect in a particular EDL (20) system will be dependent upon the properties of the solid surface (22) and upon the properties of the liquid (24). In general, the greater the localized charge (26) at the solid surface (22), the greater the EDL (20) effect and the greater the electrolytic strength of the liquid (24), the greater the EDL (20) effect.

Referring to Figure 2, the EDL (20) may be created in a channel (32). In a preferred embodiment, the channel (32) is substantially circular in cross-section, but the channel (32) may be any shape. The EDL (20) will be created in the channel (32) regardless of the size of the channel (32). The size of the channel (32) depicted in Figure 2 is such that the mobile layer (30) extends substantially to the centerline of the channel (32), with the result that the effects of the EDL (20) are exhibited across substantially the entire cross-section of the channel (32). Figure 2 as in Figure 1, the localized charge (26) at the solid surface (22) is negative, the counter-ions (33) are positive, and the co-ions (35) are negative. Figure 2 depicts the EDL (20) under static (zero flow) conditions.

Figure 3 depicts a velocity profile (34) which is typical for substantially laminar flow. The velocity profile (34) is generally parabolic in shape, with the velocity varying in a transverse direction relative to the solid surface (22) from essentially zero velocity (36) adjacent to the solid surface (22) to a maximum velocity (38) at the centerline of the channel (32). The velocity profile (34) for transitional flow or for substantially turbulent flow typically exhibits a relatively "blunt" transition between zero velocity (36) and maximum velocity (38) and is typically somewhat more unpredictable than the velocity profile (34) for laminar flow. As a result, although the invention may be practiced under any flow conditions, preferably the invention is practiced under substantially laminar flow conditions.

Figure 4 is a generalized schematic representation of an energy conversion apparatus (39) according to the invention and of a charge distribution in the channel (32) obtained by superpositioning Figure 2 and Figure 3 under steady state flow conditions. The energy conversion apparatus (39) comprises a channel assembly (40).

The channel assembly (40) includes the channel (32) and two terminals which are in communication with the liquid (24) as it passes through the channel (32). In Figure 4, the terminal on the left is a first terminal (42) and the terminal on the right is a second terminal (44), but the relative positions of the terminals (42,44) is interchangeable.

The first terminal (42) is positioned at a first axial position (46) and the second terminal (44) is positioned at a second axial position (48). The first axial position (46) and the second axial position (48) are preferably located adjacent to the ends of the channel (32), either at the ends of the channel (32), at some distance outside of the ends of the channel (32), or at some distance within the ends of the channel (32). The first axial position (46) and the second axial position (48) are separated by a finite distance. The terminals (42,44) are electrically conductive to facilitate an electrical connection between the terminals (42,44) and the liquid (24).

In Figure 4, negative co-ions (35) are preferentially transported downstream (to the right in Figure 4) as a result of the combined effects of the relative excess of co-ions (35) in the mobile layer (30) and the velocity profile (34) which provides the maximum velocity (38) at the centerline of the channel (32).

The terminals (42,44) function as electrodes. In the configuration depicted in Figure 4, the first terminal (42) functions as a cathode and the second terminal (44) functions as an anode, hi other words, there is an excess of negative co-ions (35) at the second terminal (44) relative to the first terminal (42). Where the charges of the counter-ions (33) and the co- ions (35) are reversed, the first terminal (42) will function as an anode and the second terminal will function as a cathode (44). Where the invention is practiced in an alternating manner, the first terminal (42) and the second terminal (44) will each alternate between functioning as a cathode and an anode.

The terminals (42,44) may extend outside of the channel (32) or terminate within the channel (32). Where the terminals (42,44) extend outside of the channel (32), the terminals (42,44) are preferably insulated at any points of contact with other conducting materials in order to avoid electrical energy losses due to short-circuiting. Where the terminals (42,44) do not extend outside of the channel (32), they are preferably electrically connected with wires or other conductors in order to provide an extension of the terminals (42,44) outside of the channel (32). Where provided, these conductors are preferably insulated at any points of contact with other conducting materials in order to avoid electrical energy losses due to short-circuiting.

A first connection point (50) is provided for providing a connection between the first terminal (42) and an electrically conducting path (52). Similarly, a second connection point (54) is provided for providing a connection between the second terminal (44) and the electrically conducting path (52). The electrically conducting path (52) provides an external circuit for carrying an external load current (56) between the first terminal (42) and the second terminal (44). The electrically conducting path (52) comprises an electrical load (58). In

Figure 4, the electrical load (58) is depicted as a resistive load, but the electrical load (58) may be comprised of any type of load (i.e., resistive, capacitive or inductive) or any combination of loads. For design purposes, the electrical load (58) may also comprise the inherent resistance of the electrically conducting path (52).

During flow conditions, a streaming current (60) is created by the preferential downstream transport of co-ions (35). This streaming current (60) in turn results in a streaming potential (62) between the first terminal (42) and the second terminal (44). The streaming potential (62) provides a voltage source for the external load current (56), which passes through the electrically conducting path (52) and the electrical load (58) via the first connection point (50) and the second connection point (54).

The external load current (56) is created by the conversion of fluid energy into electrical energy. The fluid energy is provided as the amount of energy which is required to pass the liquid (24) through the chamiel (32). The electrical power consumption of the electrically conducting path (52) can be calculated by multiplying the square of the external load current (56) by the amount of the electrical load (58).

Figure 5 provides a schematic representation of a circuit provided by a single channel in the absence of the electrically conducting path (52) provided by the invention. In Figure 5, the streaming current (60) is caused by passage of the liquid (24) through the channel (32), thus resulting in the streaming potential (62). In Figure 5, the streaming current (60) is shown as moving in the downstream direction in the channel (32), regardless of whether the co- ions (35) are positive ions or negative ions.

The streaming potential (62) induces in the liquid (24) and in the solid surface (22) a conduction current (64) which is in a direction opposite to the streaming current (60). The conduction current (64) is comprised of at least two separate parallel paths. A first path (66) for the conduction current (64) is through the liquid (24). A second path (68) for the conducting current (64) is through the solid surface (22). The liquid (24) provides a bulk resistance (70) and the solid surface provides a surface resistance (72). The conduction current (64) is the sum of the currents along the first path (66) and the second path (68), and is dependent upon the values of the bulk resistance (70) and the surface resistance (72). From Figure 4 and Figure 5, it can be seen that the channel assembly (40) and the electrically conducting path (52) of the invention provide an additional parallel current pathway between the first terminal (42) and the second terminal (44) so that the total current between the first terminal (42) and the second terminal (44) is the sum of the external load current (56) and the conduction current (64). The magnitude of the external load current (56) and the conduction current (64) will depend upon the relative values of the electrical load (58), the bulk resistance (70) and the surface resistance (72).

By balancing the values of the electrical load (58), the bulk resistance (70) and the surface resistance (72) and by considering the overall characteristics of the energy conversion apparatus (39), including the amount of electrical energy which is produced by the apparatus (39), the electrical power consumption of the electrically conducting path (52) can be optimized.

The value of the bulk resistance (70) will be dependent upon the properties of the liquid (24), and a balance must be achieved in the practice of the invention between selecting the liquid (24) so that it has a high electrolytic strength in order to maximize the EDL

(20) effect and selecting the liquid (24) so that it is relatively non-conductive in order to minimize the conduction current (64). The value of the surface resistance (72) can be maximized by providing that the solid surface (22) is constructed of a channel material which is relatively an electrically non- conductive material. This may be achieved either by constructing the channel (32) entirely of a relatively non-conductive material or by lining or coating an interior surface (74) of the channel (32) so that the solid surface (22) is relatively electrically non-conductive.

The invention may for some applications be practiced using a single channel assembly (40) as depicted schematically in Figure 4. For most applications, however, and in a preferred embodiment, the energy conversion apparatus (39) of the invention comprises a plurality of electrically connected channel assemblies (40). The number of channel assemblies (40) which are utilized in the invention is dependent upon the amount of electrical energy which is sought to be produced with the invention. Since the electrical energy which may be produced by a single channel assembly (40) is very low (typically in the range of about one nano-ampere or less per kilopascal of hydrostatic pressure), for most applications the invention utilizes a large number of channel assemblies (40). The maximum number of channel assemblies (40) which may be utilized in the invention is limited only by the ability to configure the channel assemblies (40) in a desired configuration.

Figure 6 provides a schematic representation of a circuit according to the invention including a plurality of channel assemblies (40) configured in parallel. Figure 7 provides a schematic representation of a circuit according to the invention including a plurality of channel assemblies (40) configured in series. Combinations of parallel configurations and series configurations of channel assemblies (40) may also be utilized in the invention. In both of the configurations depicted in Figure 6 and Figure 7, each of a plurality of channel assemblies (40) includes a channel (32), a first terminal (42) and a second terminal (44). hi both Figure 6 and Figure 7, the streaming current (60) is shown as moving in the downstream direction in the channels (32), regardless of whether the co-ions (35) are positive ions or negative ions. hi the parallel configuration of Figure 6, each of the channel assemblies (40) may comprise separate terminals (42,44) or the terminals (42,44) may be shared amongst channel assemblies (40). Where the terminals (42,44) are shared in a parallel configuration of channel assemblies (40), the first terminals (42) may be comprised of a first electrode (47) and the second terminals (44) may be comprised of a second electrode (49). In the parallel configuration of Figure 6, the plurality of first terminals (42) is preferably connected with a single first connection point (50) and the plurality of second terminals (44) is preferably connected with a single second connection point (54) so that the electrically conducting path (52) can be established between the first connection point (50) and the second connection point (54). Where the first terminals (42) are comprised of the first electrode (47) and the second terminals (44) are comprised of the second electrode (49), the first electrode (47) maybe comprised of the first connection point (50) and the second electrode (49) may be comprised of the second connection point (54).

In the parallel configuration of Figure 6, the streaming currents (60) are additive so that the electrically conducting path (52) is capable of sustaining an external load current (56) which is proportional to the number of channel assemblies (40). i the series configuration of Figure 7, the channel assemblies (40) are electrically connected so that the first terminal (42) of a first channel assembly (40) is electrically connected with the second terminal (44) of a second channel assembly (40), with the result that the channel assemblies (40) are connected "end to end" to create a chain of channel assemblies (40). In the series configuration of Figure 7, the first terminal (42) of the channel assembly (40) at one end of the chain of channel assemblies (40) is connected with the first connection point (50), while the second terminal (44) of the channel assembly (40) at the other end of the chain of channel assemblies (40) is connected with the second connection point (54) so that the electrically conducting path (52) can be established between the first connection point (50) and the second connection point (54). hi the series configuration of Figure 7, the streaming potentials (62) are additive so that the first connection point (50) and the second connection point (54) have a potential difference which is proportional to the number of channel assemblies (40).

Figures 8 through 14 are graphs depicting theoretical relationships between various parameters pertaining to the design of an energy conversion apparatus (39) according to the invention. The data for the graphs of Figure 8 through Figure 14 has been generated from equations derived from physical relationships according to the principles of electrokinetics and hydrodynamics. A thorough discussion of the development of the equations which served as the basis for Figures 8 through 14 is provided below. Figure 15 is a schematic representation of a preferred embodiment of an experimental apparatus which has been built and has been used to verify the trends observed in the graphs from Figure 8 through Figure 14. A thorough discussion of the experimental results from the use of the experimental apparatus of Figure 15 is provided below.

The experimental apparatus depicted in Figure 15 incorporates preferred features of the energy conversion apparatus (39) of the invention.

Referring to Figure 15, in a preferred embodiment the energy conversion apparatus (39) includes a plurality of channel assemblies (40) which are electrically connected in a parallel configuration, hi the preferred embodiment depicted in Figure 15, the energy conversion apparatus (39) includes approximately an estimated 4.5 x 10⁵ (450,000) channel assemblies (40) in a parallel configuration, thus demonstrating that the use of a number of channel assemblies (40) in the order of 1 x 10⁵ (100,000) and higher is feasible in the practice of the invention.

In the Figure 15 embodiment, the energy conversion apparatus (39) is comprised of a porous bulk material (76) and the channels (32) are defined by pores in the bulk material (76). The use of the bulk material (76) avoids the necessity of fabricating the plurality of channels (32) individually. The bulk material (76) may be comprised of any suitable porous material which has sufficient permeability to permit the liquid (24) to pass through the channels (32) between the first axial position (46) and the second axial position (48), including both natural and man-made materials. In the Figure 15 embodiment, the bulk material (76) is comprised of glass and is provided in the form of a commercially available porous glass filter material.

The first terminal (42) and the second terminal (44) for each of the channel assemblies (40) are shared amongst all of the channel assemblies (40) and are located at opposite ends of the bulk material (76). The first terminal (42) and the second terminal (44) are each separated from the bulk material (76) by an O-ring (78) so that the first axial position (46) and the second axial position (48) are each located adjacent to the ends of the channels (32) but are spaced from the ends of the channels (32) by a distance equal to the thickness of one of the O-rings (78). hi the Figure 15 embodiment the first terminals (42) are comprised of a first electrode (47) and the second terminals (44) are comprised of a second electrode (49). The first electrode (47) comprises a first connection point (50) and the second electrode (49) comprises a second connection point (54).

The channels (32) have a length (79) which in the embodiment of Figure 15 is defined by the width of the bulk material (76). The length (79) of the channels in the Figure 15 embodiment is about 3 millimeters. The first electrode (47) and the second electrode (49) are connected to a meter

(80) for measuring the external load current (56). The first electrode (47) is connected to the meter (80) at the first connection point (50) and the second electrode (49) is connected to the meter (80) at the second connection point (54). The electrically conducting path (52) is defined by the circuit between the first connection point (50) and the second connection point (54) and the electrical load (58) is comprised of the meter (80).

The fluid energy is provided by a fluid energy source (81). The fluid energy source (81) is comprised of a liquid reservoir (82). As a result, the fluid energy is comprised of a hydrostatic pressure or head (83) from the reservoir (82). During testing of the Figure 15 embodiment, the hydrostatic head (83) was approximately 30 centimeters and was selected to ensure that the liquid (24) has sufficient fluid energy to pass through the bulk material (76) under substantially laminar flow conditions. Any alternate fluid energy source (81) may be used in the practice of the invention. The energy conversion apparatus (39) of the Figure 15 embodiment further comprises an inlet (84) for introducing the liquid (24) into the reservoir (82) and an outlet (86) for withdrawing the liquid (24) from the apparatus (39) after it has passed through the bulk material (76). The relative elevations of the inlet (84) and the outlet (86) define the maximum hydrostatic head (83) which can be attained with the reservoir (82). Both deionized water and tap water were used as the liquid (24) during testing of the energy conversion apparatus (39) of Figure 15.

In use, the reservoir (82) is filled with the liquid (24) to a desired level and the hydrostatic head from the reservoir (82) causes pressure-driven flow of the liquid (24) through the channels (32). The passage of the liquid (24) through the channels (32) results in the streaming current (60) through each of the channels (32) and the streaming potential (62) between the first electrode (47) and the second electrode (49). The streaming potential (62) provides a voltage source for the electrically conducting path (52), resulting in the external load current (56) which is measured by the meter (80).

It has been observed during use of the energy conversion apparatus (39) of Figure 15 using water as the liquid (24) that oxygen gas as an oxidation product and hydrogen gas as a reduction product each evolve from one of the terminals (42,44). As a result, one potential application of the energy conversion apparatus (39) and of the method of the invention is as an electrochemical cell for the production of oxygen and hydrogen or other oxidation products and reduction products, depending upon the composition of the liquid (24) that is utilized in the practice of the invention.

The testing of the energy conversion apparatus (39) of Figure 15 has been carried out under steady state uni-directional flow conditions so that the streaming potential

(62) and the external load current (56) are both effectively a direct current (DC) source of electrical energy. The invention is not limited to use in this manner, and may be utilized in an alternating manner in order to produce an alternating current (AC) source of electrical energy. It is contemplated that the use of the invention as an AC source would involve an alternating means such as an alternating mechanism (88) which would facilitate the use of the fluid energy to cause the liquid (24) to pass alternately through the channels (32) in a direction toward the second axial position (48) and in a direction toward the first axial position

(46) so that the streaming current (60) is established alternately in two opposing directions, thus alternately reversing the streaming potential (62) which is observed between the first electrode

(47) and the second electrode (49). Preferably the liquid (24) is passed alternately in a manner such that the streaming potential (62) alternates sinusoidally.

Referring to Figure 16, one embodiment of an alternating mechanism (88) which could be used to provide an alternating flow of the liquid (24) could comprise a valve mechanism (90) which is controlled to alternately direct the fluid energy to opposing sides of the bulk material (76), thus causing the liquid (24) to alternately flow in opposite directions within the bulk material (76) under an alternating pressure gradient, i the embodiment of

Figure 16, the outlets (86) are alternately opened and closed in synchronization with the valve mechanism (90) so that while the fluid energy is alternately directed to either side of the bulk material (76), only the outlet (86) on the opposing side of the bulk material (76) is open, in order to ensure that the pressure gradient is exhibited through the bulk material (76).

Referring to Figure 17, a second embodiment of an alternating mechanism (88) which could be used to provide an alternating flow of the liquid (24) could comprise a reciprocating apparatus (92) associated with the apparatus (39) of Figure 15 so that the fluid energy source (81) is comprised of the liquid reservoir (82) and the reciprocating apparatus (92). The reciprocating apparatus (92) is comprised of a piston (94) within a cylinder (96). One side of the cylinder (96) is in liquid communication with the outlet (86). The liquid (24) extends continuously from the liquid reservoir (82) to the cylinder (96) via the outlet (86) so that the channel assemblies (40) are immersed in the liquid (24).

In the Figure 17 embodiment, the piston (94) is reciprocated within the cylinder (96) by a drive mechanism such as a motor (not shown) to alternately apply pressure or suction to the liquid (24) which causes the liquid (24) alternately to pass through the channels (32) in opposite directions as the level of the liquid (24) in the liquid reservoir (82) rises and falls in response to the reciprocation of the piston (94). The frequency of the reciprocation of the piston may be varied to vary the frequency of the alternating electrical energy that is produced by the apparatus (39).

For all of the embodiments of the invention, it is noted that the liquid (24) may be passed through the channels (32) in any manner which results in axial movement of the liquid (24) through the channels (32), since any axial movement of the liquid (24) will result in the streaming current (60) and the streaming potential (62). As a result, the passage of liquid (24) through the channels (32) may be performed "incrementally" in order to provide for a minimum of axial movement of the liquid (24), which may be particularly advantageous in providing for alternating passage of the liquid (24) through the channels (32) at higher frequencies. A description follows of the development of the theoretical relationships which have resulted in the graphs of Figures 8 through 14 and of the development and the experimental use of the embodiment of energy conversion apparatus (39) of Figure 15. THEORETICAL ANALYSIS FOR A SINGLE CHANNEL

A. Controlling Equations and Boundary Conditions We begin by considering a model for pressure-driven and time-dependent electrokinetic flow through a single circular channel (32). For an individual channel (32) without an electrically conducting path (52) as in Figure 2, we consider the boundary value problem for oscillating liquid (24) flow in an infinitely extended circular channel (32). Ro and R_s are the bulk resistance (70) of the liquid (24) and the surface resistance (72) of the solid surface (24), respectively, in a single channel (32). A cylindrical coordinate system (r, θ, z) is used where the z-axis is taken to coincide with the channel (32) central axis. All field quantities are taken to depend on the radial coordinate r and time t. The boundary value problem with the relevant field equations and boundary conditions are described below.

B. Electrical Field

The total potential U at location (r, z) at a given time t is taken to be:

U≡U{r,_Z,t) = ψ{r)+ [U₀ -zE' ή] (1)

where ψ (r) is the potential due to the EDL (20) at equilibrium state (i.e., no liquid motion with no applied external field); U₀ is the potential at z = 0 (i.e., Uo ≡ U (r, 0, t)); and E'_z(t) is the spatially uniform, time-dependent electric field strength. The total potential U in Eq.(l) is axisymmetric and, when E'_τ(t) is time-independent, Eq.(l) is identical to Eq.(6.1) as described in J.H. Masliyah, Electrokinetic Transport Phenomena (Alberta Oil Sands Technology and Research Authority, 1994). The time-dependent flow to be studied here is assumed to be sufficiently slow such that the radial charge distribution is relaxed at its steady state. Further, it is assumed that any induced magnetic fields are sufficiently small and negligible such that the total electric field may still be defined as - VU (see A. Shadowitz, The Electromagnetic Field (Dover, 1975) This definition can then be used to obtain the Poisson equation: V²H = -^ (2)

where p is the free charge density and sis the permittivity of the medium. Combining Eqs.(l) and (2) yields the following Poisson equation in cylindrical coordinate:

LA . ^dψi ) (3) r dr dr ε

The conditions imposed on ^(r) are:

ψ(a)= ψ_s and ψ(0) is finite (4)

where ψ_s is the zeta potential (31) at the channel (32) wall, r — a; a is the radius of the channel (32). For brevity, we shall focus on a symmetric, binary electrolytic fluid with univalent charges. The cations and anions are identified as species 1 and 2, respectively. Based on the assumption of thermodynamic equilibrium, the Boltzmann equation provides a local charge density p_t of the z^'th species. Thus:

p_ι = z en„ exp\ (i = l,2) (5) kT

where z_t is the valence of the z^'th species; e is the elementary charge; n_∞ is the ionic concentration in an equilibrium electrochemical solution at the neutral state where

= 0; k is the Boltzmann constant; and T is the absolute temperature. Invoking the Debye-Hϋckel approximation for low zeta potentials (31) (z_teψ/kT« 1), we have sinh(z oeψ/kT) —zoeψ/kT and the total charge density follows from Eqs.(3) and (5) as:

* -2n_∞e²z\ ^■ ∑P, = — - — -ψ £> ' kT ^ψ (6)

where we have used zj = — z₂ - z₀. Finally, the definition of the reciprocal of the EDL (20) thickness for a (ZQ : zo) electrolyte is given as: 2n_e^:z.

K - (7) εkT

Combining Eqs.(3) and (6) results in:

dψ{θ) _ ψ(a) = 0 and = 0 dr

C. Hydrodynamic Field

The axial electric field will induce a body force pE '_z and the modified Navier- Stokes equation becomes:

where we have taken the pressure gradient: _dp/δz≡dp/dz (t)] to be position-independent; μ is the viscosity; and v is the kinematic viscosity of the liquid. The boundary conditions for the velocity field are:

_v(_a,t)^0 and ^AΪ = 0 (10) dr

The electric current density along the channel (32) may be integrated over the channel (32) cross-section to give the electric current:

P E'L I = 2π [ pvrdr + -i=- (11) * R

where: R - « R„ +R.

R, Ro, R_s and L are the total resistance, bulk resistance (70), surface resistance (72) and the channel length, respectively. The first term on the right side of Eq.(ll) is due to bulk convection and the second term to conduction current (64). Because of the assumption of an infinitely extended channel, the contribution to the current due to concentration gradients vanishes. Using Eq.(5) for a (z₀ : z₀) electrolyte, we have p_\ — pχ = 2ezon_∞ cosh eψ =kT). The Debye-Hϋckel approximation implies that cos (zoeψ=kT) «1 and ρ — pι = 2zoera_∞. With this simplification, the conductivity of bulk electrolyte, XQ can be written as:

2z, 'e²n D (12) kT

The resistances R₀ and R_s are defined as:

where, λs is the surface conductivity and P_w - 2τa is the wetted perimeter. The flow rate q can be written as:

q = 2πζvrdr (14)

D. Analytical Solution

An analytical solution is sought here for a sinusoidal periodicity in the electrohydrodynamic fields and this is best addressed by using complex variables. Thus, a general field quantity X may be defined as the real part of the complex function (NV¹⁴*) where

X* is complex (j = ^ XJ), w is the oscillation frequency oscillation, and t is the time. The general field quantity X is written as:

The phase angle φ is defined as:

where Im(X*) and Re(N*) are the imaginary and real parts of X*, respectively. An alternative representation of Eq.(15) is given as:

where:

| | = | ^*| and

= im² (X' ) + Re² (X' ) (17) With the notation of Eq.(15), we shall seek the solution of the boundary value problem for the following specific dependencies: dp ^■-Re[p'e^JM] , E_z' =Re[E[e^ιm] (18) dz We consider the class of solutions where the amplitude of the pressure gradient and the electric field could be frequency-dependent, i.e., p* ≡≡p*(w) and E*_z ≡E*_Z (w). The solution for ψ will then follow from Eq.(8) and that for v from Eq.(9). Thus:

v = Re[v e^jm]

where:

v^* ≡v'(r,ω) = v_p' {r,ω)p'(ω)+ v_E' (r,ω)E_z'(ω) (19) The expression for v*_p(r,w) and v*_E(r, w) will be given at the end of this section.

The electric current will follow from Eq.(l 1) and may be written as: I = Re[l'e^JWI]

where:

I'

(ω)p {ω)+r_E(ω)E:(ω) (20)

The volumetric flow rate q is defined in Eq.(14) and can be expressed as:

q = Re[q e^>°^* }

where

q ≡ q^* (ω ) = q_p ^* (ω)p^*(ω) + q_E {ω)E₂ ^* (ω) (21) During pressure-driven-flow, the amplitude of the streaming potential (62)

E*z (w) is found by setting * = 0 in Eq.(20). Thus:

Kip)- I^' ) p'(ω) for I' = 0 (22) ) Equation (22) may be substituted into Eqs.(19) and (21) to determine the normalized liquid (24) velocity and the volumetric flow rate, respectively. Alternatively, the velocity, current and volumetric flow rate during electroosmosis flow follow from Eqs.(19)- (21) by setting^*(w) = 0.

The relevant quantities in Eqs.(19)-(21) are listed below:

where J₀, pj and v are the zeroth- and first-order Bessel functions of the first kind, liquid density and kinematic viscosity, respectively. We define the first term of I*__(w) as I*_E, ( v) and can be expressed as

The streaming current (60) I_str is defined as the first term of Eq.(ll) or I_str Re[(I*_pp* +I iE% )e^/wt] = itetΛ/Λ

When w → 0, Eqs.(23)-(28) reduce to those of steady state.

Φ) ε²ψ ²κ² _j J,(jm) _| J {jκa) + - ^VP* jm J₀(jκa) J₀ ³ijκa) R

q^' (θ) = πa²

^₎__£V v 2 J,(jm) _| J²(jm) 1- (30) vp_ jκa J₀(jκa) J₀ ²(jJ a)

CIRCUIT ANALYSIS FOR A PLURALITY OF CHANNELS IN PARALLEL CONFIGURATION

Since the streaming current (60) of a single channel (32) is small and is typically of the order of about one nano-amphere, we combine n channels (32) in a parallel configuration to obtain a larger current (Figure 6) for an external electrical load (58) R_L. For this circuit, there are n RQ and n R_s; the streaming currents (60) are additive and hence result in nl*_str.: nl

We can solve forE*_z as:

E; = hE- (32) -R + R \_,, _{E l} +L^ RR_L

and the external load current (56) passing the external electrical load (58) R_L is:

At steady state, Εq.(33) becomes:

-JΞMJJ XL ⁽³⁴⁾ L R n Normally, bulk conductivities of solution μ_ and surface conductivities μ_s are small. For example, the conductivity of DIUF water is of the order of 10^"4 S/m (see L.Q. Ren, D.Q. Li and W.L. Qu, J. Colloid Interface Sci. 233, 12 (2001)); the conductivity of 0.1 M KC1 is of the order of 1 S/m (see J.S. Newman, Electrochemical Systems (Prentice Hall, Englewood Cliffs, 1991), 2^nd ed.); surface conductivity is of the order of 10^"8 or 10^"9 S (see L.Q. Ren, D.Q. Li and W.L. Qu, J. Colloid Interface Sci. 233, 12 (2001) and C. Werner, H. Korber, R. Zimmermann, S. Dukhin, and H.J. Jacobasch, J. Colloid Interface Sci. 208, 329 (1998)).

In addition to the small cross section, these values will normally make the resistance (70,72) of channels (32) four or five order larger than the electrical load (58) R_L of an external electrically conducting path (52). Since R_L (58) is relatively small, the streaming potential (62) can become negligibly small. Thus, we may ignore a part of the conduction current (64) induced by streaming potential (62), ,_\E*. We can obtain the external load current (56) which passes through electrical load (58) R_L as:

When R/n »R_L , h = nReil^p*^¹}. When n → o, I_L =Re[l_p'p e^Jω']R/R_l . It is anticipated that the magnitude of external load current (56) I can be significant as n → oς depending on the ratio of R/R_L and the design of channel (32) array. Based on Eq.(34), we study here how the external load current (56) h changes with respect to the zeta potential (31) ψ_s, the reciprocal of Debye length (or EDL (20) thickness) of EDL (20) k and the length of channel (32) L. The following parameters were assumed for our parametric study: e = 1.6021 x 10^"19 C, n = 1 x 10⁵ , μ, = 10^"8 S/m, μ_ = l x 10^"4 S/m, a = 10 μm, ε= 80 x 8.854 x 10^"12 CV^'V¹, R_L = 10Ω, v = 0.9 x lO^' s^"1 and p = 10³ kgm^"3. Since άp / dz = Δp/Δz = A_p/L, we fix A_p to be 10⁴ Pa.

In Figure 8, for k = 1 x 10⁶ m^"1 and L = 10^"2 m, the effect of ^_s on I_L (56) is plotted. When zeta potential (31) increases, the external load current (56) increases linearly. Since higher zeta potential (31) causes higher charge density in EDL (20), more movable charges or ions will induce a larger streaming current (60).

In Figure 9, for ψ_s = 100 mV and L = 10^" m, the effect of reciprocal EDL (20) thickness k on the external load current (56) for k between 10⁵ m^"1 to 10⁹ m^"1 is plotted. The corresponding EDL (20) thickness varies from 10 μm to 1 nm. Phenomenologically, dilute solution causes a thicker EDL (20); concentrated solution has a thinner EDL (20). i Figure 9, we see that the external load current (56) increases as k increases due to the increase in o ι solution concentration. However, as k approaches 1 x 10 m^" , the external load current (56) reaches a plateau. Figure 10, for ψ_s = 100 mV and k = 1 x 10⁶ m^"1, the effect of channel length L on the external load current (56) II is plotted. Since the pressure gradient dp I dz is proportional to the external load current (56) h and decreases with increasing L, one would expect I_L (56) to decrease linearly with L. The non-linear behaviour given in Figure 10 can be explained as follows. Since the supplied pressure drop A_p is held constant, the pressure gradient dp I 3z decreases as length L increases and hence h (56) decreases. On the other hand, I_L = Re[rp'e^jω ]R/R_L for n → ∞. Since a longer channel causes larger R , h (56) increases with

L. The effects of pressure gradient and resistance on I_L (56) counteract each other. Since the rate of decrease in h (56) caused by pressure drop is faster than the increasing rate caused by R , I_I (56) decreases non-linearly with L.

THEORETICAL EFFICIENCY ANALYSIS

Using a traditional definition of flow work (see RE. Sonntag, C. Borgnakke and

GJ.N. Wylen, Fundamentals of Thermodynamics, Fifth Edition (John Wiley and Sons, hie,

1998)), we define the efficiency η_e// as the ratio of the rate of electrical work produced to the rate of flow work consumed. For steady state, employing the fifth and sixth equation of Eq.(30), Eqs. (32) and (34) for the definition of flow work yields:

_ the rate of electrical work produced _ the rate of flow work consumed

The specific constants have been given earlier and were employed for the calculation of efficiency.

In Figure 11, for L = 10^"2 m, R_L = 10 Ω and k = 1 x 10⁶ m^"1, the effect of channel radius a (for a circular channel 32) on the efficiency of an energy conversion apparatus (39) is plotted.

There exists a maximum efficiency between a = 0.01 μm and a = 0.1 mm.

When a → 0, the efficiency approaches zero as the solid/liquid interface approaches zero and hence the number of movable ions. In this case, there is no induced current and the efficiency becomes zero. When a → ∞, the surface area of EDL (20) increases and, because the surface area is of the order a and that of the flow rate is of the second order of a, the flow increases at a faster rate. Thus, proportionately more flow work must be performed to drive the flow and hence the efficiency approaches zero.

The radii a of a circular channel (32) may be used to calculate the cross- sectional area of a circular channel (32). For example, referring to Figure 11, for a circular cross-section a radius of 1 x 10^"8 meters corresponds to a cross-sectional area of about 3 x 10^"4 square microns, a radius of 1 x 10⁷ meters corresponds to a cross-sectional area of about 0.03 square microns, a radius of 1 x 10^"6 meters corresponds to a cross-sectional area of about 3 square microns, a radius of 1 x 10^"5 meters corresponds to a cross-sectional area of about 300 square microns, a radius of 1 x 10^"4 meters corresponds to a cross-sectional area of about 0.03 square millimeters, a radius of 1 x 10^"3 meters corresponds to a cross-sectional area of about 3 square millimeters, and a radius of 1 x 10^"2 meters corresponds to a cross-sectional area of about 300 square millimeters.

It may be theorized that there may be some correlation in the practice of the invention between channels (32) having a circular cross-section of a particular cross-sectional area and channels (32) having a non-circular cross-section of the same cross-sectional area, but this potential correlation may be influenced by factors such as the ratio of the surface area of the solid surface (22) to the cross-sectional area of the channel (32), and by factors such as the major and minor dimensions of the channel (32) in the case of non-circular channels (32). As a result, although the plot in Figure 11 may be more generally described in terms of the cross- sectional area of the channel (32) instead of the radius a of the channel (32), this more generalized description may not be directly indicative of the results to be expected for non- circular channels (32).

In Figure 12, for L = 10^"2 m, R_L = 10 Ω and a - 10 μm, the effect of k on the efficiency of an energy conversion apparatus (39) is plotted. It is observed that the efficiency for dilute solutions (small k) is smaller and that of the concentrated solutions (large k) is higher. o ι

However, when k is larger than 1 x 10 m^" , the efficiency approaches a plateau. Without intending to be limited by theory, this result may be due to the fact that when the solution concentration increases for large k, EDL (20) thickness decreases and the amount of movable ions in EDL (20) becomes saturated. In Figure 13, for k = 1 x 10⁶ m^"1, R = 10 Ω and a = 10 μm, the effect of channel length L on the efficiency of an energy conversion apparatus (39) is plotted. From Eq. (25), I_p' is independent of the channel (32) length L and contribute largely to the total streaming current (60). However, a longer channel (32) requires larger pressure drop to drive the flow and hence cannot provide a higher efficiency.

In Figure 14, for k = 1 x 10⁶ m^"1, L = 10^"2 m and a = 10 μm, the effect of the electrical load (58) R_L on the efficiency of an energy conversion apparatus (39) is plotted. When electrical load (58) Ri → 0, a large external load current (56) h can be obtained and the electrical work is zero. When electrical load (58) Rx → ∞ , we obtain a zero external load current (56) I_I and zero electrical work. In addition, there exists a maximum efficiency when electrical load (58) Ri = 10⁴ Ω.

EXPERIMENTAL RESULTS

In reality, porous and permeable bulk materials (76), such as glass filter, membrane, rock, and soil, could be considered as a natural electrokinetic battery (i.e. as an energy conversion apparatus (39)). The use of natural materials avoids complex micro/nanofabrication procedures to produce channel (32) aπays with a large surface area to volume ratio. In addition, natural porous materials can have a high porosity ratio up to 60%. To explore this, the experimental energy conversion apparatus (39) shown in Figure 15 was constructed to illustrate the concept of an electrokinetic battery, using a commercial porous glass filter as a bulk material (76) to provide the plurality of channels (32). In the experimental apparatus (39) of Figure 15, the porous glass filter (76) was

20 mm in diameter and 3mm thick with a pore size from 10 μm to 16 μm (Schott DURAN, Mainz, Germany). Two Teflon O-rings (78) of 2 mm thickness were used to hold the filter disc (76) in position. Two meshed Ag/AgCl electrodes (47,49) were used as the first terminals (42) and the second terminals (44). The meter (80) consisted of a Keithley 2000 digital multimeter (Keithley Instruments, Germering, Germany) was used to record the external load current (56). A 30 cm height difference in the liquid reservoir (82) was provided between the inlet (84) and the outlet (86) to make the liquid (24) pass through the filter disc (76) under hydrostatic pressure. Deionized water (MILLIPORE, Billerica, Massachusetts, USA) and tap water were both used as the testing liquid (24). The experiments focused on steady state flow passing in a single direction through the filter disc (76). In this case, the digital multimeter (80) measured the external load current (56) through the shunt resistor (58) in the meter (80). Since the shunt resistor is 10 Ω for 10 mA range, which is small compared to the surface resistance (72) of glass filter (76), the streaming potential (62) becomes relatively small due to the relatively high external load current (56). Thus, we ignore the conduction current (64) induced by the streaming potential (62), I*_E, _\E'_Z, so that I_str = I_p(dp 19z). The number of pores in the glass filter n was calculated from:

n -η- (37) πa

where η is the porosity of glass filter (76) and A is the effective area of the filter (76). Considering the thickness of O-rings (78), the effective area was calculated to be π(10 - 2)² mm . For the purpose of calculations, an average channel radius of a = 13 μm was selected. Since η was not available from product description, a typical porosity of η = 30% was assumed, which resulted in n = 0.3π(8 x 10³)/(π6.5²) ~ 4.5 x 10⁵. Since the bulk conductivity of pure water .λo is 0.5 μS/m and the surface conductivity λg is the order of 10^"9 S/m or 10^"8 S/m (see L.Q. Ren, D.Q. Li and W.L. Qu, J. Colloid Interface Sci. 233, 12 (2001); C. Werner, H. Korber, R. Zimmermann, S. Dukhin and H.J. Jacobasch, J. Colloid Interface Sci. 208, 329 (1998); and D. Erickson, D.Q. Li and C. Werner, J. Colloid Interface Sci. 232, 186 (2000)), I_L = nl_p(dp I dz) is employed to predict the measured current.

To predict the measured external load current (56), the following constants were employed which corresponded to the experimental conditions: n » 4.5 x 10⁵ , μ_ = 10^"8 S/m, μo = 5 x 10^"5 S/m, 1 = 3 mm, ε= 80 x 8.854 x 10^"12 CV^'W, v = 0.9 x 10^"6 mV, p = 10³ kgm^'3, and e = 1.6021 x 10^"19, ^"3p / dz = 9.8 x 10⁵ Pa m^"1. For simplicity, it was assumed that all hydrostatic pressure drop occurred in the channels (32). It should be noted that the value of ψ_s depends on both the concentration or pH of solution and channel material. The larger the zeta potential (31) ψ_s, the more noticeable the electrokinetic effect. Thus, one would expect to observe a larger streaming current (60), streaming potential (62) and external load current (56) for larger zeta potential (31) ψ_s.

TABLE 1 Predicted External Load Current (J)for Possible Values of ψ_s and k^~l

The Debye length (or EDL (20) thickness) k^'1 for distilled water (see L.Q. Ren, D.Q. Li and W.L. Qu, J. Colloid Interface Sci. 233, 12 (2001) and D. Erickson, D.Q. Li and C. Werner, J. Colloid Interface Sci. 232, 186 (2000)) ranges from several micrometers to 1 mm. However, neither ψ_s nor /^"1 is known.

Using Eq.(34), Table 1 provides the predicted external load currents (56) for a number of zeta potentials (31) ψ_s and EDL (20) thicknesses k^A. The previously derived model predicts that the external load current (56) can vary between 10² to 10³ nA. In actual measurement, an average maximum external load current (56) of 760 nA was obtained for deionized water. The measured current gradually decreases due to polarization of electrodes (42,44) at the solution/terminal interface. When tap water was used as the testing liquid (24), the measured external load current (56) reached 1500 nA due to a higher ionic concentration. The results illustrated in Table 1 are in good agreement with these experiment values. As a result, the theoretical model can be shown to predict correctly the order of magnitude for the external load current (56) I_L. The exact h (56) can be determined when ψ_s and k^'1 are known.

The theoretical and experimental results described above suggest that a relatively compact energy conversion apparatus (39) including a number of channel assemblies (40) in the order of 1 x 10⁵ or higher can be used to produce electrical energy in an amount which will result in an external load current (56) of between about 1 and about 2 micro- amperes. It is therefore feasible to suggest that the apparatus and method of the invention could be utilized with smaller or larger arrays of channels (32) and channel assemblies (40) in various configurations to produce electrical energy for a wide range of applications, with the number of channel assemblies (40) and the configuration of the channel assemblies (40) being dependent only upon the ability to configure the apparatus (39) and upon the electrical energy requirements of the particular application.

Claims

The embodiments of the invention in which an exclusive property or privilege is claimed are defined as follows:

1. An energy conversion apparatus for producing electrical energy from fluid energy, the energy conversion apparatus comprising a channel assembly, the channel assembly comprising:

(a) a channel; (b) a first terminal located at a first axial position and in communication with the channel; and

(c) a second terminal located at a second axial position and in communication with the channel.

2. The apparatus as claimed in claim 1 wherein the apparatus is comprised of a plurality of electrically connected channel assemblies.

3. The apparatus as claimed in claim 2 wherein the apparatus is comprised of at least about 1 x 10⁵ electrically connected channel assemblies.

4. The apparatus as claimed in claim 2 wherein each of the channels has an interior surface, wherein the interior surface of the channels is constructed of a channel material, and wherein the channel material is relatively an electrically non-conductive material.

5. The apparatus as claimed in claim 2 wherein the apparatus is comprised of a porous bulk material, wherein the channels are defined by pores in the bulk material, wherein the pores have an interior surface, wherein the interior surface of the pores is constructed of a channel material, and wherein the channel material is relatively an electrically non-conductive material.

6. The apparatus as claimed in claim 5 wherein the bulk material is glass.

7. The apparatus as claimed in claim 4 wherein each of the channels has a finite cross-sectional area which is less than about 300 square millimeters.

8. The apparatus as claimed in claim 4 wherein each of the channels has a finite cross-sectional area which is less than about 3 square millimeters.

9. The apparatus as claimed in claim 4 wherein each of the channels has a finite cross-sectional area which is less than about 0.03 square millimeters.

10. The apparatus as claimed in claim 4 wherein each of the channels has a cross- sectional area of between about 3 x 10^"4 square microns and about 0.03 square millimeters.

11. The apparatus as claimed in claim 4 wherein each of the channels has a cross- sectional area of between about 0.03 square microns and about 300 square microns.

12. The apparatus as claimed in claim 4 wherein each of the channels has a length and wherein the length of each of the channels is a finite distance which is less than about 10 centimeters.

13. The apparatus as claimed in claim 4 wherein each of the channels has a length and wherein the length of each of the channels is a finite distance which is less than about 1 centimeter.

14. The apparatus as claimed in claim 4, further comprising a fluid energy source for providing the fluid energy to pass an electrolytic fluid through the channels.

15. The apparatus as claimed in claim 14 wherein the fluid energy source is comprised of a fluid reservoir, wherein the fluid reservoir is configured to provide a hydrostatic pressure so that the fluid energy is comprised of the hydrostatic pressure.

16. The apparatus as claimed in claim 4, further comprising an electrolytic fluid for passing through the channels.

17. The apparatus as claimed in claim 16 wherein the fluid and the channel material are selected to provide a value for a reciprocal of the electrical double layer thickness of greater than about 1 x 107m.

18. The apparatus as claimed in claim 16 wherein the fluid is selected to provide a value for a reciprocal of the electrical double layer thickness of less than about 1 x 107m.

19. The apparatus as claimed in claim 16 wherein the fluid is selected to provide a value for a reciprocal of the electrical double layer thickness of between about 1 x 10⁶/m and about 1 x 107m.

20. The apparatus as claimed in claim 14 wherein the plurality of electrically connected channel assemblies is configured in parallel so that the first terminals of each of the channel assemblies are electrically connected and so that the second terminals of each of the channel assemblies are electrically connected.

21. The apparatus as claimed in claim 14 wherein the plurality of electrically connected channel assemblies is configured in series so that a pair of channel assemblies is electrically connected between the first terminal on one of the pair of channel assemblies and the second terminal on the other of the pair of channel assemblies.

22. The apparatus as claimed in claim 20 wherein the first terminals of the plurality of electrically connected channel assemblies are comprised of a first electrode and wherein the second terminals of the plurality of electrically connected channel assemblies are comprised of a second electrode.

23. The apparatus as claimed in claim 22 wherein the first electrode is comprised of a first connection point, wherein the second electrode is comprised of a second connection point, and wherein the first connection point and the second connection point are adapted to provide connections for an electrically conducting path between the first electrode and the second electrode for carrying an external load current between the first electrode and the second electrode.

24. The apparatus as claimed in claim 23, further comprising the electrically conducting path, wherein the electrically conducting path is comprised of an electrical load.

25. The apparatus as claimed in claim 24 wherein the electrical load is selected such that a conduction current which is induced in the fluid between the first axial position and the second axial position in the channels is minimized.

26. The apparatus as claimed in claim 25 wherein the electrical load is selected to maximize an amount of electrical work which is produced by the apparatus.

27. The apparatus as claimed in claim 26 wherein the fluid is water and wherein the electrical load is a resistive load of between about 1 ohm and about 1 x 10^s ohms or is a load which is equivalent to a resistive load of between about 1 ohm and about 1 x 10^s ohms.

28. The apparatus as claimed in claim 26 wherein the fluid is water and wherein the electrical load is a resistive load of between about 100 ohms and about 1 x 10⁶ ohms or is a load which is equivalent to a resistive load of between about 100 ohms and about 1 x 10⁶ ohms.

29. The apparatus as claimed in claim 14, further comprising an alternating mechanism for causing the fluid alternately to pass through the channels in a direction toward the second axial position and in a direction toward the first axial position.

30. The apparatus as claimed in claim 29 wherein the alternating mechanism causes a potential difference between the first terminal and the second terminal of each of the channel assemblies to alternate sinusoidally.

31. A method for producing electrical energy from fluid energy comprising the following steps:

(a) providing an energy conversion apparatus, wherein the energy conversion apparatus is comprised of a channel assembly, wherein the channel assembly is comprised of:

(i) a channel; (ii) a first terminal located at a first axial position and in communication with the channel;

(iii) a second terminal located at a second axial position and in communication with the channel; and (b) passing an electrolytic fluid through the channel.

32. The method as claimed in claim 31 wherein the energy conversion apparatus is comprised of a plurality of electrically connected channel assemblies and wherein the fluid passing step is comprised of passing the fluid through each of the channels.

33. The method as claimed in claim 32 wherein the energy conversion apparatus is comprised of at least about 1 x 10⁵ electrically connected channel assemblies.

34. The method as claimed in claim 32 wherein the fluid passing step is performed bypassing the fluid through each of the channels under substantially laminar flow conditions.

35. The method as claimed in claim 34, further comprising the step of providing the fluid with the fluid energy in order to cause the fluid to pass through the channels.

36. The method as claimed in claim 35 wherein the step of providing the fluid with the fluid energy is comprised of withdrawing the fluid from a fluid reservoir, wherein the fluid reservoir is configured to provide a hydrostatic pressure so that the fluid energy is comprised of the hydrostatic pressure.

37. The method as claimed in claim 34 wherein the plurality of electrically connected channel assemblies is configured in parallel so that the first terminals of each of the channel assemblies are electrically connected and so that the second terminals of each of the channel assemblies are electrically connected.

38. The method as claimed in claim 34 wherein the plurality of electrically connected channel assemblies is configured in series so that a pair of channel assemblies is electrically connected between the first terminal on one of the pair of channel assembUes and the second terminal on the other of the pair of channel assemblies.

39. The method as claimed in claim 37, further comprising the step of providing an electrically conducting path between the first terminals and the second terminals for carrying an external load current between the first terminals and the second terminals.

40. The method as claimed in claim 39, further comprising the step of providing an electrical load in the electrically conducting path.

41. The method as claimed in claim 37 wherein the fluid passing step is comprised of alternately passing the fluid through the channels in a direction toward the second axial position and in a direction toward the first axial position.

42. The method as claimed in claim 41 wherein the step of alternately passing the fluid causes a potential difference between the first terminal and the second terminal of each of the channel assemblies to alternate sinusoidally.

43. The method as claimed in claim 39, further comprising the step of withdrawing a reduced product from one of the first terminal or the second terminal of at least one of the channel assemblies.

44. The method as claimed in claim 43 wherein the fluid is comprised of water and wherein the reduced product is comprised of hydrogen gas.

45. The method as claimed in claim 39, further comprising the step of withdrawing an oxidized product from one of the first terminal or the second terminal of at least one of the channel assemblies.

46. The method as claimed in claim 45 wherein the fluid is comprised of water and wherein the oxidized product is comprised of oxygen gas.