Abstract:
An electro-osmotic pump, for transporting aqueous solutions in micro-fluidics, has a tubular-shaped pumping section which includes a pump tube that is connected in fluid communication with an extension tube. A thread of silica fibers is positioned in the lumen of the pump tube, and an aqueous solution that will interact with the thread is introduced into the pump tube lumen to charge the aqueous solution. In operation, a voltage potential is selectively applied between the pump tube and the extension tube to establish a ground-potential-ground electric field along the pumping section. This creates a force on the charged aqueous solution that moves it through the pump tube and, consequently, also moves fluid through the extension tube. Various embodiments of the electro-osmotic pump are envisioned, including the serial connection of several pumping sections, for use as valves, switches or pumps.

Description:
FIELD OF THE INVENTION 
     The present invention pertains generally to fluid pumps. More particularly, the present invention pertains to electro-osmotic pumps that are useful for transporting aqueous solutions in micro-fluidics. The present invention is particularly, but not exclusively, useful as a device and method for improving the pumping capacity of electro-osmotic pumps. 
     BACKGROUND OF THE INVENTION 
     It is well known that a liquid can be moved through a small diameter tube under the influence of an applied electric field by a phenomenon that is commonly known as the electro-osmotic (EO) effect. Specifically, the EO effect arises from the fact that when an aqueous solution comes into contact with certain active materials (either acidic or caustic), the solution becomes, charged. If an acidic active material is used, such as silica, the solution becomes positively charged. On the other hand, if a caustic material is used, the solution becomes negatively charged. In either case, the application of an electric field on the charged solution will generate forces on the solution that cause it to move. 
     It happens with the EO effect that only a very thin layer of the solution that is in direct contact with the active material will become charged. Typically, this layer of charged solution will have a very shallow depth that is approximately equal to the Debye length (e.g. 10 nm). The consequence of this is that only a relatively small volume of the solution can be charged by the EO effect. Nevertheless, despite the small volume of charged solution, in order to be effective in moving an aqueous solution through a tube, the forces that are generated on the charged solution by an applied electric field must somehow overcome the pressure head in the tube. 
     For micro-fluidics applications it is well known that the EO effect can be usefully employed, but with some significant limitations. Most noticeably, these limitations involve the size of the tubes that can be used, and the magnitude of the electric field that can be used to drive the charged aqueous solution through the tube. Specifically, insofar as the electric field is concerned, high current densities for generating this electric field are undesirable for at least two reasons. First, high current densities can cause excessive ohmic heating of the solution in the tube. Second, the high current densities at the electrodes that generate the electric field may evolve gases in the tube due to the electrolysis of water. This, in turn, will disrupt the electric field. Insofar as the size of the tubes is concerned, the pressure head in the tube that resists the movement of liquid through the tube is of paramount importance. Heretofore, for the EO effect to be useful in overcoming pressure head, small diameter tubes have been required (typically the radius must be less than 10-20 microns). With this in mind, a mathematical analysis of the EO effect, and its interaction with the resistive pressure head in the tube, is instructive. 
     For an example of conventional flow in a tube due to the EO effect, in resistance to a pressure head, consider a tube which is made of an EO active material, such as silica, and which has a lumen of radius “a”. 
     The bulk flow velocity of the EO flow that is driven by an electric field, within a thin layer near the wall of the tube, is given by 
     
       
           u=λΣV/ 2η L   
       
     
     where λ is the layer thickness (typically 10 nm), Σ is the wall surface charge density (typically 10 −2  Coulomb/m 2 ), V is the voltage, ηis the absolute viscosity absolute viscosity of the fluid and L is the length of the tube. The velocity can be written in terms of zeta potential ζ defined as 
     
       
         ζ=λΣ/∈ 
       
     
     where ∈ is the dielectric constant of the fluid. 
     The Poiseille flow which is driven by the pressure head, and which resists the EO flow described above, has a parabolic velocity profile given by 
     
       
           v=u−[pa   2 /4 Lη][I−r   2   /a   2 ] 
       
     
     where p is the pressure head, and where a value for a &gt;&gt;λ is assumed. Under these conditions, total flow discharged role in the tube is given by 
      Γ=∫ 0   a 2π v r dr=πa   2   {u−pa   2 /[8 Lη]}.   
     The condition that the EO drive overcomes the pressure head is then given by 
     
       
           a   2 &lt;4λΣ V/p.   
       
     
     From the above expression it will be appreciated that when a large pressure head is desirable, the radius of the tube “a” must be quite small. The consequence is a very small throughput. The optimal radius with other parameters fixed is given by 
     
       
           a   2 =2λΣ V/p   
       
     
     and the total flow becomes 
     
       
           Γ=πa   2   u/ 2. 
       
     
     From the above expression, it is to be appreciated that the electro-osmotic (EO) effect is a surface effect. As such, the EO effect is significantly dependent on the amount of surface area of the active material that is exposed to the aqueous solution. 
     In light of the above, it is an object of the present invention to provide a tubular shaped electro-osmotic pump for pumping an aqueous solution which effectively increases the amount of active material surface area that is exposed to the solution per length of tubing used. Another object of the present invention is to provide a tubular shaped electro-osmotic pump which can effectively employ lumens of increased cross sectional areas. Yet another object of the present invention is to provide an electro-osmotic pump which has increased efficiency with little or no increase in voltage requirements in order to avoid ohmic heating of the pump and the unwanted evolution of gas due to electrolysis. Still another object of the present invention is to provide an electro-osmotic pump that can be variously used as a switch or a valve, as well as a pump. Another object of the present invention is to provide an electro-osmotic pump that can effectively incorporate a trapped air isolator which will prevent clogging of the active element of the pump, and maintain low electrical conductivity. Also, it is an object of the present invention to provide an electro-osmotic pump that is relatively simple to manufacture, is easy to use, and is comparatively cost effective. 
     SUMMARY OF THE PREFERRED EMBODIMENTS 
     The electro-osmotic pump of the present invention provides structure which significantly increases the interface surface area between an active element (e.g. silica fibers) and an aqueous solution in which the active element is submerged. Consequently, more of the aqueous solution can be charged by the active element, and a lower electric field charge is effective for generating a pumping force on the solution. 
     In accordance with the present invention, a container is provided for holding an active element in an aqueous solution. Preferably, the container is tube-shaped and has a lumen which defines an axis that extends from one end of the tube to the other. In the preferred embodiment of the present invention, the active element will include a plurality of fibers that are spun together into a thread. This thread is then positioned inside the lumen of the tube-shaped container to create a pump tube. Importantly, the thread will extend between the ends of the pump tube with the fibers of the thread aligned substantially parallel to the axis of the pump tube. The lumen of the pump tube is then filled with an aqueous solution that will interact with the thread to charge the aqueous solution. As envisioned for the present invention, the cross sectional area of the pump tube lumen, taken in a plane perpendicular to the axis of the pump tube, will have an area equal to “A”, while the collective cross sectional areas of the fibers in the thread in this plane will be equal to approximately one half of “A” (i.e. A/2). 
     In order to create an electric field in the lumen of the pump tube, electrodes are positioned at each end of the pump tube. Preferably, one of these electrodes will have a zero potential while the other electrode has either a negative or a positive potential and the resultant electric field will be oriented substantially parallel to the axis of the pump tube. Accordingly, whenever an electric field is applied to the pump tube, a force will be created on the charged aqueous solution that will move the aqueous solution through the pump tube. 
     In combination, an extension tube can be connected in fluid communication to one end of the pump tube. Importantly, depending on whether the extension tube is connected to a voltage potential V or zero potential (ground) at the end of the pump tube, the extension tube will respectively return from a zero potential (ground) to the voltage potential V or vice versa. Together, a pump tube and the extension tube will then define a pumping section for the electro-osmotic pump of the present invention. Further, in order to increase the pumping force of the electro-osmotic pump, a plurality of these pumping sections can be serially joined together with an alternation between pump tubes and extension tubes. Importantly, because voltages can be applied in parallel to the serially connected pumping sections, there is no requirement for using higher voltages. 
     An important option for the present invention involves the extension tube. For one embodiment, the extension tube can be filled with the aqueous solution. This, however, is not a requirement. Specifically, for situations wherein it may be desirable to pump a fluid other than the aqueous solution, the extension tube may be at least partially filled with an air bubble. The air bubble will then isolate the aqueous solution and thread in the pump tube from whatever different fluid is in the extension tube and is being pumped by a pumping section. Other options for the present invention involve various orientations for the pump and extension tubes, as well as changes in their respective cross sectional areas. As envisioned for the present invention, these various orientations and changes can allow the electro-osmotic pump of the present invention to be used as a valve or a switch in addition to its more conventional use as a pump. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The novel features of this invention, as well as the invention itself, both as to its structure and its operation, will be best understood from the accompanying drawings, taken in conjunction with the accompanying description, in which similar reference characters refer to similar parts, and in which: 
     FIG. 1 is an exploded perspective view of an electro-osmotic pump according to the present invention, showing a thread of active material before it is positioned inside the lumen of a pump tube; 
     FIG. 2 is a side elevation view of a preferred embodiment of the electro-osmotic pump of the present invention which incorporates a plurality of end-to-end pumping sections; 
     FIG. 3 is a cross-sectional view of a pump tube as seen along the line  3 — 3  in FIG. 2; 
     FIG. 4 is a plan view of an alternate embodiment of the present invention; 
     FIG. 5 is a plan view of an alternate embodiment of the present invention which is useful as a valve or switch; 
     FIG. 6 is an elevation view of an air isolator that can be incorporated into the electro-osmotic pump of the present invention; and 
     FIG. 7 is an experimental set-up for testing the efficacy of the present invention. 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENT 
     Referring initially to FIG. 1, an exploded view of an electro-osmotic (EO) pump in accordance with the present invention is shown and is generally designated  10 . Specifically, the EO pump  10  includes a container, such as the elongated tube  12  shown in FIG.  1 . For purposes of the present invention, the tube  12  is formed with a lumen  14  and has an electrode  16  that is attached to, or mounted at, one end of the tube  12 . The tube  12  will also have an electrode  18  that is attached to, or mounted at, the other end of the tube  12 , opposite the electrode  16 . One of these electrodes (e.g. electrode  16 ) is grounded, while the other electrode (e.g. electrode  18 ) is connected to a voltage source  20 . With this structure, a voltage potential can be placed on the electrode  18  that will create an electric field, E, in the lumen  14  of tube  12 . Importantly, the electric field, E, will be generally oriented in a direction that is parallel to the axis  22  of the tube  12 . 
     Still referring to FIG. 1, it is seen that the EO pump  10  of the present invention includes a thread  24  that is spun from a plurality of individual fibers  26 . Preferably, the fibers  26  are made of silica, or of some other active material well known in the pertinent art, which, when in contact with an aqueous solution, will develop a charge in the aqueous solution. Regardless of what active material is used for the thread  24 , for the EO pump  10  of the present invention, it is envisioned that the diameter  28  of the thread  24  will be substantially the same as the diameter of lumen  14  of the elongated tube  12 . Also, the length of the thread  24  will be substantially the same as the length of the tube  12 . Thus, as implied in FIG. 1, the thread  24  can be inserted into the lumen  14  of tube  12  and positioned therein between the electrodes  16  and  18 . In combination, when the thread  24  is positioned in lumen  14  of tube  12 , these components of the EO pump  10  establish a pump tube  30 . 
     Referring to FIG. 2, it will be seen that the present invention envisions joining a pump tube  30  in fluid communication with an extension tube  32 . For a combination of pump tube  30  and extension tube  32 , such as shown in FIG. 2, an aqueous solution  34  will fill both the pump tube  30  and the extension tube  32 , and they will have a common electrode (e.g. electrode  18 ). Note that at the end of the extension tube  32 , which is opposite the common electrode  18 , another grounded electrode  16 ′ can be used. Together, in this combination, the tubes  30  and  32  establish a pumping section  36 . As intended for the present invention, a pumping section  36  can be used by itself. Also, a pumping section  36  can be positioned end-to-end with other pumping sections  36  in an alternation that will position grounded electrodes (e.g. electrodes  16 ) between voltage sources  20  (e.g. electrodes  18 ). In this manner, pumping sections  36  can be serially aligned to increase their pumping pressure head without requiring additional voltage. 
     Still referring to FIG. 2, it is to be appreciated that the present invention contemplates an EO pump  10  which is effective for pumping a liquid  38  other than the aqueous solution  34  that is necessary for creating the EO effect. In particular, it can happen that it may be necessary to pump a liquid  38  (e.g. blood) which would tend to clog the thread  24  if they were ever to come into contact with each other. For such situations, the present invention envisions creating an air bubble  40  in the extension tube  32  that will effectively isolate the thread  24  and aqueous solution  34  from the different liquid  38 . It can be shown mathematically, that pressures created by the EO effect in a pump tube  30  on the aqueous solution  34  are effectively transmitted to the different liquid  38  through the air bubble  40 . With this in mind, the importance of the present invention is to increase the pressures that can be created in the pump tube  30  by the EO effect. 
     It is interesting to note that for a lumen  14  having a cross sectional area of a value “A” in a plane perpendicular to the axis  22 , as shown in FIG. 3, the collective cross sectional areas of the fibers  26  in this same plane will be equal to approximately “A/2”. Mathematically, the consequence of this relationship on the resultant EO effect is significant. For example, consider the situation wherein a thread  24  is placed in the tight fitting tube  12 . The number of fibers N in the thread  24  satisfies the expression 
     
       
           N=b   2 /[2 a   2 ] 
       
     
     where the diameter  28  of lumen  14  is equal to a value of “2b” (i.e. the radius is “b”) and the individual fibers  26  each have a radius “a”. The volume of the microchannels between the fibers  26  in the thread  24  will then be approximately equal to the volume of the fibers  26 . Thus, the channels will collectively behave as tubes which have the radius “a” on the average. The total flow through the tube  12  is then given by 
     
       
           Γ=[πb   2 /2]{ u−pa   2 /[8 Lη]}   
       
     
     where p is pressure head, L is the length of tube  12  and η is the absolute viscosity of the fluid in the tube  12 . For the condition where the EO drive balance the pressure head, p, this equation shows that the pressure head is one of the factors determining the radius “a” of the fibers, the throughput, Γ, is governed by the tube diameter  28 . Thus, even with large pressure head, p, large throughputs become possible when the number of fibers N is large. 
     Several variations are envisioned by the present invention for the structure for pumping sections  36 , and for the combined incorporation of several pumping sections  36  into a single EO pump  10 . For one, as shown in FIG. 4, the pumping sections  36  can be arranged in a ladder-like structure. Such a structure will effectively decrease the overall length of serially connected pumping sections  36 . More specifically, in a general ladder-like arrangement as shown in FIG. 4, a series of parallel pump tubes  30  can be alternated between a series of mutually parallel extension tubes  32 . In this arrangement, partitions  42  will need to be employed as shown to separate sequential extension tubes  32  from each other. The legs  44  and  46  of the ladder-like arrangement can then be respectively used as electrodes  18  (connected to voltage source  20 ) and electrodes  16  (grounded). In another combination, shown in FIG. 5, one pump tube  30   a  can be connected with another pump tube  30   b  to establish two legs of a Y-shaped conduit. In this combination, the base of the conduit can then be established as an extension tube  32 . Then, depending on how voltage potentials are applied to the respective electrodes  18   a  and  18   b  of pump tubes  30   a  and  30   b , the aqueous solution  34  can be selectively driven in the directions indicated by the arrows  47   a  and  47   b.    
     An alternative embodiment for the structure of an EO pump  10  which incorporates an air bubble  40  is shown in FIG.  6 . For this embodiment, it is seen that a valve  48  is associated with that portion of extension tube  32 ′ where the air bubble  40  is to be located. The air bubble  40  can then be injected into the extension tube  32 ′ through the valve  48 . Subsequently, the air bubble  40  can be regulated and controlled by the valve  48 . Alternatively, and more particularly for a linear EO pump  10  as shown in FIG. 2, the air bubble  40  can be located in the extension tube  32  by using a syringe type instrument (not shown). 
     The efficacy of the present invention can be demonstrated using a test set-up such as the one shown in FIG.  7 . In this set-up, two substantially parallel, vertically-oriented reservoirs  50  and  52  are connected to each other via a pump tube  30 . Each reservoir  50 ,  52  has an inner diameter  54  that is fifteen millimeters (15 mm), and the pump tube  30  has a length  56  that is five centimeters (5 cm) and an inner diameter  58  that is three millimeters (3 mm). The thread  24  in the pump tube  30  is spun from silica fibers that are approximately five microns in diameter (5 μm). For experimental (demonstration) purposes, the electrodes  16  and  18  can be platinum wires that are placed in the aqueous solution  34  in the reservoirs  50 ,  52 . As discussed above, this arrangement will establish a voltage potential between the voltage source  20  and ground that will create an electric field, E, in the pump tube  30 . Electrodes  60   a  and  60   b  can then be inserted into the reservoirs  50 ,  52  and connected with a voltmeter  62  to measure the electric field, E. 
     To test the EO effect of the set-up shown in FIG. 7, the pump tube  30  and the reservoirs  50 ,  52  are filled with de-ionized water (aqueous solution  34 ). After the water levels of the reservoirs  50 ,  52  settle down to equal level, the voltage source  20  is turned on. The water level difference between two reservoirs  50 ,  52  is then measured as a function of time. 
     According to the theoretical analysis, the water level difference y should behave 
     
       
           y=y   0 {1−exp[− t/τ]}   [1] 
       
     
     where 
     y 0 =4λΣV/[a 2 ρg] 
     τ −1   32  b 2 a 2 ρg/[16 R 2 ηL] 
     the experimental data are used to obtain the values of y 0  and τ from eq. [1] above. An example set of values are: y 0 =4.82 cm and τ=3.48=10 4  sec. By using the experimental parameters: V=65 volt, b=1.5 mm, R×7.5 mm, L=5 cm, η=10 −3  kg/m s and ρg=10 4  hg/m 2 s 2 , we obtain 
     λΣ=1.1×10 −10  Coulomb/m 
     ζ=λΣ/∈=155 mV 
     a=7.5×10 −6  m 
     Σg y 0 /V=7.5 pascal/volt. 
     The values of λ, Σ and ζ are reasonable for silica. The effective channel radius “a” is also reasonable considering the fact that the viscous flow is weighted by a 4  while the area is weighted by a 2 . There is, however, some statistical distribution of the channel radius in the thread  24  and the value of the effective radius of pump tube  30  should be larger than the value estimated from its area. 
     Experiments have shown that the pressure head equivalent of an ordinary tube with 5 micron radius is obtained with the pump tube  30  with 7.5 mm radius. Also, the volume flow of the pump tube  30  is b 2 /2a 2 =2×10 4  times greater compared to a single ordinary tube of radius “a”. Thus, the experimental results confirm that a pump tube  30  can generate a high pressure head and a large volume flow simultaneously. 
     While the particular Fiber Filled Electro-Osmotic Pump as herein shown and disclosed in detail is fully capable of obtaining the objects and providing the advantages herein before stated, it is to be understood that it is merely illustrative of the presently preferred embodiments of the invention and that no limitations are intended to the details of construction or design herein shown other than as described in the appended claims.