Abstract:
A microfluidic device includes one or more microchannels providing a passageway for transmitting an electrolyte fluid. A field source provides a defined field in the one or more microchannels, wherein at least one conductor element that is placed in at least one specific location in the device. Interactions between the defined field and the at least one conductor element produce electro-osmotic flows so that the electrolyte fluid is driven across the one or more microchannels.

Description:
PRIORITY INFORMATION 
     This application claims priority from provisional application Ser. No. 60/341,777 filed Dec. 18, 2001. 
    
    
     BACKGROUND OF THE INVENTION 
     The invention relates to the fields of microfluidics, micro-total-analysis systems (μTAS) and micro-electro-mechanical systems (MEMS), in particular microfluidic pumps and mixers driven by induced-charge electro-osmosis. 
     The ability to transport fluids in micron-sized channels is essential for many emerging technologies, such as in vivo drug delivery devices, micro-electro-mechanical systems (MEMS), and micro-total-analysis systems (μTAS). New methods for the rapid mixing of inhomogeneous fluids in micron-scale devices are also required, since the absence of turbulent mixing on these small length scales implies that mixing occurs by molecular diffusion alone. This typically takes from seconds to minutes—far too slow for envisioned applications. New technologies are thus required for the manipulation, transport and mixing of fluids on these small length scales. 
     Although MEMS-based mechanical pumps with moving parts have recently been developed, including peristaltic pumps, a variety of non-mechanical pumping strategies without moving parts have been used, e.g. based on electrical fields, thermal gradient, electrochemical reactions, surface tensions gradients, and patterned surfaces. Non-mechanical strategies for fluid manipulation become more efficient at very small scales because they are driven by surface phenomena. Moreover, they can be much cheaper to implement than mechanical MEMS-based strategies because they take advantage of nano-scale chemical effects already exhibited by many fluids used in biomedical and chemical engineering applications. They can also possess fewer parts, and are better suited for flexible devices, such as microfluidic fibers. 
     Perhaps the most popular non-mechanical fluid manipulation strategy is based on the phenomena of electro-osmosis, i.e. the fluid slip at a solid-electrolyte interface induced by a tangential electric field. The fluid is set into motion by strong electrostatic body forces exerted by excess ionic charge in diffuse boundary layers of thickness λ=1–100 nm near a solid interface. This effect, which has been studied extensively for more than a century in colloidal science and electrochemistry, is well suited for biomedical applications because the majority of bodily fluids, such as blood or lymph, are electrolytes with comparable ionic strengths. Moreover, the working electrode imposing spatially or temporally varying electric fields can be easily and cheaply built into microchannels with existing silicon-based micro-fabrication technology. Driving fluids with electric fields also facilitates integration with logic circuits for sensing and integration microfluidic devices. 
     The simplest electro-osmotic pumping technique is based on applying a DC field tangential to a field solid channel surface, presumed to have a uniform equilibrium zeta potential ζ or diffuse charge density q. In this case, the fluid-solid surface develops a ‘slip velocity’ given by the classical Helmholtz-Smoluchowski formula defined as 
                       u   -&gt;          =         -     (         ɛɛ   0     ⁢   ζ     η     )       ⁢       E   -&gt;            =       (       q   ⁢           ⁢   λ     η     )     ⁢       E   -&gt;                      EQ   .           ⁢   1               
with a prescribed ζ or q, where ε 0  is the permittivity of vacuum, and ε and η represent the dielectric constant and viscosity of the electrolytic fluid.
 
     In spite of its appealing simplicity, however, there are several drawbacks to the use of DC electric fields, related to the fact that a steady current ({right arrow over (J)}=σ{right arrow over (E)}) must exist in order to maintain a steady field because every electrolyte has a non-negligible bulk conductivity. A steady current in turn implies the creation of ions at one electrode and removal of ions at the other via electrochemical reactions. This can cause a variety of problems. For example, the dissolution of the anode eventually destroys the electric circuit, causing irreversible failure. Microfluidic devices employing DC electric fields thus typically have short lifetimes, which can be acceptable in some applications, such as one-time drug delivery, but not in others, such as μTAS. A shorter lifetime also translates into a higher cost per unit of time of operation. The dissolution of the anode also injects metallic ions into the fluid, which can present safety hazards in biomedical applications or can interfere with chemical reactions in μTAS. Also, the depositions of ions at the cathode can lead to unstable deposits, which can break off or otherwise interfere with the bulk fluid. Furthermore, electrochemical reactions at electrodes inevitably cause electrolyte concentration gradients, which create complicated and potentially unwanted secondary bulk electric fields, as well as secondary electrokinetic phenomena at surfaces. 
     These problems can be solved using high-frequency AC fields, which can be safer, more reliable and more durable than using DC fields. Because AC fields are typically applied along closely spaced electrode arrays, much smaller voltages are required to achieve strong electric fields. Furthermore, the change in electrode polarity frustrates electrochemical reactions, helping avoid unwanted electrolysis reactions at the electrodes. 
     Since the fluid slip velocity of standard electro-osmosis used in EQ. 1 is linear in the applied field E, it averages to zero in an AC field. Therefore, different phenomena must be used to drive steady microfluidic flows using AC fields. For example, AC traveling waves on electrode arrays have been used to drive flows by coupling to thermal gradients. A pair of electrodes adjacently located on a glass slide, to which an AC voltage is applied, has recently been shown to drive a steady swirling flow, and a stationary AC wave on a locally asymmetric electrode array has been shown to pump fluid. Both of these applications work in a limited range of frequencies and rely on a subtle form of electro-osmosis involving induced charges on the electrodes. The electro-osmotic flow is driven by transient interactions between the high-frequency field and the self-induced changes in the diffuse-layer charge density along the electrode surfaces. The pumping effect is therefore a strictly non-equilibrium phenomenon which violates the ubiquitous assumption of a constant zeta potential underlying the classical theory of electro-osmosis. A similar generalization of existing theories is needed to understand another electro-osmotic phenomena described, which is the basis for the invention. 
     Although the available pumping techniques based on AC electric fields offer various advantages over DC methods, there are still serious drawbacks. Foremost among these is the need to microfabricate complex patterned-surface electrodes with elaborate micro-circuitry, which can be more costly, difficult, and prone to failure than their very simple DC counterparts. Another potential drawback is that patterned-surface devices are the “hard-wired” into the electrical circuitry and the physical structure of the surface itself, rendering them less versatile. These drawbacks of existing AC pumping methods, however, can be addressed by another form of induced-charge electro-osmosis, which form the basis for the present inventions, making very simple and versatile AC electro-osmotic microfluidic devices possible. 
     SUMMARY OF THE INVENTION 
     According to one aspect of the invention, there is provided a microfluidic device. The microfluidic device includes one or more microchannels providing a passageway for transmitting an electrolyte fluid. A field source provides a defined field in the one or more microchannels, wherein at least one conductor element that is placed in at least one specific location in the device. Interactions between the defined field and the at least one conductor element produce electro-osmotic flows so that the electrolyte fluid is driven across the one or more microchannels. 
     According to another aspect of the invention, there is provided a method of forming a microfluidic device. The method includes providing one or more microchannels transmitting a passageway for sending an electrolyte fluid. At least one conductor is provided element that is placed in at least one specific location in the device. Interactions are allowed between the defined field and the at least one conductor element. Electro-osmotic flows are produced so that the electrolyte fluid is driven across the one or more microchannels. 
     In yet another aspect of the invention, there is provided a microfluidic device. The microfluidic device comprising at least one conductor element that is placed in at least one specific location in said device. Interactions between a defined field and said at least one conductor element produce electro-osmotic flows. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIGS. 1A–1C  are schematics of the evolution of an electric field around a solid conducting cylinder immersed in a liquid electrolyte; 
         FIGS. 2A–2B  are induced-charge electro-osmotic flows around an uncharged and charged cylinder; 
         FIGS. 3A–3C  are induced charge distribution and slip velocities for various asymmetric conducting objects in a DC or AC field; 
         FIGS. 4A–4C  are schematics of induced-charge electro-osmotic micropump designs for sample cross, elbow, and T junctions; 
         FIGS. 5A–5B  are schematics of induced-charge electro-osmotic mixers; 
         FIGS. 6A–6B  are schematics of sample pumps driven by induced-charge electro-osmotic flows generated at asymmetric conducting posts; and 
         FIGS. 7A–7B  are schematics of linear-channel pump-mixers driven by electro-osmotic flows. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       FIGS. 1A–1C  are schematics of the evolution of an electric field around a solid conducting cylinder immersed in a liquid electrolyte, which illustrates the basic physical mechanisms underlying this invention. Just after an electric field is applied, it must intersect a conducting surface at right angles, as shown in  FIG. 1A . Mobile ions in the liquid electrolyte are driven along electric field lines—positive ions in the direction of the field, and negative ions opposite the field direction. At the conductor/electrode surface, the field lines terminate, causing ions to accumulate in a small ‘diffuse layer’ and inducing an opposite ‘image charge’ in the conductor. From the geometry of the field lines, one can see that positive ions accumulate around the side of the conductor nearest the field source, on the top half of the cylinder in  FIGS. 1A–1C , and negative ions around the side nearest the field sink. This induced-charge ‘diffuse layer’ grows, gradually expelling field lines, as shown in  FIG. 1B , until all field lines are expelled ( FIG. 1C ). The steady state field configuration, as shown in  FIG. 1C , is the same as that found around a perfect dielectric cylinder, and is attained after a time t c =λa/D, which is essentially the “RC” time of an equivalent resistor-capacitor circuit, where D is the diffusivity constant of the electrolyte. 
     This has important implications for the induced electro-osmotic fluid velocity. The cylinder is surrounded by a dipolar diffuse charge cloud that is positive on one hemisphere and negative on the other. On the top of the cylinder, the positively-charged diffuse cloud is driven along the field lines towards the ‘equator’ of the cylinder; on the bottom, the negatively-charged diffuse cloud is driven against the field direction—also towards the ‘equator’ of the cylinder. The resulting ‘induced-charge electro-osmotic’ slip velocity is quadrupolar in nature and will be described further in  FIG. 2A . Generically, the induced fluid flow is driven from the ‘poles’ of the conducting body, towards its ‘equator’. 
     The classical theory of electro-osmosis is based on the assumption that a solid object has a uniform charge density, or zeta potential, which is taken to be a constant material property. While this can be appropriately applied to insulating materials, such as latex, it is certainly not for conductors with free charges, especially out of equilibrium. Although it is not commonly appreciated, the double layers in such conductors will generally develop non-uniform polarizations in space and time in response to applied fields. In simple terms, the interfacial double layer acts as a nonlinear capacitor “skin” between the bulk liquid electrolyte and the conducting solid, and the local electro-osmotic slip, which varies in space and time, is simply given by the product of the tangential field and the potential difference across the capacitor “skin”. For an arbitrary shaped conductor, this generally produces an electro-osmotic flow, which draws fluid along the field axis and ejects perpendicular to the field axis, for both AC and DC fields. Weaker flows of the same type can be produced around dielectrics, relying upon polarization by the orientation of bound dipoles rather than the separation of free charges. 
       FIGS. 2A–2B  show electro-osmotic flows around an uncharged and charged conducting cylinder. The induced-charge electro-osmotic flow, a shown in  FIG. 2A , around the conducting cylinder in  FIGS. 1A–1C  can arise either from an applied background DC field after the charging time λa/D or from an applied field AC field with a frequency less than ω c =D/λa. Using Eq. 1, one can identify the general sense of the electro-osmotic flow. On the side of the conductor facing the field source, the diffuse charge q is positive, so the fluid slips in the direction of the tangential field E ∥ , forward toward the equator. On the other side, away from the field source, the diffuse charge is negative, so the fluid slips opposite the tangential field direction, toward the equator. Therefore, the electro-osmotic flow for any uncharged conductor generally pulls fluid in along the field axis toward both poles and expels it, radially from the equator, as shown in  FIG. 2A . 
     In weak AC fields, if the field direction is reversed, then so are the signs of the induced charges, and thus the flow remains unchanged. Therefore, this electro-osmotic flow will persist even in an AC applied field. For example, it can be shown that the time averaged slip velocity for a conducting cylinder in a weak background AC field E 0  cos(ωt) is given by, 
                     〈     u   θ     〉     =       (           E   ⁢             0   2     ⁢   ɛ   ⁢           ⁢   a     η     )     ⁢     (       2   ⁢           ⁢   sin   ⁢           ⁢   2   ⁢   θ       1   +       (     ω   /     ω   a       )     2         )               EQ   .           ⁢   2               
where ω a =D/λa (≈10 3–10   5  for a ≈1–10 μm and λ≈1–10 nm) is the characteristic double-layer charging frequency, above which the average electro-osmotic slip velocity vanishes because ions cannot relax quickly enough to keep up with the oscillating field. Note that the typical pumping velocities in weak fields are of the order of microns per second or more, depending on the applied field, which is comparable to other existing electrokinetic phenomena of potential use for microfluidic pumping, and much greater velocities can be achieved with strong fields. Note that the induced-charge electro-osmotic fluid velocity grows with the square of the applied field. This favorable nonlinear response can be exploited in our microfluidic devices to achieve much larger pumping velocities than with “normal electro-osmosis.”
 
     If there are no electrochemical reactions at the electrodes, the same diffuse-layer charging effect occurs at the electrode surfaces. It can be shown that following a suddenly imposed DC voltage, the electrode diffuse layers become charged and screen out the bulk electric field at the time scale, τ L =λL/D, where L is the distance between the electrodes. Similarly, for an AC field with applied voltage V 0  cos(ωt), the bulk electric field amplitude is given by 
                     E   0     =       (       V   0     L     )     ⁢     (     1     1   +       (     2   ⁢       ω   L     /   ω       )     2         )               EQ   .           ⁢   3               
which decays to zero above the characteristic frequency ω L =D/λL≈10 2–10   4  Hz for L≈10–100 μm and λ≈1–10nm. Therefore, strong induced-charge electro-osmotic flows driven by AC applied voltages can persist only in a certain band of driving frequencies, ω L ≦ω≦ω a .
 
       FIG. 2B  demonstrates the induced-charge electro-osmotic flow around a charged cylinder. If the cylinder is electrically isolated with a non-zero charge, then the electro-osmotic flow described herein is combined with the familiar normal electro-osmotic flow, which simply wraps around the object, like the field lines shown in  FIG. 1C . The induced-charge electro-osmotic flow is a combination of the two flows, and is shown in  FIG. 2B . Since the latter flow is proportional to the field and the total charge, it changes direction if the electric field is reversed, and therefore, it averages to zero in an AC field, leaving only the quadrupolar induced-charge electro-osmotic flow as shown in  FIG. 2A  once again, regardless of the total charge of the conductor. 
       FIGS. 3A–3C  are induced-charge distributions and slip velocities for various asymmetric conducting objects in a DC or AC field. By manipulating the fore-aft symmetry of a conductor in a DC or AC applied field, a net osmotic flow along the field axis or a net phoretic swimming velocity can be produced. For example,  FIG. 3A  demonstrates a conducting cylinder whose fore-aft symmetry is broken through the application of a metallic coating with a higher Stern compact layer capacitance, shown by the dashed lines, which absorbs ions and prevents them from producing electro-osmotic slip. This reduces the pumping effect on the coated side relative to the uncoated side, resulting in a net flow past the object. 
       FIG. 3B  shows a different arrangement that produces a directed electro-osmotic osmotic flow, even in an AC field. The arrangement includes a cylinder, which is partially insulated with a dielectric coating used to suppress double-layer charging (schematically represented with a layered strip). Following a time-dependent diffuse-layer charging analogous to that in  FIGS. 1A–1C , the effect of the dielectric coating (for the field direction indicated) is to bring the negative ions towards the sides of the cylinder and the positive ions on the bottom region of the cylinder. The slip velocity produced by the negative charges is directed downward past the equatorial region of the cylinder, towards the uncoated side. The positive charges also produce a slip velocity directed upward toward the equatorial region of the cylinder. Note that the magnitude of the slip velocity formed by the negative charges is larger in magnitude than the slip velocity formed by the positive charges, due to the stronger tangential field near the equator compared to that near the pole. The net osmotic flow would thus be directed downward, toward the uncoated side. It is important to note as well that a conducting cylinder, which is entirely coated with a dielectric layer has a greatly reduced induced-charge electro-osmotic fluid flow; it is thus important to work with clean conductor/electrolyte surfaces. 
       FIG. 3C  is another asymmetric arrangement that can produce a directed induced-charge electro-osmotic flow under the influence of an AC electric field. The arrangement includes a tear-drop asymmetric shaped conductor—or more generally, any asymmetrically-shaped body. When a background field is applied, the tear-drop asymmetric shaped conductor produces positive and negative charge regions. The negative charge regions include the most curved region, the upper region in  FIG. 3C , of the tear-drop shaped conductor. The positive regions include the less curved portion of the tear-drop shaped conductor, the lower region in  FIG. 3C . The direction of the slip velocity formed by the negative charge regions is directed downward, and the direction of the slip velocity formed by the positive charge regions is upward along the tear-drop shaped conductor. The magnitude of the slip velocity produced by the negative charge regions is larger than the magnitude of the slip velocity produced by the positive charge regions. Therefore, the net electro-osmotic flow is directed towards the region of lower curvature, downward along the tear-drop shaped conductor shown in  FIG. 3C . 
     Note if the direction of the background field changes, the charge distribution also changes. For example, the negative regions will include the bottom regions of the tear-drop shaped conductor, and the positive charge regions will include the upper most curve regions of the tear-drop shape conductor. However, the field driving the induced-charge electro-osmotic flow is also reversed, so that the net electro-osmotic flow remains a net downward, away from the pointed edge. The same is true of all of the symmetry-breaking situations in  FIGS. 3A–3C : The net flow persists in an AC field. This is very different from normal electro-osmosis, which averages to zero in an AC field. 
     All of the conductor configurations in  FIGS. 3A–3C  have a symmetry, which is broken in the fore-aft sense, measured relative to the applied field direction. The left-right symmetry of the conductor could also be broken, leading to induced-charge electro-osmotic flows which are driven perpendicular to the applied field, and which persist even in AC fields. 
       FIGS. 4A–4C  are schematics of electro-osmotic micropump designs for cross, T, and elbow junctions. Using the principles hereinbefore regarding electro-osmotic flow, one can design different junction pump arrangements. By using a working conductor in conjunction with an applied electric field, the induced-charge electro-osmotic flow generally drives fluid flow in along the field axis and ejects it out from the ‘equator’, perpendicular to the field axis. This effect can be used to pump fluid at right angles, by simply placing a cylindrical conducting wire in the junction, perpendicular to the field axis and the plane of flow. 
     For example,  FIG. 4A  demonstrates a microfluidic cross-shaped micropump design  10 . The cross-shaped micropump design  10  includes four junction walls  32 ,  34 ,  36 , and  38 , four electrodes  12 ,  14 ,  16 , and  18 , and a cylindrical conductor  30 . The cylindrical conductor  30  has transient surface charges in the applied field, which drive the electro-osmotic flow. In the configuration of  FIG. 4A , electrodes  12  and  14  have the same polarity whereas electrodes  16  and  18  have the opposite polarity, which sets up a field in the vertical direction, causing a pumping of fluid from the vertical channels into the horizontal channels. By switching electrode polarity so that electrodes  12  and  16  have the same polarity and electrodes  14  and  18  have the opposite polarity, the field can be switched from vertical to horizontal, and the pumping direction can be reversed. Also, the cylindrical conductor is strategically placed at the intersection point between the microchannels  20 ,  22 ,  24 , and  26 . 
       FIG. 4B  demonstrates a T-junction micropump arrangement  58 . The T-junction micropump arrangement  58  includes junction walls  40 ,  42 , and  44 , a pair of electrodes  46  and  50 , and a conducting plate  48  placed on the junction wall  40  between the pair of electrodes  46  and  50 . The flow is directed into the microchannel  52 . In this embodiment, the polarities of the pair of electrodes  46  and  50  cannot be reversed, thus preventing the reversal of the pump. However, a reversible T-junction can also be designed with four electrodes and a conduction post, like in  FIG. 4A  with one channel closed. This allows the flow direction to be driven either into or out of microchannel  52 . 
       FIG. 4C  demonstrates an elbow junction arrangement  78 . This arrangement includes four electrodes  66 ,  68 ,  70 , and  72 , a cylindrical conductor  73 , and junction walls  60 ,  62 , and  64 . The electrodes  66 ,  68 ,  70 , and  72  are aligned on the junction walls  60 ,  62 , and  64 . The cylindrical conductor  73  is strategically placed in the center of intersection point between microchannels  74  and  76 . By placing the cylindrical conductor  73  in the junction, perpendicular to the field axis and the plane of flow, the fluid is driven around a corner to microchannel  76 . In this embodiment, the electrodes  66  and  70  have the same polarity and the electrodes  68  and  72  have the opposite polarity, and the direction of the pumping is from microchannel  74  toward microchannel  76 . However, by driving electrodes  66  and  68  with the same polarity, and  70  and  72  with polarity opposite to that of electrodes  66  and  68 , the direction of flow is reversed, pumping fluid into microchannel  74 . 
     The junction pumps shown in  FIGS. 4A–4C  and described above can be operated using a DC electric field or an AC electric field, or a pulsed AC electric field. Furthermore, the ‘working’ conductor in each of these devices can be electrically isolated from the electrodes, which drive the electric field; or the working conducting element can be held at a fixed potential or grounded. Holding the working conductor at a fixed potential induces an additional induced-charge electro-osmotic flow that is proportional to the square of the applied field, and is directed away from the nearest wall. This additional flow can be incorporated into any of the devices described herein, enhancing the fluid flow driven into certain channels in the micropumps, or providing an additional mixing flow in the mixers described below. 
       FIGS. 5A–5B  are schematics of AC electro-osmotic mixers. In  FIG. 5A , a design is provided for a fast induced-charge electro-osmotic mixer  80 . The mixer  80  includes a pair of microelectrodes  82  and  84  and an array of conducting posts  88 . The electrode  82  is positive and the electrode  84  is negative, and their polarities can be reversed. The conducting posts  88  include metallic wires, as in the junction pumps described herein. A background flow passes through the array of conducting posts  88 . Also, an AC field in the appropriate frequency range (ω L ≦ω≦ω a ) is applied perpendicular to the posts  88  and to the mean flow direction, which generates an array of persistent convection rolls via the same electro-osmotic mechanism used in the junction pumps, described herein. The particles in the background flow are advected through convection rolls along complicated trajectories, which stretch fluid elements. This enhances diffusive mixing. Using pulsed AC fields to produce chaotic flows can also further enhance the degree of mixing. 
       FIG. 5B  demonstrates another design for a fast electro-osmotic mixer  90 . The mixer  90  includes four electrodes  98 ,  100 ,  102 , and  104  and metal strips  92  embedded in the interior of the channel walls  94  and  96 . This design produces the same kind of convective mixing produced by the mixer  80 . By applying an AC or DC field along the channel with the metal strips  92  embedded within channel walls  94  and  96  in between electrodes  98 ,  100 ,  102 , and  104 . Various arrows illustrate the convection mixing. As with posts  88  described herein, are electrically isolated from the electrodes  98 ,  100 ,  102 , and  104 . If the metal strips  92  were grounded or held at a fixed potential, an additional induced-charge electro-osmotic flow would result, in addition to the flow described here. 
       FIGS. 6A–6B  are schematics of pumps driven by electro-osmotic flows generated at asymmetric conducting posts. As described herein, a conductor in AC or DC applied fields with broken fore-aft or left-right symmetry generally produce net electro-osmotic pumping along the direction of broken symmetry. Therefore, it is possible to produce linear channel pumps using conducting posts, which possess broken asymmetry. Triangular conducting posts  120  are shown in  FIGS. 6A–6B  and represent any method of breaking the symmetry of the conducting array, of which three examples are shown in  FIGS. 4A–4C . Furthermore, the applied field can either be along the direction of the channel as shown in  FIG. 6A  or across the channel, perpendicular to it as shown in  FIG. 6B . In all cases, fluid flow is driven along the channel. 
       FIG. 6A  demonstrates a linear-channel pump  106 . The linear-channel pump  106  includes electrodes  108 ,  110 ,  112 , and  114 , asymmetric conducting posts  120 , and a microchannel  122 .  FIG. 6B  demonstrates a linear-channel pump  107 . The linear-channel pump  107  includes electrodes  116  and  118 , asymmetric conducting posts  121 , and a microchannel  123 . The posts  120  and  121  are schematically represented by triangles to indicate any of the general symmetry-breaking mechanisms, of which three are shown in  FIGS. 4A–4C . The linear channel pumps  106  and  107  are driven by electro-osmotic flows generated by posts with symmetry broken in the channel direction, and an AC or DC field directed along or across the microchannels  122  and  123 . Other broken symmetry conducting posts, such as conducting posts having a cross-section of a tear-drop or triangle, dielectric or metallic partial coatings, can also be used. In the case of a broken fore-aft spatial symmetry, as shown in  FIG. 6A , the sharpest point of the cross section is directed opposite to the desired flow direction of induced-charge electro-osmotic pumping. In the case of a broken left-right spatial symmetry, as shown in  FIG. 6B , the sharpest point of the cross section is directed in the desired direction of induced-charge electro-osmotic pumping. A more economical approach to such posts  120  and  121  may be to simply place two or more wires of different cross sections against each other to approximate the triangle&#39;s shape. In this way, an AC electro-osmotic linear-channel pump can be built out of ordinary metal micro-wires of circular cross-section. 
     Unlike the junction pumps described herein, which are driven by a single electro-osmotic source that cannot drive flows across very large distances, the asymmetric posts can be arranged in extended arrays to provide the distributed forcing needed to drive fluid quickly along lengthy channels. 
       FIGS. 7A–7B  are schematics of linear-channel pump-mixers driven by electro-osmotic flows. The design of the linear-channel pump can be altered to produce microfluidic devices, which can simultaneously pump and mix fluids.  FIG. 7A  demonstrates a pump-mixer arrangement  124  that includes electrodes  126 ,  128 ,  130 , and  132 , asymmetric conducting posts  136  associated with a cylinder covered with a dielectric or metallic coating, and a microchannel  134 . The electrodes  126 ,  128 ,  130 , and  132  permit reversing their polarities and producing AC or DC fields. Instead of four electrodes, two electrodes, as in  FIG. 6B , placed on either side of the channel and driving an AC or DC electric field perpendicular to the channel direction can also be used. The coatings of the conducting posts  136  are directed opposite the flow direction, in an AC or DC field directed along the microchannel  134 . Given that each of the conducting posts  136  produces flows that are directed in along the field axis and out perpendicular to the field axis, this provides an overall mixing pattern shown in  FIG. 7A . Also, the asymmetric shape provides the necessary force to pump fluid through the microchannel  134 . Of course, any broken symmetry will be sufficient to produce a pump/mixer, as discussed above. 
       FIG. 7B  demonstrates another arrangement of a linear-channel pump-mixer  138 . The pump-mixer  138  includes four electrodes  140 ,  142 ,  144 , and  146  and asymmetric metal ridges  152  patterned on the walls  148  and  150  of a microchannel  154  between the electrodes  140 ,  142 ,  144 , and  146 . The electrodes  140 ,  142 ,  144 , and  146  allow reversing their polarities and producing AC or DC fields. The asymmetric ridges  152  are designed to lean in the direction of the flow, in an AC or DC field directed along the microchannel  154 . The surface of the asymmetric ridges  152  is a grooved metallic surface, not connected in any way to the external circuit, which includes normal electrodes positioned in the channel walls  148  and  150  on either side of the grooved surface. 
     While we have indicated electrode and field polarities as “+” and “−” signs throughout, all fields can also be AC or DC corresponding to electrode polarities oscillating between + and −, giving rise to the same induced-charge electro-osmotic flow. Thus all of the devices presented here can operate in AC or DC. 
     The invention provides a number of designs for microfluidic devices taking advantage of induced-charge electro-osmotic flows around conductors. Although these devices can operate with DC voltages, the invention also works with AC applied voltages. Moreover, the flow speeds generated by these devices grow nonlinearly with applied voltage, and thus can in principle greatly exceed the speeds achieved in existing electro-osmotic devices. Also, the invention is simple to produce without requiring very sophisticated microfabrication. 
     Although the present invention has been shown and described with respect to several preferred embodiments thereof, various changes, omissions and additions to the form and detail thereof, may be made therein, without departing from the spirit and scope of the invention.