DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

[0052] Electroosmotic flow in open channels and in porous media is a well-know phenomena and has been the subject of many experimental and theoretical studies. When a liquid (e.g. water) is in contact with a dielectric solid (e.g. glass, silica, many plastics and ceramics) the natural electrochemistry of the interaction produces a thin layer of net charge density in the fluid that is localized to the liquid-solid interface. An electrical field applied so as to produce a component tangential to this interface will produce a Lorentz force on this net charge density. This net force will cause a motion of the net charge and this motion will be imparted by viscous action to the remaining neutral fluid. Thus in a channel packed with a porous dielectric material that is filled or saturated by an appropriate liquid, a potential difference ΔV applied end-to-end will produce what is known as an electroosmotic flow of the liquid. This electroosmotic flow may compete with or even dominate the flow that could be produced by application of a pressure difference across the same channel.

[0053] Electroosmotic flows may be generated using a wide variety of fluids and dielectric materials. The fluid should provide conditions that yield a high zeta potential with respect to the porous dielectric material. The fluid may be a pure fluid or a mixture of pure fluids that may have in addition some small concentration of a conducting species such as various ions. Preferably, the pure fluids should have high dielectric constant (between about 5 and 100 relative units), low dynamic viscosity (between about 0.1 and 2 centipoise) and low conductivity (between about 10 ⁻⁴ and 10 ⁻¹⁴ mho/m). Additives are preferably introduced to define or control the pH and ionic strength of the fluid. Additives should be of a kind and of a concentration to completely dissolve in the fluid. The kind and concentration of these additives preferably are chosen so as to enhance or optimize the zeta potential under the conditions imposed by the size of the pores in the porous dielectric medium.

[0054] Suitable pure fluids include by way of example, but not limitation: distilled and/or deionized water, cyclic carbonates, methanol, ethanol, 1-propanol, 2-propanol, 1-butanol, 1-pentanol, 1-hexanol, 1-heptanol, benzyl-alcohol, nitromethane, nitrobenzene, butanone, dimethoxymethane, dimethylacetamide, dioxane, p-dioxane, acetonitrile, formamide, tetrahydrofuran, dimethyl formamide, acetone, acetic acid, triethylamine, dichloromethane, ethylene glycol, dimethylsulfoxide, ammonium acetate.

[0055] The zeta potential may be thought of as a property of a fluid-solid interface. It is desirable that the magnitude of this zeta potential be in the range of about unity to 150 mV. The zeta potential may be either positive or negative in sign. It is known that the sign and magnitude of the zeta potential are dependent on the dielectric constant of the fluid, the pH of the fluid, on the ionic strength of the fluid and on the type of ions in the fluid. To yield a zeta potential, generally, the surface of the porous dielectric material exhibits acidic or basic sites that become ionized in the presence of the fluid. These ionizable surface sites may be native to the material or may be the result of adsorption of some species onto the surface material.

[0056] Native ionizable materials include by way of example, but not limitation: silica, which exhibits acidic surface sites, alumina (amphoteric) which can exhibit basic or acidic surface sites, Nylon (zwitterionic) which exhibits both acidic (carboxyl) and basic (amine) surface sites. The sign of the zeta potential is the same as the sign of the net surface charge.

[0057] As an example of adsorption leading to surface charge, consider admixtures of polyethylene or polypropylene with ionic surfactants. Polyethylene and polypropylene are non-polar polymers having no native ionizable sites. In an aqueous solution containing certain ionic surfactants (e.g. sodium dodecyl sulfate), the hydrophobic tail of the surfactant adsorbs to the polymer. The charged end of the surfactant then appears as a charge site on the surface.

[0058] The degree of ionization of the surface sites depends on the pH of the fluid. In most cases there is a pH at which the surface is net neutral and hence the zeta potential is zero. The zeta potential reaches a maximum value for pH values well-above (for acidic surface sites) or pH values well below (for basic surface sites) the pH value at which the surface is net neutral. Ionizable surface sites can be added to a material by chemical reaction or grafting, or induced by creation of reactive surface chemistry or creation of defects via plasma or radiation treatment.

[0059] The host dielectric material is selected for properties of: high zeta potential, sign of the zeta potential, insolubility and stability in the fluid with additives, low electrical conductivity, and sufficient mechanical strength.

[0060] Examples of suitable oxide materials include: silica, alumina, titania, zirconia, cerium oxide, lanthanum oxide, yttrium oxide, hafnium oxide, magnesium oxide, tantalum oxide. These oxides may be amorphous or glassy or crystalline and may be combined in mixtures having other minor oxide components.

[0061] Examples of suitable glass materials include: crown or float or boro-silicate glasses, lanthanum or flint or dense flint glasses, Pyrex™.

[0062] Examples of suitable nitride materials include: silicon nitride, boron nitride, aluminum nitride.

[0063] Examples of suitable polymers include: Nafion™ (Dupont Trade name, a sulfonated PTFE), polysulfone, polyethersulfone, cellulose acetate, mixed cellulose esters, polycarbonate, polyacrylonitrile, polyvinylidene fluoride, polyamide (Nylon), silicone elastomers, polymethacrylate, and nitro-cellulose (also called collodion).

[0064] Other classes of suitable materials include certain semiconductors, carbides (e.g. titanium carbide) and silicides (e.g. germanium silicide).

[0065] Ionic species in the fluid are termed counterions (ions that have a charge sign opposite the sign of the zeta potential) and coions (ions that have a charge sign the same as the sign of the zeta potential). It is the net excess of surface charge-balancing counterions near the surface/fluid interface that determines the zeta potential. Increasing the concentration of counterions in the bulk fluid tends to shield the surface charge and thus reduces the magnitude of the zeta potential. For example, consider silica as the dielectric material exposed to water at pH 7 as the pure fluid and KCl as an additive. The zeta potential for this system is measured to be negative with magnitudes of: 120 mV, 100 mV, 70 mV and 30 mV for KCl concentrations of 0.1, 1, 10 and 100 millimolar, respectively. The valence of the counterion may also have a pronounced effect on the character of the zeta potential. Polyvalent (i.e. multiply charged) counterions may bind to the surface sites thus changing the pH of zero net charge (i.e. the “isoelectric pH”). For example: silica in the presence of a singly valent counterion (e.g. Na ⁺ ) displays an isoelectric pH of about 2.8. Whereas silica in the presence of a bivalent counterion (e.g. Ca ²⁺ or Ba ²⁺ ) displays an isoelectric pH in the range of 6 to 7. In this regard, the transport fluid preferably is selected or purified so as to be substantially free of polyvalent counterions.

[0066] Ionic additives to the fluid maybe broken into two general classes: those that fully ionize (e.g. salts, strong acids and strong bases) and those that partially ionize. The former class is often employed primarily to establish the ionic strength of the fluid. The latter class is often employed primarily to buffer the fluid and thus establish and maintain the pH of the fluid. The two classes often are used in conjunction. It is important to note that many but not all buffering species can exist in polyvalent states (e.g. formate exists as neutral or singly charged whereas phosphate exists as neutral, singly, doubly and triply charged). Thus the choice of a buffering compound must be made in view of the issue of polyvalent counterions discussed above.

[0067] Examples of ionic and buffering additives include but are not limited to: alkali-halide salts, mineral acids and bases, organic acids and bases, phosphates, borates, acetates, citrates, malates, formates, carbonates, chlorates, nitrates, sulfates and sulfites, nitrates and nitrites, ammonium-, methylammonium-, ethylammonium-, propylammonium-salts, BIS, MES, TRIS, TES, HEPES, TEA.

[0068] Certain compounds (sometimes termed anti-static agents) are known to alter or eliminate the zeta potential. For example special agents are added to hydrocarbon fuels to eliminate zeta potentials and thus prevent static buildup during pumping and transport. As a further example, special agents are added to shampoos and conditioners again to eliminate the zeta potential and prevent static buildup. Certain surfactants represent one class of these agents. In this regard the transport fluid is selected or purified so as to be substantially free of agents that degrade or eliminate the zeta potential. As examples: addition of small quantities of the surfactant SDS (sodium dodecyl sulfate) is known to increase the zeta potential of silica in aqueous solutions. Whereas the effect of the surfactant CTAB (cetyl trimethylammonium bromide) on silica in water is to reduce the zeta potential upon addition at low concentrations, to a value near zero as the concentration is increased, and to reverse the sign of the zeta potential at even higher concentrations. Addition of polyamines are also known to reduce or reverse the zeta potential of silica. Surface modification properties of surfactants are reviewed by M. J. Rosen, ‘Adsorption of surface-active agents at interfaces: the electrical double layer,’ Chapter II in, Surfactants and Interaction Phenomena (Wiley, N.Y., 1986), pp. 33-107.

[0069] The region of net charge in the fluid and adjacent to the dielectric surface extends some distance into the fluid. The one-on-e (1/e) thickness of this layer is approximately the Debye length in the bulk fluid. The Debye length at a temperature of 20° C. has a value of 0.048 nm times the square root of ratio of the fluid dielectric constant to the fluid ionic strength (the later taken in units of mols/liter). For one millimolar KCl in water the Debye length is about 9.6 nm.

[0070] This Debye length scale can be altered by changing the ionic strength of the fluid and is preferably less than about one-fifth the characteristic pore size of the porous dielectric medium. For Debye lengths greater than about one-fifth the characteristic pore size, the charged layers on opposing walls of the pore begin to substantially merge having the effect of reducing the apparent zeta potential. For quantitative determination of the degree of double layer overlap the characteristic pore size, D _pore , is preferably taken as defined by D. L. Johnson and P. N. Sen, Phys. Rev. B 37, 3502-3510 (1988); D. L. Johnson, J. Koplick and J. M. Schwartz, Phys. Rev. Lett. 57, 2564-2567 (1986); and D. L. Johnson, J. Koplick and R. Dashen, J. Fluid Mech. 176, 379-392 (1987). This definition of D _pore produces a strong weighting in favor of the larger through-pores in a porous medium.

[0071] The flowrate through a porous medium is given by Darcy's law:

Q=−k _D ΔP A/L

[0072] Here ΔP is the applied pressure difference driving the flow, A and L are the geometrical cross sectional area and thickness of the porous medium, respectively, k _D is the flow or Darcy permeability of the medium. Using the definition of D _pore given above, the Darcy permeability is given by:

k _D =D _pore ² M/F

[0073] where M is termed the ‘pore geometry number’ and F is the ‘formation factor’ of the porous media. The formation factor, F, may be related to more common descriptors of porous media via F=τ ² /φ where ρ is termed the tortuoisty and φ is the connected porosity of the solid. The connected porosity is the wetted volume fraction that represents the through-connected pores and excludes dead-ended pores. Each of these descriptors may be determined using any of the methods well known in the art.

[0074] The effect of charge-layer overlap in simple geometries (e.g. slit or circular pores) has been studied theoretically. See, e.g., C. L. Rice and R. Whitehead, ‘Electrokinetic flow in a narrow cylindrical pore,’ J. Phys. Chem. 69 pp. 4017-4024 (1965); and D. Burgreen and F. R. Nakache ‘Electrokinetic flow in ultrafine capillary slit,’ J. Phys. Chem. 68 pp. 1084-1091 (1964). The conclusions of these studies can be applied analogously to a general porous medium through the use of D _pore as defined above.

[0075] Pores in a porous material vary in size along the length and a variety of pore sizes may be present. Thus a general porous material, saturated with a fluid at some given ionic strength, may have some subset of pores that contain substantially overlapped regions of net charge (here termed ‘nanopores’) with the balance of the pores containing some amount of core fluid that is free of charge-layer overlap (here termed ‘regular’ pores). All of the pores will transport current hence ionic species, but the nanopores will transport flow at a greatly reduced rate compared to the regular pores. An object of the present invention is to apply a current so as to create a flow with minimal alteration of fluid ionic composition. The presence of nanopores reduces the efficiency of this process and may also lead to substantial and performance-degrading ionic strength, composition, and pH gradients across the porous element.

[0076] Experimental and theoretical studies of a wide range of porous media suggest that the pore geometry number falls into the range {fraction (1/32)}<M<{fraction (1/16)}, whereas the formation factor, F, is simply greater than or equal to the inverse of the connected porosity. No particular conditions are placed on the values of M or F for practice of the present invention, except to the extent that both values remain finite (essentially a condition that the porous material is indeed porous and connected end-to-end). Note that the topology properties of a porous material are important design parameters and also that optimization of a particular design may involve the specific choice of porous materials having particular values for these parameters.

[0077] Porous materials may be fabricated by a wide variety of methods, examples include but are not limited to the following:

[0078] Packed particles where the particles may be glass or ceramic or polymers. The particles may be held in place (i.e. confined in the channel) by any method known in the art, including but not limited to end-frits or other mechanical restrictions, or by cold welding under pressure or chemical bonding.

[0079] Synthetic porous opaline materials, such as those described in, for example, A. P. Philipse, ‘Solid opaline packings of colloidal silica spheres,’ J. Mat. Sci. Lett. 8 pp. 1371-1373 (1989), and porous materials created by using opalines as a template, as described in, for example, J. E. G. J. Wijnhoven and W. L. Vos, ‘Preparation of photonic crystals made of air spheres in titania,’ Science 281 pp. 802-804 (1998).

[0080] Phase separation and chemical leaching of a glass, for example the Vycor process as applied to a borosilicate or other composite glass as described in, for example, T. Yazawa, ‘Present status and future potential of preparation of porous glass and its application,’ Key Engineering Materials,’ 115 pp. 125-146 (1996).

[0081] Solgel or aerogel process in silica, alumina, titania, zirconia and other inorganic-oxides or mixtures thereof.

[0082] Zeolite and zeolite-like porous media as described in, for example, Y. Ma, W. Tong, H. Zhou, S. L. Suib, ‘A review of zeolite-like porous materials,’ Microporous and Mesoporous Materials 37 pp. 243-252 (2000).

[0083] Phase separation of polymer—inorganic oxide solutions as carried out using, for example the SilicaRod process described in, for example, K. Nakanishi and N. Soga, ‘Phase separation in silica sol-gel system containing polyacrylic acid I. Gel formation behavior and effect of solvent composition,’ J. Non-crystalline Solids 139 pp. 1-13 (1992).

[0084] Direct machining by lithography and etching, molding, casting, laser ablation and other methods known in the arts.

[0085] Porous polymers as prepared by film stretching, sintering, track etching, casting followed by leaching or evaporation, slip casting, phase inversion, thermal phase inversion. Like methods are often employed in the manufacture of polymer filter membranes.

[0086] Porous polymer monoliths as described in, for example, E. C. Peters, M. Petro, F. Svec and J. M. Frechet, ‘Molded rigid polymer monoliths as separation media for capillary electrochromatography,’ Anal. Chem. 69 pp. 3646-3649 (1997).

[0087] Anodic etching as applied to silicon, as described in, for example, J. Drott, K. Lindstrom, L. Rosengren and T. Laurell, ‘Porous silicon as the carrier matrix in micro structured enzyme reactors yielding high enzyme activities,’ J. Micromech. Microeng. 7 pp 14-23 (1997) or as applied to aluminum as described in, for example, O. Jessensky, F. Muller and U. Gosele, ‘Self-organized formation of hexagonal pore structure in anodic alumina,’ J. Electrochem. Soc. 145 pp. 3735-3740 (1998).

[0088] The porous materials may be fabricated in-channel or may be fabricated, possibly machined or cut, and then inserted or sealed into the channel. The surface properties may be altered before or after placement within a channel.

[0089] The sign and magnitude of the zeta potential can be altered or enhanced by modification of the surface or bulk chemistry of the porous material as described above. Modification of surface chemistry is generally done by reaction with sites (e.g. silanol, hydroxyl, amine) that are present on the native material. Modification of the bulk chemistry is generally done by synthesis of a material that directly incorporates ionizable sites. Examples include but are not limited to the following:

[0090] Modification of the bulk chemistry of a polysulfone or polyethersulfone to convert some portion of the S═O groups to sulfonic acids. The sulfonic acid groups then providing a strongly acidic surface site.

[0091] Modification of the bulk chemistry of PTFE to attach side chains terminated in sulfonic acid groups (Dupont product Nafion™). The sulfonic acid groups then provide a strongly acidic surface site.

[0092] Modification of the bulk chemistry of a polyethersulfone or a polyvinyledene fluoride to introduce quaternary amines. The quaternary amine groups then provide a strongly basic surface site.

[0093] Modification of the bulk or surface chemistry of a polyamide (Nylon) to provide a material with only carboxy (acidic) or amine (basic) surface sites.

[0094] Modification of a zwitterionic material (e.g. Nylon) to terminate one of the existing ionizable sites with a nonionizable end group. The material is then converted to one having only a basic or an acidic site, rather than one having both types.

[0095] Activation of a polymer material by introduction of defects or creation of cross-links via exposure to a plasma, ultraviolet or ionizing radiation. This creates reactive surface sites such as carboxyls.

[0096] Modification of surface silanol groups with methoxy- or chloro-silanes to create amino groups or sulfonic acid groups.

[0097] The porous dielectric material is contained in a fluid-impermeable ‘channel’ having a fluid inlet and outlet and spaced electrodes for applying a potential difference to the fluid. Channel materials are selected to meet requirements for mechanical strength, dielectric breakdown strength, transport fluid and fluid additive compatibility, and the capacity to retain the porous dielectric material. The geometry of the channel covers the entire range from long in length and small cross section to short in length and large cross section. An example of the former geometry is a channel that may be a capillary tube or a covered microchannel formed in a substrate having cross sectional shapes including round to rectangular to rectangular with sloped or curved sides. This channel may be formed by any of the means known in the art. An example of the later geometry is a large diameter and thin porous membrane as sandwiched between two electrodes

[0098] The choice of pore size, topology numbers and physical geometry (e.g. porous element thickness and cross-sectional area) are particular to a given application. This then drives the needs for ionic strength and buffering capacity. In general, the following considerations may be taken into account for practicing preferred embodiments of the present invention.

[0099] Use of singly valent counterions for a well defined hence well-behaved zeta potential.

[0100] Use of absence of compounds in the fluid that degrade or eliminate the zeta potential.

[0101] Use of the lowest concentration of ionic species compatible with ‘minimal’ double layer overlap (i.e. a concentration yielding a fluid Debye length that is less than about one-fifth the characteristic pore size).

[0102] Use of the lowest concentration of buffering ionic species consistent with establishing and maintaining the pH of the fluid.

[0103] Use of ionic species that are compatible with, well soluble, and well dissociated in the fluid.

[0104] A pore size distribution that is preferably monodisperse and if polydisperse does not contain occasional large pores or defects (e.g. cracks or voids) and contains no or a minimal number of ‘nanopores’

[0105] Use of a porous dielectric material that is less conducting than the fluid with additives.

[0106] Use of a porous dielectric material with a dielectric strength sufficient to withstand the potentials applied without dielectric breakdown.

[0107] Use of a porous dielectric material that is mechanically strong enough to withstand the pressures applied both as regards the ability to withstand compression and collapse, and the ability to remain attached to the material of the bounding channel.

[0108] Use of a porous dielectric material that is resistant and insoluble in the transport fluid with additives.

[0109] Use of a channel material that is an insulator, and in particular the channel material should be less conducting than the fluid with additives.

[0110] Use of a channel material with a dielectric strength sufficient to withstand the potentials applied without dielectric breakdown.

[0111] Use of a channel material that is mechanically strong enough and thick enough to withstand the pressures applied.

[0112] Use of a channel material that is resistant and insoluble in the transport fluid with additives.

[0113] Use of a fluid with a high value of the dielectric constant and a low value of the dynamic viscosity.

[0114] Use of a combination of fluid, surface chemistry and additive ionic species chemistry that provides a high value of the zeta potential.

[0115] Use of a fluid that is a pure fluid or a highly miscible mixture of pure fluids.

[0116] The principles and operation of the invention will now be described by reference to the following figures which are intended to serve as illustrative embodiments but not to limit the scope of the invention.

[0117] FIG. 1 illustrates an “in-line” or “series type” flow controller embodiment of the invention. With respect to FIGS. 1 and 1 a, consider a channel 100 of total cross-section A and of total length L that is packed with a porous dielectric medium 104 . The channel 100 has an inlet 101 that is in fluid communication with a fluid source 102 at pressure P 1 and an outlet 103 at pressure P 2 , where P 2 <P 1 . Throughout this description, we have assumed negligible resistance to fluid flow (and so negligible pressure drops) between the fluid source 102 and the inlet 101 , and between the fluid outlet 103 and the fluid-collection reservoir 109 . Under such circumstances, the pressure drop ΔP across channel 100 is equal to P 2 -P 1 . One of skill in the art readily will appreciate how to modify the equations below to account for pressure drops between the fluid source 102 and the inlet 101 , and between the fluid outlet 103 , and the fluid collection reservoir 109 by adjusting the term ΔP so that it accurately reflects the pressure drop across channel 100 . The flow rate Q is produced by the combined action of a potential difference ΔV generated by power source 107 , and applied to the fluid within the channel through spaced electrodes 105 , 106 , and a pressure difference ΔP between the channel inlet 101 and channel outlet 103 .

[0118] It is well-known to one of skill in the art that application of an electrical potential to a fluid via electrodes 105 , 106 in that fluid can generate a current through the fluid, and that gas will be generated at the electrodes 105 , 106 via electrolysis of the fluid. It is further appreciated that gas generation within a closed fluid channel may be undesirable. Thus, as shown in FIG. 1, a bridge 108 may be used to connect electrodes 105 , 106 in the fluid-filled reservoirs 102 , 109 to the fluid in the channel 100 . Such bridges are well-known in the art, and are described, for example, in C. Desiderio, S. Fanali and P. Bocek, ‘A new electrode chamber for stable performance in capillary electrophoresis,’ Electrophoresis 20, 525-528 (1999), and generally comprise a porous membrane or porous solid selected to have sufficiently small pores so as to minimize fluid flow through the bridge, while at the same time to provide for the transport of ions (i.e. to allow current flow). Typical bridge materials include Nafion™ (an ion-selective polymeric membrane) or porous Vycor™ (a phase-separated and etched porous glass having a pore size on the order of 5 nm).

[0119] The flow rate may be written as: Q=(νΔV−κΔP)A/LF. This relation is a well known combination of Darcy's law for pressure driven flow and the Helmholtz-Smoluchowski relation as adapted for electroosmotic flow in porous media. Here ν is the effective electroosmotic mobility, κ is the Darcy permeability of the porous media as divided by the dynamic viscosity of the liquid, and F is the above-described the formation factor. The effective mobility may be written as ν=∈ζ(1−ξ)/μ where ∈ and μ are the dielectric permittivity and dynamic viscosity of the fluid, respectively, ζ is the zeta potential and ξ is a factor that provides for the effect of overlapping net charge layers (i.e. a reduction of the apparent zeta potential under conditions that the thickness of the charge layers becomes on the order of the size of the pores in the media). The zeta potential, hence the electroosmotic mobility, may be signed positive or negative depending on the nature of the fluid and the dielectric material (e.g. for a porous dielectric material 104 composed of TiO ₂ saturated with an aqueous solution, the zeta potential will have a positive sign at low pH and a negative sign at high pH and will be negligibly small at the material iso-electric point which for TiO ₂ is at about pH 6.2).

[0120] The present invention employs a combination of pressure- and electroosmotically-driven flows in a channel 100 filled with a porous dielectric material 104 . The applied potential preferably is selected to yield an electroosmotic flow in the same direction as the pressure-driven flow (e.g. for TiO ₂ at high pH, hence a negative zeta potential hence a negative electroosmotic mobility, the potential would be applied with the negative terminal downstream with respect to direction of the pressure-driven flow). In this configuration the maximum flow rate through the channel 100 will be given by the flow rate equation above and only limited by the magnitude of the potential applied, whereas the minimum flow rate will be for purely pressure-driven flow, that is with ΔV=0, hence Q=−κΔP A/LF. Thus the combination of pressure- and electroosmotically-driven flow in a channel 100 filled with a porous dielectric material 104 provides a voltage-controlled means to vary the flow rate through that channel. In effect, flow control is provided by varying the degree of electroosmotic ‘assist’ to the pressure-driven flow through the channel. As is explained in greater detail with respect to other preferred embodiments described below, sensors may be used to monitor parameters such as pressure, flow rate, etc. at one or more points in the flow controller system. Signals arising from these sensors may be used in a sense and control or servo loop to maintain the signal within a predetermined range by adjusting the voltage outputted by the power supply in response to deviations between the signal and a predetermined set point.

[0121] The system of FIG. 2 illustrates another preferred embodiment of the invention resulting in a device that acts as a voltage-controlled flow splitter. Fluid is supplied from a source 102 at a gauge pressure P 1 and subsequently split at node 202 to flow through the device to a pair of fluid outlets 103 , 204 at gauge pressures P 2 and P 3 , respectively. The system of FIG. 2 may include flow element 205 with an inlet 206 that is in fluid communication with fluid source 102 at pressure P 1 and an outlet 207 in fluid communication with node 202 at pressure P _node . Flow element 205 can be included to provide a pressure-driven flow resistance, or Darcy flow resistance, between the fluid source 102 at pressure P 1 and node 202 so as to reduce the flow rate and pressure available at P _node such that the maximum available pressure and maximum available flow rate established at node 202 is compatible with the electroosmotic flow rate of channel 100 . This is accomplished by making the resistance of flow element 205 to be some fraction or multiple of the flow resistances of channel 100 and flow element 201 .

[0122] Consider the gauge pressure P 2 to be zero, that is, ambient pressure. However, this embodiment is not limited to this condition which is provided purely for illustration of this application. The flow rate Q ₃ through flow element 201 is given by:

Q ₃ =k ₃ ( k ₁ P ₁ (1 −x )−( k ₁ +k ₂ ) P ₃ )/( k ₁ +k ₂ +k ₃ )

[0123] Here we define the quantities: k≡κA/LF and x≡(ν ₂ /κ ₂ )k ₂ ΔV/k ₁ P ₁ . Those skilled in the art will note that the variable k can be considered effectively as the above-mentioned pressure-driven flow resistance parameter for each flow element or channel. Thus for ΔV=0, hence x=0, the flow rate through flow element 201 has a value of:

Q ₃ =k ₃ ( k ₁ P ₁ −( k ₁ +k ₂ ) P ₃ )/( k ₁ +k ₂ +k ₃ )

[0124] whereas this flow rate Q ₃ (i.e. the flow rate through flow element 201 ) is zero when:

x= 1−( k ₁ +k ₂ ) P ₃ /k ₁ P ₁

[0125] hence this flow rate is zero when the potential is set to a value of

ΔV= ( k ₁ P ₁ −( k ₁ +k ₂ ) P ₃ (κ ₂ /ν ₂ )

[0126] The flow rate Q ₃ through flow element 201 can be made negative (i.e. the flow direction through flow element reversed) by the application of even higher values of the potential.

[0127] The Darcy flow resistance for flow element 205 is selected based upon on the desired range of flow rates through flow element 201 and the electroosmotic flow rate that is achieved when a maximum voltage is supplied across channel 100 by power source 107 . For example, if one desires the ability to halt flow through element 201 , P _node must be equal to P 3 . The pressure at node 202 is given by: P _node =(k ₁ P ₁ (1−x)+k ₃ P ₃ )/(k ₁ +k ₂ +k ₃ ). Thus, the relative resistances of flow element 205 and channel 100 should be designed to allow electroosmotic flow through channel 100 to be equal to the pressure driven flow through flow element 205 . Appropriate selections of relative flow resistances for channel 100 , flow element 205 , and flow element 201 for a particular application are readily determined using the equations provided above by those skilled in the art.

[0128] FIG. 3 illustrates an embodiment similar to that illustrated in FIG. 2 , except for the addition of a sensor, 301 , to monitor the pressure at the common node 202 of the flow elements shown in FIGS. 2 and 3 . Sensor 301 can be employed along with servo loop controller 302 as part of a sense-and-control loop to regulate the pressure at the common node 202 and hence the flow rate, Q ₃ , through flow element 201 . Flow rate Q ₃ through flow element 201 also may be monitored directly or indirectly through sensor 311 as described in greater detail below. Such regulation may be desirable to compensate for variations in source pressure P 1 (resulting, for example, from fluctuations in the output of a pump providing the pressure P 1 ). Again referring to the example in which the gauge pressure P 2 is zero (and again not limiting the invention to this particular condition), the flow rate Q ₃ through flow element 201 is given by Q ₃ =k ₃ (P _node −P ₃ ) where the pressure at the node 202 is given by: P _node =(k ₁ P ₁ (1−x)+k ₃ P ₃ )/(k ₁ +k ₂ +k ₃ ). Thus variations in P 1 can be compensated by adjustments to ΔV, hence x, so as to maintain a constant pressure at the node 202 and hence a particular flow rate Q ₃ through flow element 201 .

[0129] The control so achievable is limited by the condition that the pressure at P 1 remains sufficiently high to supply the required flow rate. This type of feedback control may be accomplished by any of the means that are well-know in the art, for example: observing a pressure or flow reading at node 202 by use of sensor 301 and manually adjusting the potential applied by power source 107 ; measuring the pressure or flow at node 202 with sensor 301 and supplying this measurement to an analog electronic (or mechanical) servo loop controller 302 driving an electronically (or mechanically) adjustable power supply 107 ; measuring the pressure or flow at node 202 with a sensor 301 connected to a computer and using the computer to adjust power supply 107 , optionally, with higher order corrections applied (e.g. corrections for fluid or sensor temperature variations) in light of other data being supplied to the computer.

[0130] One of skill will readily appreciate that multiple devices such as those illustrated in FIGS. 2 and 3 , with or without servo-loop control, may be run in parallel to deliver multiple parallel sources of variable flow rate from one common source of fluid 102 . The outlets of these parallel implementations need not but may terminate in loads at the same pressures. Similarly, the flow resistances and mobility coefficients of these parallel devices need not but may be the same.

[0131] The servo loop described above may employ a variety of control inputs and action outputs. By way of example, but not limitation, with the object of providing a constant flow rate Q ₃ through flow element 201 the input to the servo loop is taken as, e.g., the differential pressure across flow element 201 (see FIG. 4 , where sensors 301 and 311 may be used to measure pressure) or the differential pressure across some other passive pressure drop arranged in series with flow element 201 . This differential pressure then provides a measure of the flow rate via Darcy's law. Alternatively the flow rate may be detected by other means know in the art, such as but not limited to: a turbine flowmeter, a thermal convection flowmeter, a Doppler flowmeter measured at or beyond fluid outlet 204 .

[0132] With the object to supply a flow rate of liquid used for heat transfer and by this the control of a temperature or heat flux as a result of the flow of liquid through flow element 201 sensors 301 and 311 (as shown in FIG. 4 ) may be used to measure temperature and flow element 201 is taken to be one side of a liquid heat exchanger or some further downstream element. For control of temperature the input to the servo loop may be a thermocouple or thermistor or RTD or other devices know in the art. For control of heat flux the input to the servo loop may be from a heat flux sensor or the temperature change of the fluid or other means know in the art.

[0133] With the object of applying a mechanical force or displacement through the application of fluid pressure to a bellows 501 (see FIG. 5 ) or a piston or diaphragm or other means know in the art, the sensor 301 may be used to generate a signal for input to the servo loop from a load cell (for force) or a displacement sensor as know in the art. One of skill in the art readily will appreciate that hydraulic mechanical systems are preferably applied under compressive load conditions. For the case where the load is naturally compressive (e.g. gravitationally or spring return loaded) a single flow control system may be used to apply and control the hydraulic force acting against the load. For this case the potential applied by power supply 107 across channel 100 is reduced to increase flow towards the load thus pushing against the load, whereas the potential across channel 100 is increased to increase flow of fluid from the hydraulic actuator when the load is being returned. For the case where the load is neutral or where an active return force is required, two such flow control/servo systems may be used in a push-pull configuration.

[0134] The designs represented in FIGS. 1 through 5 illustrate several embodiments of the invention. It will be appreciated by those of skill in the art that these embodiments may be combined in a variety of series and parallel arrangements dictated by the problem or application at hand. In this regard, the embodiment illustrated in FIG. 1 may be considered as a form of in-line or series flow controller and the embodiments illustrated in FIGS. 2 through 5 may be considered forms of shunt or bleed flow controllers.

[0135] The system illustrated in FIG. 6 shows a further embodiment of the invention useful for metering two fluids into a common stream. As one possible application and to illustrate this embodiment, such a system could be used to perform controlled mixing of two reagents or buffers to be used for gradient-type high pressure liquid chromatography (HPLC). As described above, the use of pressure sensing and servo-feedback control may be applied (as shown in FIG. 6 ) to monitor and/or control and/or regulate both the mixture and the output flow rate. Again this system and the invention is not limited to this particular example.

[0136] In the example of FIG. 6 sources of two fluids, A, and B, 102 , 602 , at gauge pressures PA and PB, are fed to two shunt-type controllers (having nodes 202 , 610 and sensors 301 , 614 , monitoring node pressures P 2 A and P 2 B respectively) that feed fluid to a common junction 612 (at gauge pressure P 3 monitored by sensor 613 ) where the fluids mix. This mixture is further supplied to sample injector 616 and then to a pressure-driven chromatographic column 617 (essentially a channel packed with porous media selected to provide different retention times for some set of chemical species). For purposes of this illustration, the outlet pressure of chromatography column 617 and of collection reservoirs 109 , 629 for elements 100 and 600 are taken as ambient (however the invention is not restricted to these outlet pressures, nor by these outlet pressures being the same).

[0137] The objective in this illustration is to provide constant flow rate to the column 617 while providing a programmed variation in fluid composition. The flow rates of fluids A and B from sources 102 and 602 are independently measured and servo-controlled by two sense-and-control loops involving elements 301 , 302 , 107 , 613 , 614 , 615 , 607 that are provided with set-point inputs 618 , 619 . The programmed variation in fluid composition may be in the form of a series of step changes, or in the form of a continuous ramp (i.e. a gradient) or any of the other forms known in the separation arts. In applications requiring more than two sources of fluid, attendant flow controllers and servo loops may be combined to provide for more complicated or broad ranging fluid composition variations. Such configurations can be run in parallel from common sources of fluids to be able to perform multiple separations in parallel.

[0138] For the purpose of this illustration, sample injection through a sample loop 626 connected to a sample injector valve 616 at the head of the separation column 617 is taken to be performed by any of the means known in the HPLC arts (e.g. by a specialized sample injection valve e.g. 616 , or by electroosmotic/electrophoretic injection through a porous media). For the purpose of this illustration, the end-use of the separation is taken to be any of the end-uses know in the HPLC arts (e.g. such as analyte detection by a detector 620 that measures, e.g., laser-induced fluorescence, optical absorption, refractive index or electrochemical potential; collection of the separation components; input to a mass spectrometer or ICP or NMR spectrometers; input to a next stage of separation by HPLC or LC or electrochromatographies; or preparative HPLC).

[0139] FIGS. 7 and 8 show examples of flow control using the shunt-type flow controller configuration shown in FIG. 3 . The flow elements were constructed from a section of 150 mm inner diameter silica capillary packed with 0.6 mm diameter non-porous silica beads. The flow elements, pressure transducers and pressure source were connected using conventional miniature HPLC fittings.

[0140] The data shown in FIG. 7 were generated using a commercial “lead-screw” type syringe pump as the pressure source (the ripples on the driving pressure curve (line 700 ) correspond to the well-known pressure fluctuations produced by a syringe pump). A time t=0 the controller was switched on with a set-point of ca. 225 psi. By t≈2.5 minutes the set point was achieved as illustrated by controlled pressure trace 701 . Over the remainder of the test the feed rate of the syringe pump was changed several times, resulting in changes in the driving pressure 700 but the changes in the driving pressure 700 produced less than 2% variation in the controlled pressure 701 . The driving pressure oscillations apparent in trace 700 were effectively removed by the flow controller, and so are absent in the controlled pressure trace 701 .

[0141] The data shown in FIG. 8 also were generated using a commercial “lead-screw” type syringe pump. Again at t=0 the controller was switched on and the controlled pressure 801 set point of ca. 225 psi was quickly achieved. In this example the driving pressure 800 was increased and the syringe pump then was switched off resulting in decay of driving pressure 800 over a period of time. By ca. 190 minutes the driving pressure 800 had fallen to ca. 240 psi. whereas the controller maintained the controlled pressure set point of ca. 225 psi. Thus, flow control was achieved with a driving pressure only slightly greater than the set point pressure. The top trace 802 in FIG. 8 shows the current drawn through the flow control element.

[0142] FIG. 9 shows pressure data from a nanobore capillary system driven by a traditional HPLC pump. The flow rate of the HPLC pump monitored by trace 900 showing pump output pressure is unstable in the microsystem causing 150 psi spikes monitored by a pressure transducer at the column head, the output of which is shown by trace 901 . Switching on the flow controller (between approximately 60 and 120 minutes) allows the pressure and flow rate to the column to be precisely controlled. Over the range where the flow controller operates the root mean squared (“RMS”) variation in pressure around the 650 psi set point is 1.7 psi. At the 8.5 nL/sec flow rate in the column, this correlates to a RMS variation in flow rate of 0.02 nL/sec.

[0143] Since the set point of the flow controller can be changed to almost any value less than the driving pressure, two or more flow controllers may be combined to deliver fast, accurate, and reproducible gradients for use in microscale separations. A single pressure source can be used to drive all of the different fluids used in the gradient. Since the flow controller is a microscale device, it is compatible with being operated in a multiple parallel configuration.

[0144] FIG. 10 shows the performance of a dual flow controller system such as the system illustrated in FIG. 6 , programmed to generate water/acetonitrile gradients, illustrated in traces 1000 and 1001 . The traces 1000 and 1001 correspond to pressures measured at nodes 202 and 610 illustrated in FIG. 6 . Six gradients are repeated in the figure, starting at approximately 3, 12, 21, 30 and 39 minutes. The water and acetonitrile are both sloped several hundred psi from their starting to ending pressures over the 3 minute gradient and sent to a mixing tee at the head of the nanobore separation column. The gradient changes the composition of the mixed fluid while controlling the rate at which fluid is delivered to the nanobore separation column. The starting conditions of the gradient can be reestablished in less than 1 minute. In this system a simple hand-operated pump provides the driving pressure. The majority of the flow goes directly into the HPLC column; very little waste is produced. The flow rate in the separation column is compatible with feeding directly into a mass spectrometer. This demonstrates the ability of a dual flow controller system to quickly and reproducibly generate fast gradients in a nano bore HPLC system.

[0145] As noted above, the presence of a current-carrying electrode in a closed channel may produce undesirable side effects. Bridges provide one method of removing the electrode from the channel but still providing current. As also noted above, the zeta potential is a function of fluid composition and pH. As such any given flow control porous element may operate under some limited range of fluid conditions. FIG. 11 shows an embodiment of the invention that provides both a method of removing the electrode from the closed channel and increasing the range of operating conditions. In FIG. 11 the flow control element channel 100 is replaced by two such channels in parallel 100 and 1100 . The fluid outlets 103 , 1103 of the two channels 100 , 1100 are led into separate fluid reservoirs 109 , 1109 , both at the terminal pressure P 2 that is less than source 102 pressure P 1 . Power from power supply 107 is supplied via electrodes 105 , 106 in the these reservoirs. Current is then carried from power supply 107 through one channel (e.g. 100 ), back through the other channel (e.g. 1100 ) to the power supply 107 . The common fluid connection of the channels (e.g., at node 202 ) may then be held at an arbitrary potential (preferably but not necessarily system ground). The channels 100 and 1100 comprise different zeta potential porous dielectric materials 104 , 1104 having pore sizes sufficiently large to support electroosmotic flow. Note that this configuration reduces to the case of a bridge in the limit that one of the channels contains material having a pore size too small to support electroosmotic flow but large enough to still carry a current.

[0146] For example, the material 104 in channel 100 may be silica with a nominal iso-electric point of pH 3 and the material 1104 in channel 1100 may be alumina with an iso-electric point of pH 9.2. As a further example, the material 104 may be modified to display a sulfonic acid group (nominal iso-electric point of pH 1.5) and the media 104 may be modified to support a quaternary amine (nominal iso-electric point higher than pH 14). For a fluid with a pH between the iso-electric points of the two materials the electroosmotic flow through one channel will be towards the supply anode and the electroosmotic flow through the other channel will be towards the supply cathode. This then provides flow hence flow control over a wider range of pH conditions than could be supported using a single channel and at the same time removes the current-carrying electrodes 105 , 106 from the closed channels 100 , 1100 .

[0147] As a specific example consider the materials 104 , 1104 in channels 100 and 1100 to be silica and alumina, respectively. With fluid having pH 3 channel 100 filled with silica has a negligible zeta potential and thus does not provide electroosmotic flow, but still carries current. Channel 1100 filled with alumina has a high positive zeta potential with fluid having pH 3 and thus provides the electroosmotic flow (from the common junction 202 of the channels towards the supply anode) needed for flow control. With fluid having pH 9 the roles are reversed, the silica displays a high negative zeta potential whereas the alumina has a negligible zeta potential, thus the electroosmotic flow is through channel 100 filled with silica (from the common junction 202 of the channels towards the supply cathode). For a fluid having a pH between pH 3 and pH 9 channels 100 and 1100 both supply some degree of electroosmotic flow and thus contribute to the ability to achieve flow control.

[0148] The foregoing description and figures are intended to illustrate but not limit the scope of the invention. Variations of what has been described will be apparent to those skilled in the art and are encompassed by invention described above. All references to patents, patent applications, and other publications are herein incorporated by reference in their entirety for any and all purposes.