Abstract:
A switching device for controlling fluid motion. The device includes a capillary filled with a first fluid into which a wall-confined bubble of a second fluid is introduced to achieve a first switching event. Capillary geometry and wetting properties provide a pressure-related asymmetric energy potential distribution for controlling the flow of the bubble, and the device is called an asymmetric bubble chamber, or ABC. The bubble is initially trapped in an energy potential well, and upon increase of its volume moves from the well into a region of low energy potential to achieve a second switching event. The first switching event may be blocking of a fluid channel or reflection of an optical beam in an optical crosspoint switch, while the second switching event may be unblocking of a fluid channel or restoration of transmission of an optical beam. The increase in bubble volume between the first and second switching events can act as the stroke of a fluidic piston to pump a volume the first fluid within the capillary. The device can be employed to thermally degas a liquid. The use of large-magnitude geometry-related energy potentials permits rapid cyclical operation of the device in a manner resistant to mechanical shock.

Description:
FIELD OF THE INVENTION 
     The invention relates generally to movement of a bubble of one fluid in another fluid within a capillary, and more particularly to switches for optical signals, to fluid valves, to fluid pumps, and to liquid degassers. 
     BACKGROUND 
     Bubbles in capillaries are useful in several respects. In optical devices they possess a different index of refraction than a surrounding liquid and so can reflect or refract optical signals. In addition they can be moved about within capillaries by exploiting temperature-dependent surface tension effects which tend to force bubbles from colder regions to warmer regions, by exploiting geometric effects which tend to squeeze bubbles out of small capillaries into larger capillaries, and by exploiting wetting effects which tend to favor the presence of a first fluid which easily wets a capillary wall over a bubble of a second fluid which does not wet that same wall as well. 
     Capillary devices that exploit the change in surface tension of a bubble with temperature are said to work by thermocapillarity, also known as the Marangoni effect (see, for example, L. E. Scriven and C. V. Sterling, “The Marangoni Effects,” Nature, V 187, p 186 (1960)). An example of recent work published on an optical switching device that exploits thermocapillarity is Makoto Sato, et al, “Waveguide Optical Switch for 8:1 Standby System of Optical Line Terminals,” paper WM16, Technical Digest, OFC &#39;98 Optical Fiber Communication Conference and Exhibit, Feb. 22-27, 1998, San Jose Convention Center, San Jose, Calif., pp 194,195. The Marangoni effect is also exploited to control bubble movement for optical switching in the invention “TOTAL INTERNAL REFLECTION OPTICAL SWITCHES EMPLOYING THERMAL ACTIVATION,” U.S. Pat. No. 5,699,462. In that patent, for example, the embodiment showed in FIG. 29 therein, in a capillary  304  with a tapered width, a bubble is generated at the resistor  308 , and is held in place at that resistor by the Marangoni effect which counteracts the geometry-induced force on the bubble due to the tapered width of the capillary. When heating of the resistor is terminated, the bubble moves from resistor  308  toward the top left of the figure along tapered capillary  304 , where movement is generated by geometric forces. Thus the operation of the device in FIG. 29 of that patent depends on an opposing balance between Marangoni forces and geometry-induced forces. 
     It will be understood from the description of the present invention that forces due to geometric effects can be much larger than forces due to the Marangoni effect. Because of the relative feebleness of the Marangoni effect, the geometric effect designed into the device of FIG. 29 of U.S. Pat. No. 5,699,462 to balance the Marangoni effect must also be feeble and the operation of that device is relatively slow and susceptible to interference from mechanical shock. There still exists a need for a microfluidic device which uses large-magnitude forces to provide rapid and stable optical switching, and the present invention meets that need. 
     Bubbles are also usefull as valve elements to control fluid flow in capillaries. A bubble can be made to reside at a given position in a capillary by some combination of temperature effects and geometric effects which creates a local energy potential minimum for the bubble, and by blocking or nearly blocking the capillary can then impede the flow of a surrounding fluid. See, for example, John Evans, et al, “Planar Laminar Mixer,” Proceedings of the Tenth annual International Workshop on Micro Electro Mechanical Systems, Nagoya, Japan, Jan. 26-30, 1997, IEEE Catalog Number 97CH36021, pp 96-101. However, the Evans et al. paper teaches no technique for removing the bubble from its local energy potential minimum. Devices that do not provide adequate bubble removal can suffer from “vapor lock” if the bubble is composed of gas liberated from dissolved gas in the liquid, because such a bubble will fail to disappear when the heating resistor which creates it is turned off. There still exists a need for a reliable technique for confining a bubble in a channel securely, and when desired, for releasing and removing the bubble from the channel, in a repeatable and efficient manner. As will be seen in detail below, the present invention teaches such a technique. 
     Bubbles are also useful as pumping elements in capillaries. An expanding bubble in a capillary or chamber can act as a piston, displacing the surrounding fluid and causing it to move in a direction dictated by the capillary geometry. The same work by John Evans, et al, “Planar Laminar Mixer,” referenced above, employs an alternately expanding and contracting bubble in a chamber as a piston element. Like the valve described in the same work, the piston bubble can suffer from “vapor lock.” There still exists a need for a pump employing a bubble piston which removes that bubble from the pumping chamber when desired, and the present invention teaches such a pump. 
     SUMMARY 
     The present invention uses the difference in energy potential associated with a bubble in different regions of a capillary to trap the bubble within a region of the capillary when such trapping is desired, and does so while providing resistance to perturbations, which could lead to undesired changes in state. The difference in energy potential can be geometry-dependent and/or materials-dependent. The present invention also uses difference in energy potential to remove the bubble from the trap when desired, and does so more rapidly than prior art devices. The invention is useful for optical switching, for fluid valving, for fluid pumping, and for liquid degassing. 
     Operation of the device is as follows. In a capillary containing a first fluid, a wall-confined bubble of a second fluid is introduced into a designed-in trap in the capillary by some means, for example by boiling a liquid constituting the first fluid using a heating resistor to create a bubble of a vapor which constitutes the second fluid. Bubbles can also be introduced using electrical, chemical, electrolytic, pneumatic, hydraulic, optical, inertial, ultrasonic, and microfluidic techniques, including injecting bubbles from a source (e.g., a gas bubble from a gas source). Introduction of the bubble accomplishes a first desired event, such as switching of an optical beam or blocking of a fluid channel. The bubble is trapped because it sits at a local energy potential minimum within the capillary, and moving it would require an input of energy. 
     Next, the energy of the bubble is increased by, for example, increasing the power input to a heating resistor to introduce more gas, thereby increasing the size of the bubble. As the bubble grows its energy increases, and as it grows it encounters a designed-in spatial asymmetry (geometrical and/or material) in the energy potential of the capillary adjacent to the trap. It tends to grow in the direction of least energy potential. Growth of the bubble can accomplish a second desired event, such as pumping of the volume of the first fluid displaced by the bubble during its growth. 
     Then, the growing bubble reaches a metastable energy maximum and it encounters a designed-in region of low spatial energy potential within the capillary. Further growth of the bubble causes it to intrude into the region of low spatial energy potential, and the bubble becomes positionally unstable. In a manner analogous to the siphoning of water through a hose from a hillside pond to a lower pond due to gravitational energy potentials, the bubble moves from the trap and flows rapidly into the region of low spatial energy potential. As it moves, it accomplishes a third desired event, such as switching of an optical beam or unblocking of a fluid channel. 
     In some embodiments, as the bubble leaves the trap in a direction defined as downstream, it pushes downstream some of the first fluid ahead of it and sucks a volume of the first fluid from a direction defined as upstream to refill the volume of the trap. 
     Because the invention employs designed-in asymmetries in energy potential to accomplish bubble trapping and bubble movement, it is referred to as an asymmetric bubble chamber, or “ABC.” 
     The following terminology is used below to refer to the various spatial regions of the ABC. 
     The trap volume in which the bubble is initially trapped is called the “gate.” The region of low spatial energy potential into which the bubble exits from the gate is called the “drain.” The region of relatively higher energy potential between the gate and the drain constitutes a potential barrier and is called the “barrier.” The region from which the first fluid enters to refill the gate after the bubble has exited from the gate to the drain is called the “source.” In the usual mode of operation of the device in which the first fluid enters from the source, the source is upstream of the gate, the gate is upstream of the barrier, and the barrier is upstream of the drain, where “upstream” and “downstream” refer to the usual direction of flow of the first fluid. 
     The source has an energy potential for a wall-confined bubble of a second fluid in the first fluid called the “source potential.” However, in some embodiments, provided that fluid can refill the gate region, the source may be absent or plugged. For example, a device can have two barriers and one of them can act as the source. 
     The gate has an energy potential for a wall-confined bubble of a second fluid in the first fluid called the “gate potential” which is less than the source potential. 
     The barrier has an energy potential for a wall-confined bubble of a second fluid in the first fluid called the “barrier potential” which is higher than the gate potential but lower than the source potential. 
     The drain has an energy potential for a wall-confined bubble of a second fluid in the first fluid called the “drain potential” which is less than the gate potential. 
     From the above description of relationships among the four energy potential regions it will be appreciated that the gate has a region of local energy potential minimum called a “potential well.” 
     Prior-art microfluidic switches employing a bubble in a capillary tended to be unstable and the speed of operation tended to be slow. In the present invention a bubble is initially trapped in a potential well, but then can overcome a substantial energy barrier and rapidly move outside the well. Thus, a system with a switch, valve, or pump of the present invention is stable and is resistant to unintended perturbation by vibration or temperature, but can also operate rapidly. 
     It will be appreciated that the invention can be operated in cycles, where the speed of operation is limited first by the speed at which a bubble can be introduced into the gate, and second by the speed at which a bubble can be moved from the gate to the drain. 
     Moreover, this operation need not be accomplished by the mechanical motion of solid parts. Rather, the energy potentials of the source, gate, barrier, and drain are defined by the geometry of the channel, or by the materials composition of the channel plus the first fluid plus the second fluid, or by a combination of geometry and materials composition. The invention allows bubbles to be introduced and moved entirely by fluidic means which, for example, can be controlled thermally by electrical heating. 
     In one embodiment of the present invention a capillary is filled with a liquid such as water and the walls of the capillary are a hydrophilic material such as glass. A steam bubble is introduced into the gate by using a small electrical resistor to boil the water. The bubble is large enough to substantially fill the gate, and its introduction causes a first switching event. If the capillary is part of an optical crosspoint switch such as that described in U.S. Pat. No. 5,699,462, the presence of the bubble causes a first optical switching event. If the capillary is part of a fluid flow system, the presence of the bubble acts to block fluid flow within the capillary and so causes a first fluidic switching event. In either case the local energy potential minimum within the gate acts to trap the bubble, even in the presence of disturbances such as mechanical acceleration or liquid pressure fluctuations. In such a hydrophilic setting the gate is a chamber of larger width than the adjacent source and barrier portions of the capillary. 
     In a second switching event for the same embodiment of the invention, which returns the system to its initial state, the volume of the bubble is increased, by increasing the heating power to the resistor, so that it fills the volume of the gate plus the volume of the barrier and begins to intrude into the volume of the drain. The enlarged bubble is then siphoned by surface tension forces from the gate, through an adjacent narrowing of the capillary (which is the barrier in a hydrophilic setting), and into an even wider portion of the capillary (which comprises the drain in a hydrophilic setting). At the same time, liquid refills the gate from upstream through a narrow portion of the capillary (which is the source in a hydrophilic setting). 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The following figures are included to better illustrate the embodiments of the apparatus and technique of the present invention. 
     FIG. 1 is a schematic view showing a bubble in a capillary with two different radii of curvature at different free surfaces of the bubble. 
     FIG. 2 is a sectional view showing liquid drops on a surface illustrating good surface wetting and poor surface wetting. 
     FIG. 3A shows a plan sectional view of an embodiment of the present invention for use in optical switching. 
     FIG. 3B shows a sectional view of the embodiment of FIG.  3 A. 
     FIGS. 4A and 4B show the embodiment of FIG.  3 A and FIG. 3B when a bubble is present. 
     FIG. 5 is a schematic depiction of the energy potentials in the various regions of the embodiment of FIGS. 3 and 4. 
     FIGS. 6A to  6 F are schematic plan views showing the time evolution of switching action of the embodiment of FIGS. 3 and 4. 
     FIG. 7 shows a sectional view of an embodiment of the invention involving capillary walls which are fluiphobic to fluid  1 . 
     FIG. 8A shows a schematic plan view of an embodiment of the present invention in which the properties of the capillary materials rather than geometry are employed to create the desired asymmetries in energy potential. 
     FIG. 8B shows a schematic plan view of an embodiment of the present invention in which the properties of the capillary materials are employed to create the desired asymmetries in energy potential and having a heater. 
     FIGS. 9A and 9B show an embodiment of the invention with multiple source channels for use as a thermal degasser for liquids. 
     FIG. 10 shows a plan view of an embodiment of the present invention which exploits the Marangoni effect to control which of two barriers acts as the exit path for a bubble. 
     FIG. 11 shows a sectional view of an embodiment of the present invention in which two ABC devices are placed in tandem to maximize the switching transition speeds of the downstream ABC. 
     FIG. 12 shows a plan view of an embodiment of the present invention which has no source region. 
     FIG. 13A shows a sectional plan view of an embodiment of the present invention having regions laid out on different planes. 
     FIG. 13B shows a sectional view of the embodiment of FIG. 13A taken at a plane right angle to the plane of FIG.  13 A. 
     FIG. 14A shows a sectional plan view of an embodiment of the invention in which there is no separate source region. 
     FIG. 14B shows a sectional view along line  14 B— 14 B of FIG. 14A of an embodiment of the invention in which there is no separate source region. 
    
    
     DETAILED DESCRIPTION 
     The physics of bubble movement in capillaries must be understood in some detail in order to understand the mode of operation of the present invention. This physics is presented below. 
     A capillary is defined as a channel of small dimensions in which forces due to fluid surface tension and wetting, called “capillary forces,” are comparable to or predominate over forces due to the density of the fluid in a gravitational field or other acceleration field. A “microfluidic” device is a device of small linear dimensions in which capillary forces typically play an important role. 
     The walls of a capillary can act to confine a bubble of a second fluid within a first fluid and to control the directions in which the bubble can move. The first fluid and second fluid may be either gas or liquid, although both the first and second fluids cannot be gas simultaneously because a mixture of two gases cannot sustain a bubble surface between the two gases. The first fluid and second fluid may be the same substance in different physical form; for example, the first fluid can be liquid water while the second liquid is water vapor. 
     A bubble within a capillary is said to be “wall-confined” if it is large enough to touch the walls of the capillary on two substantially opposite sides. For example, in one extreme case the capillary can be a long tube of circular cross section. An air bubble in water which touches the tube walls around its entire periphery while being free to move along the length of the tube is wall-confined. If the bubble becomes so small that it touches the capillary walls along less than 180 angular degrees of its periphery, then it is no longer wall-confined. 
     In another extreme case, the capillary can include two nearly-parallel plates of glass. The first fluid can be water, and the wall-confined bubble can be a flattened disk of air within the water between the two plates. The bubble is free to move in two dimensions between the plates. If the bubble becomes so small that it only touches one of the plates, then it is no longer wall-confined. 
     Between the above two extreme cases are capillaries of many cross-sectional shapes, such as those of square or rectangular cross section. A bubble in such a capillary is wall-confined if less than 180 contiguous angular degrees of its cross-sectional periphery is free of contact with the capillary walls. 
     The term “wall-confined” has previously been used in high-energy plasma physics, but in that field describes a different concept. The concept of wall confinement of a bubble in a capillary presented herein was developed in the course of describing the present invention. Those portions of a bubble in a capillary not in contact which the capillary walls are called the “free surfaces” of the bubble. Those portions of the bubble in contact with solid walls are called “bounded surfaces” of the bubble. 
     If a wall-confined bubble encounters a condition where it is no longer free to move in any direction in the capillary, it is said to be “trapped” and the volume of the capillary in which the bubble is trapped is called a “trap.” A trapped bubble may nevertheless have free surfaces. 
     Between a fluid bubble such as a gas bubble and its fluid surroundings such as a liquid, there exists an interfacial surface which can be characterized by a radius of curvature r and a surface tension σ(T), where T is temperature and so σ is a function of temperature T. Across this surface there exists a pressure difference given by P=2σ(T)/r (see, for example, Physical Chemistry, Walter J. Moore, fourth edition, Prentice-Hall, Englewood Cliffs, N.J., page 478). 
     The bubble surface can be manipulated by varying one or more of the pressure difference, the surface tension, the surface radius of curvature, and the wetting properties of the capillary walls. 
     Good wetting and poor wetting can be quantified in terms of equilibrium contact angles of fluid against surface. For example, a drop of water in air contacting a clean plate of silicon dioxide glass has a very low equilibrium contact angle taken within the water, and the glass surface is said to be well wetted. However, the contact angle taken within the air is large, and so the air is considered to “wet” poorly in comparison to water. On the other hand, a drop of mercury in air resting on a clean glass plate has a very high equilibrium contact angle taken within the mercury droplet. The glass surface is said to be poorly wetted by the mercury, and the air is considered to wet well in comparison to the mercury. 
     For aqueous liquids good wetting is called hydrophilicity and is characterized by an equilibrium contact angle less than ninety degrees; the wetted material is described as hydrophilic. Similarly, poor wetting is called hydrophobicity and is characterized by an equilibrium contact angle greater than ninety degrees; the wetted material is described as hydrophobic. The terms hydrophilic and hydrophobic can be generalized to “fluiphilic” and “fluiphobic” to describe the equilibrium contact angle taken within any fluid where it meets a second immiscible fluid at a solid wall. 
     If a bubble surface intersects a wall of solid material, the equilibrium contact angles depend on the wetting properties of that wall for both the fluid surrounding the bubble, which for convenience can be called “fluid  1 ,” and the fluid within the bubble, which can be called “fluid  2 .” If the angle, taken for example within fluid  1 , becomes greater or less than the equilibrium contact angle, the bubble will tend to move and exhibit an “advancing contact angle” or a “receding contact angle.” 
     The pressure difference across a bubble&#39;s surface is inversely proportional to the radius of curvature of that surface. As an example of the magnitude of the pressure difference, boiling water produces bubbles at temperatures of roughly 100 degrees C and above. For water at 100 degrees C the surface tension of an air bubble is equal to 59 milliNewtons per meter (mN/m). If an air bubble in that water has a radius of 25 micrometers (25 μm), then its internal pressure relative to the external water is equal to P=2 (59 mN/m)/25 μm)=4.72 kiloPascals (kPa), equal to the pressure exerted by a column of water approximately 18 inches (46 cm) tall. If the radius of the bubble is halved to 12.5 μm, then the internal pressure doubles to 9.44 kPa. 
     The pressure difference also depends directly on the bubble&#39;s surface tension, and that surface tension varies with temperature. For example, the surface tension of liquid water in air decreases by approximately 22% as temperature varies from 0 C to 100 C, or 0.22% per degree C. 
     From the above example of air bubbles in water it can be appreciated that even for a relatively large temperature change, the change in the pressure due to the temperature dependence of surface tension can be small relative to changes in pressure due to changing the radius of curvature. Controlling the radius of curvature is thus a relatively powerful mechanism for controlling a bubble, and is exploited in the present invention. 
     Like any fluid, bubbles tend to flow from a region of higher energy potential to a region of lower energy potential. To understand this concept it is necessary to understand a little about both energy and energy potential. 
     The introduction of a bubble into a capillary includes displacing a portion of a first fluid and replacing it with a volume of a second fluid, where for example the first fluid may be water and the second fluid may be steam introduced through generation by boiling the water. Introducing a wall-confined bubble into a capillary requires more energy than introducing the same volume of bubble where it is not wall-confined. 
     The minimum energy required to introduce a wall-confined bubble of a given volume into a given portion of a device is determined by the spatially-dependent energy potential, called herein the “energy potential,” or more simply the “potential” of that portion of the device. For example, in a given portion of a capillary it may be necessary to provide x Joules of energy per cubic centimeter of bubble volume to introduce a bubble. The quantity x is the energy potential. If a bubble within that region has a volume of y cubic centimeters, then the energy require to introduce that bubble is just x multiplied by y and is given in Joules. 
     Assume that at an adjacent but different location within the same capillary the energy potential has a value of z Joules of energy per cubic centimeter of bubble volume. Then for the same bubble volume y, the bubble energy in this second region is z multiplied by y and is again given in Joules. If z is less than x, then the bubble will prefer to be in the second location rather than the first because its overall energy is less in the second location than in the first. Thus it can be seen that the bubble seeks the region of lowest energy potential. 
     The energy contained within a bubble due to pressure is just the internal pressure of the bubble with respect to its surroundings multiplied by the volume of the bubble. Thus, the pressure is one measure of the energy potential, and this type of energy potential can be called a “pressure energy potential.” Other factors such as gravity and temperature can contribute their own energy potentials. 
     The energy potential of a region for a wall-confined bubble in a fluid can be influenced both by geometry and by temperature. For example, for a bubble of gas within a liquid which is fluiphilic to the capillary walls, narrow capillaries have a higher energy potential than wider capillaries, and cooler regions have a higher energy potential than warmer regions. 
     The pressure difference between two fluids across the interfacial surface of a fluid bubble is inversely proportional to the radius of curvature of the free surface of the bubble. The present invention exploits this relationship in a capillary system. For a wall-confined bubble of a second fluid within a first fluid, where the bubble has two free-surface ends in a capillary of non-constant cross section, the radii of curvature at the two free ends of the bubble can be different. That difference in radii corresponds to a pressure difference between the two regions of the first fluid separated by the bubble, and that pressure difference can either move the bubble or hold it in place against an applied pressure as one desires. 
     FIG. 1 illustrates these principles but is not an embodiment of the present invention. The figure is a sectional view through a capillary of variable width which contains a wall-confined bubble of a second fluid in a first fluid which easily wets the walls of the capillary. The bubble tends to flow from the narrow portion of the capillary to the wider portion of the capillary unless an external pressure is applied to the wide portion of the capillary to force the bubble into the narrow portion. 
     The physics which describe the forces on such wall-confined bubbles in capillaries are as follows. 
     For any point on a free surface of a bubble it is possible to define a local radius of curvature in terms of two principal radii of curvature: a maximum local radius of curvature r max  taken along one direction at that point, and a minimum local radius of curvature r min  taken along a direction perpendicular to the direction of r max . The magnitude of the local radius of curvature r local  is then found from the equation 
     
       
         1/r local =(1/r max +1/r min )/2  Eq. 1 
       
     
     For a wall-confined bubble of a second fluid at rest within a first fluid, each free surface of the bubble has a characteristic radius of curvature which is defined by the surface tension, σ, of the interface between the two fluids, by the dimensions of the capillary, and by the wall-wetting characteristics of the dual-fluid system. This characteristic radius is called the “equilibrium free-surface radius,” r f,e . 
     The equilibrium free-surface radius, r f,e , is conceptually different from the well-known “effective hydraulic radius,” r h,eff , of a capillary. The effective hydraulic radius is the radius of a hypothetical capillary with a circular cross section that has the same resistance to fluid flow as an actual capillary being considered. Thus the effective hydraulic radius pertains to the capillary&#39;s resistance to fluid flow and is a property of the capillary geometry only. The equilibrium free-surface radius, in contrast, is a property of the capillary geometry, plus the properties of both the first and second fluids, plus the materials properties of the capillary walls. The equilibrium free surface radius does not concern resistance to fluid flow, but rather concerns the shape a bubble surface at rest would take at a particular location. 
     For clarity, it simplifies discussion to relate a local r f,e  only to local capillary geometry, and that simplified route is taken in much of the discussion below with the understanding that the underlying relationship can be more complex. If the equilibrium wetting angle of the first fluid against the capillary walls is zero at the interface between the first fluid and the bubble, then r f,e  is determined only by the geometry of the capillary. In this case, for a capillary with a rectangular cross section of width w and height h, 
     
       
         1/r f,e ={1/(w/2)+1/(h/2)}/2=(1/w+1/h)  Eq. 2 
       
     
     The pressure difference, ΔP, across the bubble wall is then equal to 
     
       
         ΔP f,e =2σ/r f,e =2σ(1/w+1/h)  Eq. 3 
       
     
     The above ΔP f,e  is called the “equilibrium free surface differential pressure,” a term newly developed to describe the mode of operation of the present invention. The pressure difference, ΔP f,e , is also the pressure difference between the bubble pressure, P bubble , and the adjacent pressure of the first fluid, P f1 : 
     
       
         ΔP f,e =P bubble −P f1 =2σ/r f,e   Eq. 4 
       
     
     In FIG. 1 a first fluid (fluid  1 ) resides in a capillary  100  defined by walls  102  and  104  which are perpendicular to the plane of the sectional drawing and by two other walls parallel to the plane of the sectional drawing. Fluid  1  is divided into two regions  106  and  108 . A second fluid (fluid  2 ) is immiscible in fluid  1  and forms a bubble  110  with free surfaces  112  and  114  and with bounded surfaces  116  and  118 . Surfaces  112  and  114  have different equilibrium free-surface radii, r f,e . Fluid  1  can be a liquid whereas fluid  2  can be a gas (e.g., an air bubble in water), but other arrangements are possible (e.g., fluid  2  can be liquid mercury, which can contain a bubble, whereas fluid  1  can be air). For the purposes of illustration, FIG. 1 shows an equilibrium wetting angle of zero for fluid  1  where it touches the capillary walls at locations  120 ,  122 ,  124 , and  126 . 
     In FIG. 1, region  106  has a rectangular cross section with a width, w 1 , designated by dimension line  128 , and a height, h, perpendicular to the plane of the page. Fluid  1  in region  106  has a pressure of P f1  and the pressure across the free surface  112  between fluid  1  and fluid  2  is 
     
       
         ΔP 1 =P bubble −P f1 =2σ/r 1   Eq. 5 
       
     
     where r 1  is the equilibrium free surface radius (r f,e ) of the free surface  112  and is defined by the relation 
     
       
         1/r 1 =1/w 1 +1/h  Eq. 6 
       
     
     so that ΔP 1  becomes: 
     
       
         ΔP 1 =P bubble −P f1 =2σ/r 1 =2σ(1/w 1 +1/h)  Eq. 7 
       
     
     Also in FIG. 1, region  108  has a rectangular cross section with a width, w 2 , designated by dimension line  130 , and a height, h, perpendicular to the plane of the page which is equal to the height of region  106 . Fluid  1  in region  108  has a pressure P f2 . The pressure difference across free surface  114  is 
     
       
         ΔP 2 =P bubble −P f2 ×2σ(1/w 2 +1/h) Eq. 8 
       
     
     For a uniform temperature and when the bubble is not moving, the pressure difference between regions  106  and  108  is then equal to: 
     
       
         ΔP f1 −ΔP f2 =2σ(1/w 1 −1/w 2 )  Eq. 9 
       
     
     Thus for a rectangular capillary of uniform height but variable width, the capillary height does not influence the pressure difference between the two regions  106  and  108 . 
     The foregoing illustrates that, assuming there is no difference in temperature and no movement, a pressure exists to urge the bubble from a smaller channel to a larger channel to which the smaller channel is connected. Such a pressure will also tend to prevent the bubble from going into a narrower capillary from a wider capillary. 
     Not all fluids wet the walls of a capillary well. FIG. 2 illustrates cases of good wetting and poor wetting for two fluids on a surface. On the surface of a material  200  are placed fluid volumes  202  and  204 . Typically such fluid volumes may be liquid in an ambient surrounding of air, but they can also be liquid in an ambient surrounding of liquid or gas in an ambient surrounding of liquid. For the purposes of discussion it will be assumed that volumes  202  and  204  are droplets of liquid in air. Droplet  202  is characterized by an equilibrium contact angle, θ e , designated as feature  206  and taken within the droplet at the location where it meets the surface of material  200 ; because this angle is less than ninety degrees the surface of material  200  is said to be well-wetted by droplet  202 . Droplet  204 , on the other hand, is characterized by an equilibrium contact angle, θ e , designated as feature  208  and taken within the droplet; because this angle is greater than ninety degrees the surface of material  200  is said to be poorly wetted by droplet  204 . 
     For the descriptions below the generalized terms “fluiphilic” and “fluiphobic” refer to the equilibrium wetting angle taken within fluid  1  where it meets the capillary wall at a bubble surface with fluid  2 . The capillary wall is called fluiphilic if the equilibrium contact angle taken within fluid  1  is less than ninety degrees and is called fluiphobic if the equilibrium contact angle taken within fluid  1  is greater than ninety degrees. 
     The present invention employs large-magnitude geometry-related energy potentials rather than the small-magnitude temperature-related energy potentials employed in prior-art devices. As an example of the magnitude of energy potentials in a fluiphilic (and hydrophilic) system, consider water at 100 degrees C in a glass capillary of circular cross section with a radius of 25 μm and with perfectly hydrophilic walls. A wall-confined air bubble in this capillary has a radius of curvature of 25 μm, and as calculated above has in internal pressure 4.72 kiloPascals (kPa) higher than the surrounding water. 
     If an attempt is made to squeeze this 25 μm radius bubble into a capillary of circular cross section 5 μm in radius with perfectly hydrophilic walls, then the bubble&#39;s equilibrium free surface radius (r f,e ) must decrease to 5 μm and its internal pressure must be increased by a factor of 5 to 23.6 kPa, equal to the pressure exerted by a column of water 90 inches (230 cm) tall, roughly 1/4 of atmospheric pressure. The difference in the radii of curvature at the two ends of the bubble as it is being squeezed into the 5 μm radius capillary creates a resisting pressure difference of ΔP=(23.6 kPa−4.72 kPa)=18.9 kPa, 400% as large as the original pressure within the bubble of 25 μm radius. 
     In contrast, the magnitude of pressure differences due to the change in surface tension of water at atmospheric pressure can never be more than 22%, because the surface tension of water decreases only 22% from freezing to boiling. This change in surface tension is responsible for the Marangoni effect as can be appreciated from Eq. 4 above. In practice, it is difficult to sustain a temperature difference of more than 10 degrees C across a small bubble because thermal conduction tends to equalize temperature across the bubble, and so it is difficult to create a pressure difference of more than 2.2% using the Marangoni effect. 
     Thus, employing geometry-related energy potentials provides advantages on the order of (400%/2.2%)≈18,000% in pressure, force, and speed over prior techniques of bubble control based on the Marangoni effect alone, or based on opposing the Marangoni effect against a geometric effect. The present invention exploits these geometric effects plus wetting effects to achieve bubble trapping and rapid bubble movement as illustrated in FIGS. 3-6. 
     The present invention may be used for controlling bubble movement in conjunction with optical switching of the prior invention “TOTAL INTERNAL REFLECTION OPTICAL SWITCHES EMPLOYING THERMAL ACTIVATION,” U.S. Pat. No. 5,699,462, which is incorporated by reference in its entirety herein. U.S. Pat. No. 5,699,462 describes the use of electrical resistors to control bubble movement in either capillaries of uniform width or capillaries of varying dimensions for optical switching purposes. Briefly stated, in such an optical switch device, the switching element has a transmitting state and a reflecting state. In the transmitting state, an index-matching liquid fills a gap placed at the intersection of two optical waveguides and light can pass from a first waveguide segment to a second waveguide segment across the gap. In the reflecting state, a bubble introduced into the gap displaces the index-matching fluid and creates an index mismatch in the gap so that light is reflected from the first waveguide segment into a third waveguide segment, and is prevented from passing from the first waveguide segment to the second waveguide segment. In U.S. Pat. No. 5,699,462 bubble movement is controlled either by the Marangoni effect alone or by balancing the Marangoni effect against geometric effects which are necessarily of low magnitude in order to achieve such balance. 
     FIG.  3 A and FIG. 3B show an embodiment  300  of the present invention used for optical switching purposes similar to that of U.S. Pat. No. 5,699,462, but with the advantages in pressure, force, speed, and acceleration resistance of the present invention due to exploiting high-magnitude geometry-related forces. Embodiment  300  is intended primarily for optical switching purposes but also exhibits fluid valving and fluid pumping characteristics which are advantageous capabilities of the present invention. 
     FIG. 3A is a sectional view as indicated in FIG. 3B looking perpendicular to a major surface of an embodiment  300  of the present invention used for optical switching as per U.S. Pat. No. 5,699,462 and incorporating the features of the present invention, and FIG. 3B is a sectional view as indicated in FIG. 3A looking parallel to a major surface of the same embodiment. In FIG.  3 A and FIG. 3B, only a volume  302  of fluid  1  is present and no bubble of fluid  2  is present. 
     Material  304  is the cladding portion of a planar optical waveguide array, and it includes the side walls  306  and  308  and roof  310  of a capillary  312  of substantially rectangular cross section, while layer  314  is an electrical insulating layer such as silicon carbide which defines the floor of the capillary. Layer  314  provides electrical insulation over electrical heating resistor  316  which sits beneath layer  314  adjacent to the gate region. 
     Material  315  is a deformable and adhesive polymer which bonds the waveguide array material  304  to the underlying layer  314 . Layer  318  beneath resistor  316  is an electrically insulating and thermally insulating layer such as silicon dioxide. Substrate  320  provides mechanical support and may be a thermally conducting material such as silicon to maximize speed of operation of the device. 
     In this embodiment, capillary  312  includes four regions  321 ,  323 ,  325 , and  327  designated by dimension lines  322 ,  324 ,  326 , and  328  above the drawing of FIG.  3 A. 
     Dimension  322  designates the length L source  of the source region  321 . Source region  321  extends out of the field of view of the drawing and connects to an inlet reservoir, not shown, of fluid  1 , where preferably the inlet reservoir has a low hydraulic resistance. 
     Dimension  324  designates the length L gate  of the gate region  323 . 
     Dimension  326  designates the length L barrier  of the barrier region  325 . 
     Dimension  328  designates the length L drain  of the drain region  327 . Drain region  327  extends out of the field of view of the drawing and connects to an outlet reservoir, not shown, of fluid  1 , where preferably the outlet reservoir has a low hydraulic resistance. 
     The source  321  has a width, w source , designated by dimension line  330 . The gate  323  has a width, w gate , designated by dimension line  332 . The barrier  325  has a width, w barrier , designated by dimension line  334 . The drain  327  has a width, w drain , designated by dimension line  336 , and which in this embodiment increases with distance from the barrier. The relationship between the various widths is given by 
     
       
         w source &lt;w barrier &lt;w gate &lt;w ,drain   Eq. 10 
       
     
     In this embodiment, for the sake of simplicity of construction, the height h of the capillary is uniform and is designated by dimension line  338  in FIG.  3 B. It is to be understood that the height of the capillary in the various regions of the capillary need not be uniform as long as the cross-sectional areas of the regions differ to result in the desired differences in energy potentials. In the case where the capillary having the source, gate, barrier, and drain regions is used for switching optical signals that propagate in a generally planar waveguide array, it is preferred that the walls of the capillary which the light impinges upon and exits from are flat and perpendicular to the plane in which the optical signals propagate. 
     Present in FIG. 3 are optical waveguide core regions  340 ,  342 ,  344 , and  346 , and optical signal  348 . In FIG. 3B the intersecting portions of waveguide core regions  340  and  342  are labeled as one object. 
     Optical signal  348  enters the gate region  324  from core region  340 , transits across the gate region, and exits through core region  346 . When fluid  1  occupying volume  302  is well matched in index of refraction to the material of the waveguide core regions, the optical signal suffers little loss. 
     FIG. 4A depicts the same view as FIG. 3A of the same embodiment of the invention, but in which a bubble  402  of fluid  2  has been introduced. In this embodiment fluid  2  is vapor produced by boiling fluid  1  which is a liquid. Boiling is accomplished by electrically heating resistor  316 . The electrical connections to the resistor are not shown but are obvious to practitioners of silicon fabrication technology. 
     FIG. 4B depicts the sectional view designated in FIG.  4 A and is the same as FIG. 3B except that bubble  402  has been introduced. The bubble resides at a local minimum in energy determined by the width w gate  of the gate region given in FIG. 3A by dimension line  332 . 
     Because the bubble present in FIG. 4 is poorly matched in index of refraction to the adjacent waveguide core regions  340 ,  342 ,  344 , and  346 , optical signal  448  is reflected off of interface  404  between the bubble  402  and waveguide core regions  340  and  342 . In contrast to optical signal  348  which passes through the gate region and exits through waveguide core region  346 , optical signal  448  is reflected and exits through waveguide core region  342 . This difference between signals  348  and  448 , due to the presence of bubble  402 , is considered as the desired first switching event of this embodiment of the invention. 
     It should be noted that in addition to achieving the primary purpose of optical switching in the present embodiment, the presence of bubble  402  acts to block the flow of fluid  1  between regions  406  and  408  in FIG.  4 A. When bubble  402  is present, fluid  1  can only flow through the narrow gaps  410 ,  412 ,  414 , and  416  in FIG.  4 B. It is well known that the resistance to fluid flow of a channel varies as the fourth power of the effective hydraulic radius of that channel. Gaps  410 ,  412 ,  414 , and  416  constitute “blow-by” paths through which fluid  1  can pass, but these paths have much smaller effective hydraulic radii than the capillary does when no bubble is present, and the fluid resistance of these blow-by paths is very high, so that bubble  402  can be seen to form a very effective plug. The embodiment shown thus can also serve as a fluid valve for flow between regions  406  and  408 . 
     The inequality of Eq. 10 is key to the desired operation of the device in this generally fluiphilic embodiment. Using Eq. 10 in conjunction with Eq. 2 above it can be appreciated that 
     
       
         r f,e,source &lt;r f,e,barrier &lt;r f,e,gate &lt;r f,e,drain   Eq. 11 
       
     
     Eq. 11 can be used in conjunction with Eq. 4 above to calculate a characteristic equilibrium free surface differential pressure which would be required to introduce a wall-confined bubble into each region of the device of FIGS.  3  and  4 . 
     
       
         ΔP f,e , source &gt;ΔP f,e,barrier &gt;ΔP f,e,gate &gt;ΔP f,e,drain   Eq. 12 
       
     
     Each term in Eq. 12 denotes a differential pressure within a wall-confined bubble of fluid  2  relative to fluid  1 . Because the direction of curvature of the bubble is away from fluid  1  and toward fluid  2 , each term in Eq. 12 denotes a pressure within fluid  2  greater than that in fluid  1 . 
     As noted above, pressure is a measure of energy potential. If other sources of energy potential such as gravity are ignored, the pressure ordering given by Eq. 12 can be used to define energy potential differences between the four regions by subtracting one differential pressure from another. Such considerations lead to an ordering of the energy potentials in the four regions as follows: 
     
       
         Π source &gt;Π barrier &gt;Π gate &gt;Π drain   Eq. 13 
       
     
     In Eq. 13 the greek symbol Π(capital “pi”) is chosen to designate energy potential. If the gate is chosen as the reference point at which energy potential is defined to be zero, then for example Π source =ΔP f,e,source −ΔP f,e,gate . 
     Eq. 13 defines the energy potential relationships necessary to the operation of the present invention. While Eq. 13 has been derived with respect to a specific embodiment, it is a general result which applies to all embodiments of the present invention, and is in fact one of the starting points from which the present invention was conceived. 
     FIG. 5 depicts the energy potential distribution  500  for the embodiment of FIG.  3  and FIG. 4 as given by Eq. 13. Axis  502  is distance along the capillary channel, and axis  504  is energy potential for a wall-confined bubble in that channel. Dimension lines  322 ,  324 ,  326 , and  328  correspond to those in FIG.  3 . In each region, the energy required to introduce a wall-confined bubble of fluid  2  in fluid  1  is given by multiplying the pressure difference between the two fluids by the volume of the bubble, and the energy potential is just the differential bubble pressure as given by Eq. 7. Energy potential  522  is Π source , energy potential  524  is Π gate , energy potential  526  is Π barrier , and energy potential  528  is Π drain . The zero point of axis  504  is arbitrarily chosen so than Π gate =0. 
     It will be appreciated that, since gate potential  524 , Π gate , is less than either of the surrounding energy potentials (i.e., source potential  522  and barrier potential  526 ), the gate region constitutes a potential well. It will also be appreciated that, if enough energy is added to raise a bubble to energy potential level  526 , that it will then tend to flow downhill in energy potential, or equivalently downhill in pressure, in the direction of drain potential  528 . 
     In FIG. 5 the energy potential  528 , Π drain , decreases with distance from the barrier region  326 , which as will be seen below is advantageous for rapid switching but is not necessary to the basic operation of the invention. The invention would function, though not as well, if the energy potential were constant with distance in the drain region. 
     The foregoing provides the background necessary to understand the time evolution of the operation of the present invention as illustrated in FIG.  6 . 
     FIGS. 6A-F are sectional views looking perpendicular to a major surface of an embodiment of the present invention used for optical switching. This embodiment  300  is the same as that presented in FIGS. 3 and 4, and features numbered in the range of  300 - 499  are the same as those in FIGS. 3 and 4. 
     FIG. 6A corresponds to FIG.  3 A. 
     FIG. 6B corresponds to FIG.  4 A. Bubble  402  has free surfaces  602  and  604  and has bounded surfaces  606  and  608 . The radii of curvature of surfaces  602  and  604  are equal and are given by 
     
       
         1/r f,e,gate =(1/w gate +1/h) Eq. 14 
       
     
     At the time corresponding to FIG. 6B bubble  402  blocks the flow of fluid  1  in the capillary in both downstream and upstream directions, and so accomplishes a first fluid valving function, which is an advantageous capability of the present invention. 
     In FIG. 6C, the power applied to resistor  316  has been increased in comparison to that applied in FIGS. 4A and 6B, so that the bubble volume has increased. Because the barrier potential Π barrier  is less than the source potential Π source , the bubble grows in the direction of the barrier and free surface  610  moves to the right into the barrier region. Free surfaces  610  and  612  have equal radii of curvature given by 
     
       
         1/r f,e,barrier =(1/w barrier +1/h)  Eq. 15 
       
     
     In the time period between FIG.  6 B and FIG. 6C, the volume of fluid  1  in the barrier region has been pumped from the barrier region into the drain region. This pumping action is an advantageous capability of the present invention. 
     In the condition depicted in FIG. 6C, the bubble is still trapped within an energy potential well and resists movement due to perturbation, such as acceleration, along the capillary. 
     It will be appreciated that the energy of the bubble is minimized when it maintains cohesiveness as a single volume rather than separating into two or more bubble volumes, each requiring the energy associated with supporting two or more free surfaces. Thus the bubble tends to remain a single cohesive unit unless it is disrupted by some high-energy event, and during flow in the capillary it does not tend to split into more than one bubble. 
     In FIG. 6D, the power applied to the resistor  316  has been increased in comparison to that applied in FIG.  6 C. The bubble free surfaces  614  and  616  have increased in radius of curvature from r f,e,barrier  to r f,e,gate , as the bubble begins to move past the potential barrier, and the bubble has reached a point of metastability. Any further increase in volume will cause it to become unstable and flow into the drain. 
     FIG. 6E shows the state of the device after the power applied to resistor  316  has been incrementally increased in comparison to that applied in FIG.  6 D. The bubble has become unstable so that it begins to flow into the drain. Free surface  618  is larger in radius than free surface  620 , creating a pressure difference that siphons the bubble in the downstream direction. At some time between the states shown in FIGS. 6D and 6E, the power applied to the heating resistor can be ended and the bubble will still be siphoned into the drain. Optical signal  448  is shown as still reflecting, but in fact optical core region  340  is no longer completely covered along wall  306  by bubble  402  and so some optical scattering can occur during this switching transient period. 
     As the bubble moves from its position in FIG. 6D towards that in FIG. 6E, it unblocks the downstream flow of fluid  1  and so accomplishes a second aspect of the fluid valving capability of the present invention. Upstream flow of fluid  1  is still blocked, however, until a time subsequent to that of FIG. 6F as discussed below. 
     FIG. 6F shows the state of the device when the moving bubble has exited the optical switching area of the gate. Optical signal  348  once again transits from waveguide core region  340  to waveguide core region  346 , and the second desired optical switching event of this embodiment of the invention has been accomplished. Free surface  622  is larger in radius than free surface  624 , so the bubble continues to be forced into the drain region. 
     In addition, and advantageously, free surface  622  is larger in radius than free surface  620  in FIG. 6E, so that the bubble accelerates from the time corresponding to FIG. 6E to the time corresponding to  6 F. This acceleration shortens the switching time and increases the speed of operation of the device. This advantage is provided by having the drain widen with distance from the barrier. 
     At the time depicted in FIG. 6F, the bubble is still wall-confined. As it continues to move away from the barrier at a time subsequent to the time of FIG. 6F, it must eventually lose contact with one or more walls of the capillary in the drain region in order to completely unblock the upstream flow of fluid  1 , as well as the downstream flow of fluid  1  which became unblocked at a time subsequent to that of FIG.  6 D. 
     Such complete unblocking is a further advantageous feature of the fluid valving capability of the present invention, and may achieved in at least five ways. First, the bubble may lose contact with the drain walls merely because the drain width increases with distance from the barrier. Second, if the bubble is composed substantially of vapor created from boiling of a liquid fluid  1 , it will tend to shrink as it leaves the heat source which created the vapor and so will tend to detach from one or more walls of the drain. Third, if the bubble is composed substantially of gas which was liberated from solution in a liquid fluid I to create the bubble, it may also tend to shrink as it encounters cooler regions in which fluid  1  can dissolve more gas. If the bubble is a mixture of gas and vapor, it tends to shrink rapidly as it cools and vapor is transformed to liquid; it may then tend to shrink more slowly as its gas content dissolves into liquid. Fourth, the bubble may enter the outlet reservoir for fluid  1  to which the drain is connected and detach from the drain walls as it enters the reservoir. Fifth, the bubble may be extracted from the drain by some means which separates it from the volume of fluid  1 , for example by encountering a filter, a membrane, a pore, and the like which allows the passage of fluid  2  but not of fluid  1 . 
     The power noise margin of the ABC switching operation is defined as the difference between the power needed to maintain bubble  402  in its state as shown in FIG.  6 B and the power needed to reach the point of metastability as in FIG.  6 D. For robust device operation it is desirable to have the power noise margin be greater than expected fluctuations due to environmental influences. It will be appreciated that as the volume of the barrier increases the power noise margin increases. For embodiment  300  the volume of barrier  325  can be calculated as V barrier =(h×w barrier ×L barrier ), and the volume of the gate can be calculated as V gate =(h×w gate ×L gate ). The ratio given by (V gate +V barrier )/V gate  provides an indication of the relative noise margin for various design choices. 
     The resistance of bubble  402  to acceleration along the capillary is determined by the ratio of equilibrium free-surface radii at a junction between two regions which acts to prevent bubble movement. The sustainable force per unit area on the bubble in the direction of flow at a junction between two regions, such as either source and gate or gate and barrier, is simply the difference in equilibrium free surface pressures between those two regions, or equivalently the energy potential difference. The local effective mass per unit area of the bubble for acceleration purposes is just the length of the bubble multiplied by the density difference between fluid  1  and fluid  2 . Thus the maximum sustainable acceleration without displacing the bubble from the potential well is given by multiplying the energy potential difference, the density difference, and the bubble length. 
     The above descriptions consider only the low-frequency, quasistatic operation of embodiment  300  of the invention in which fluid momentum effects play little role. It will be appreciated by those skilled in the art that at higher frequencies fluid momentum effects will be present, and ultimately both fluid momentum effects and thermal effects limit the upper operating frequency of the invention. 
     Embodiment  300  is considered a preferred mode of embodiment of the present invention as of the time of this writing. It has been found that switching time for an instance of embodiment  300  is less than 3 milliseconds for the transition between the state of FIG.  6 D and that of FIG. 6F where fluid  1  is cyclohexane. Typical dimensions for an instance of embodiment  300  are h=50 μm, w source =15 μm, L source =250 μm, w gate =18 μm, L gate =90 μm w barrier =18 μm, L barrier =30 μm, w drain &gt;30 μm, and L drain =170 μm. 
     In embodiment  300  as shown is FIGS. 3,  4 , and  6 , walls  306  and  308  are substantially perpendicular to the plane of propagation of optical signals  348  and  448 , which is advantageous for optical transmission and reflection purposes. In other embodiments capillaries with a variety of cross-sectional shapes including round, oval, or polygonal can be made and used without departing from the scope of the present invention. For example, a tapered trench etched in one substrate can be capped by a flat second substrate to form a capillary of substantially trapezoidal cross section which can be employed in alternative embodiments of the present invention. It is not a requirement that the capillary have continuous walls. Segmented walls, walls with continuous grooves along their length, or arrays of closely spaced pillars can also serve to wall-confine a bubble while providing the desired energy potential relationships of Eq. 13. 
     Alternative embodiments of the present invention can function in fluiphobic capillaries. FIG. 7 illustrates in sectional view such a fluiphobic embodiment  700 . A bubble  702  of fluid  2  is confined by capillary walls of a material  704  which is poorly wetted by fluid  1 . For example, fluid  1  may be liquid mercury and fluid  2  may be air while material  704  may be glass. Bubble  702  is introduced through valve  716 . Valve  716  may be a mechanical valve, may itself be a separate ABC device, or may be a separate fluidic device. In any case the internal operation of embodiment  700  in switching, valving, or pumping is purely fluidic, and the means by which the bubble is introduced is incidental. 
     The capillary includes source  721 , gate  723 , barrier  725 , and drain  727 . The necessary relationship among the effective free surface radii of the various regions for a fluiphobic embodiment is given by 
     
       
         r f,e,source &gt;r f,e,barrier &gt;r f,e,gate &gt;r f,e,drain   Eq. 16 
       
     
     In such a fluiphobic embodiment, the direction of curvature of the bubble of fluid  2  is reversed from that in the fluiphilic embodiment of FIG. 3, and so the pressure within a wall-confined bubble of fluid  2  is less than that in fluid  1 . 
     Fluid  2  may be either a gas or a liquid and its introduction through valve  716  is thus either pneumatic or hydraulic in nature. 
     It might be naively expected that the bubble would collapse if it were a gas and its internal pressure were less than that of fluid  1 , but such is not the case because the greater pressure within fluid  1  is supported by the confining interfacial surface tension of the bubble rather than supported by the gas volume within the bubble. 
     For embodiment  700 , the signs of the differential pressures are reversed in comparison to those of embodiment  300 , and each differential pressure as per Eq. 4 is less than zero. The magnitude of each differential pressure satisfies the relationship 
     
       
         |ΔP f,e,source |&lt;|ΔP f,e,barrier |&lt;|ΔP f,e,gate |&lt;|ΔP f,e,drain |  Eq. 17 
       
     
     In Eq. 17 the vertical brackets, | |, signify the absolute value (magnitude) of the differential pressure. The energy potential relationships given by Eq. 13 are nevertheless achieved for embodiment  700  because the sign of the subtraction between any two differential pressures must be reversed, in comparison to that for embodiment  300 , in order to compute the energy potential differences between two regions. Thus, for example, for embodiment  700 , if the gate is chosen as the reference point at which energy potential is defined to be zero, then Π source =ΔP f,e,gate −ΔP f,e,source . 
     Operation of embodiment  700  is analogous to operation of embodiment  300 . The bubble is introduced to gate region  723 , grows with the input of energy to fill barrier region  725 , becomes unstable, and exits into drain region  727 . The state of bubble  702  as shown is one of metastability, and any further growth toward the drain region will cause it to become unstable and flow into the drain. Thus the state of embodiment  700  in FIG. 7 corresponds in time to that of embodiment  300  in FIG.  6 D. 
     It will be appreciated that, because the width of drain region  727  decreases with distance from barrier region  725 , bubble  702  cannot detach from the capillary walls as it moves merely because the capillary becomes wider as was the case with embodiment  300 . Thus there is at least one less mechanism available in embodiment  700  for restoring the free flow of fluid  1  than there was in embodiment  300  above. 
     Alternative embodiments of the present invention can also employ differences in surface wetting properties rather than differences in geometry. FIG. 8 illustrates an embodiment  800  of the present invention in which geometry is uniform through source, gate, barrier, and drain but in which the relationship of Eq. 13 is achieved through the use of different materials. 
     FIG. 8A illustrates four wall-confined bubbles in the four regions of device  800  to demonstrate the different equilibrium free surface radii of the four regions. Source  802 , gate  804 , barrier  806  and drain  808  have walls having materials  810 ,  812 ,  814 , and  816  respectively, and contain wall-confined bubble  818 ,  820 ,  822 , and  824  respectively. In embodiment  800  the walls are generally fluiphilic, although their wetting characteristics vary to achieve by design the relationships among equilibrium free surface radii given by Eq. 11. 
     FIG. 8B illustrates the operation of embodiment  800  as an ABC. A single bubble  826  of fluid  2  is created by bubble generator  828  which may be, for example, a patch of light-absorbing material heated by a laser beam to create a bubble by boiling fluid  1 . Free surfaces  830  and  832  have equal radii of curvature determined by the equilibrium free surface radius, r f,e,barrier , of the barrier region. The bubble fills both the gate and the barrier and is at the point of metastability wherein an incremental increase in bubble volume will cause it to intrude into barrier region  808  and exit gate region  804 . The illustrated state of embodiment  800  shown in FIG. 8B thus corresponds to the state of embodiment  300  as shown in FIG.  6 D and to that of embodiment  700  as shown in FIG.  7 . 
     FIG. 9 illustrates a fluiphilic embodiment  900  of the present invention for use in removing dissolved gas from a liquid. FIG. 9A is a top sectional view and FIG. 9B is a side sectional view. Bubble  902  contains dissolved gas liberated from liquid  904  by heater  906  plus the vapor of liquid  904  generated by heater  906 . Multiple source necks  908 ,  910 , and  912  admit liquid  904  to gate  914 . Barrier  916  traps bubble  902  until sufficient energy is added to make the bubble flow into drain  918  and so to remove it from proximity to liquid flow  920 . Flow  920  of liquid  904  may be rich in dissolved gas where it enters the device at point  922  and is less rich in dissolved gas where it exits at point  924 . It should be appreciated that, while only three source necks  908 ,  910 , and  912  are shown for purposes of illustration, in practice many source necks acting in parallel are desirable for efficient removal of dissolved gas from liquid  904 , and that in addition multiple instances of a device such as embodiment  900  may be placed in series in flow  920  to efficiently reduce dissolved gas concentration. 
     The structural details of embodiment  900  are as follows. Material  926  which may be a photodefinable polymer such as photoresist or photosensitive epoxy into which a groove can be defined by lithographic means to form the sidewalls of the capillary. Material  928  may be a glass layer bonded on top of material  926  to form the roof of the capillary. Layer  930  is an electrically insulating material such as silicon dioxide covering heater  906 . Layer  932  is an electrically and thermally insulating layer such as silicon dioxide, and substrate  934  is a thermally conductive material such as silicon. 
     The present invention does not rely on primarily on thermocapillarity, i.e., the Marangoni effect, but instead relies primarily on capillary geometry and materials properties to control bubble movement. The invention can function in embodiments such as  300  and  700  above whether the Marangoni phenomenon helps or hinders its operation because geometric effects on radius of curvature can be designed to be much larger than temperature effects on surface tension. However, the Marangoni effect can be employed as a second-order controlling effect in a multiple-drain version of the present invention to choose a direction in which the bubble will exit from the gate. 
     FIG. 10 shows a schematic top sectional view of a fluiphilic embodiment  1000  of the present invention with multiple barriers  1002  and  1004  and with multiple drains  1006  and  1008 . The materials set for embodiment  1000  may be the same as that for embodiment  900 , although this is not necessary. 
     Heater  1010  generates a bubble  1012  in gate  1014  which is trapped by relatively higher energy potentials in barrier  1002 , barrier  1004 , and source  1016 . Barriers  1002  and  1004 , even though designed to have the same equilibrium free surface radii, will almost always have some difference in those radii due to manufacturing variations. Thus bubble  1014  will almost always exit gate  1016  through one or the other of barriers  1002  and  1004 , and hardly ever through both at the same time. 
     However, the Marangoni effect can be used to decrease the equilibrium free surface pressure in one barrier relative to the other by locally reducing the surface tension of the bubble, as can be appreciated by considering Eq. 4 above. The equilibrium contact angle, θ e , taken within fluid  1  is nearly constant with temperature, and in association with the capillary geometry sets the equilibrium free surface radius r f,e  within a barrier region to be nearly constant with temperature. However, surface tension, σ, decreases as temperature increases and so the equilibrium free surface pressure, ΔP f,e , also decreases as temperature increases. If one barrier region, for example  1002 , is heated by heater  1018  while heater  1020  is cold, the equilibrium free surface pressure, ΔP f,e , decreases in barrier  1002  and so the energy potential of that barrier decreases relative to barrier  1004 . It thus becomes easier to the bubble  1014  to exit gate  1014  through barrier  1002  than through barrier  1004 . 
     Source  1016  may serve as the path for liquid refill as in embodiments described above. However, it can be seen that, if there is no restriction to reverse flow from drain  1008  through barrier  1004 , refill may also or instead occur from drain  1008  through barrier  1004  into gate  1014 . Thus in embodiment  1000  a barrier may function also as a source, demonstrating that the functional roles of source and barrier can be reversed by means of local heating. In such an embodiment the source  1016  can be plugged or absent and the device can still function because one or the other barrier acts as a source. FIG. 12 shows an embodiment similar to that of FIG. 10 but in which the source  1016  is absent. In the embodiment of FIG. 12, one of the barriers (similar to barriers  1002  and  1004  of FIG. 10) can function as the source. At position  1216  (which correspond to the position of the source  1016  of FIG.  10 ), solid material forms the wall of the gate. 
     Advantageously, embodiment  1000  controls the direction of fluid movement without using a solid moving part such as a swinging gate or other mechanical valve which may be slow, prone to failure, and difficult to make in a small size. 
     FIG. 11 shows an embodiment  1100  of the present invention in which two ABC devices  1102  and  1104  are placed in tandem so that region  1106  includes both the barrier of upstream ABC  1102  and the source of downstream ABC  1104 , while region  1108  includes both the drain of upstream ABC  1102  and the gate of downstream ABC  1104 . This arrangement can be advantageous to the operation of the downstream ABC  1104  because both bubble introduction to the gate  1108  of the downstream ABC and extraction from that gate occur by the same type of mechanism. 
     Bubble  1110  is pre-generated in the gate  1112  of the upstream ABC using bubble generator  1114  which may, for example, be a set of electrodes which electrolyze water constituting fluid  1  into a mixture of oxygen and hydrogen gases constituting fluid  2 . 
     Bubble  1110  can then be grown in volume by energy input to fill or nearly fill barrier  1106  of the upstream ABC so that it is just below the point of metastability in energy. It can then be rapidly injected by a small additional energy input into the gate  1108  of downstream ABC  1104 . Thus, introduction of the bubble  1110  into downstream ABC  1104  is accomplished by microfluidic means. Advantageously, the volume of bubble  1110  when it is at the point of metastability can be designed to equal the volume of the gate  1108  of downstream ABC  1104 , so that it completely fills region  1108  when first injected into that region. 
     In downstream ABC  1104  the bubble is maintained by element  1116  which may, for example, be a heating resistor. Increasing the power to element  1116  increases the size of the bubble, as in embodiment  300  above, and eventually leads to a second switching operation as the bubble exits through barrier  1118  and into drain  1120  of the downstream ABC  1104 . 
     Embodiments  300  (FIG.  3 ),  700  (FIG.  7 ),  800  (FIG.  8 ), and  900  (FIG. 9) above illustrate instances of devices such as heating resistors, valves, or laser-heated patches which provide all aspects of bubble introduction, bubble maintenance, and bubble growth in a unitary fashion. Embodiments  1000  (FIG. 10) and  1100  (FIG.  11 ), in contrast, illustrate a separation of bubble movement functions. In embodiment  1000  heater  1010  generates the bubble and maintains the bubble in the gate, while heater  1018  provides control of the direction of bubble growth and can also provide heat to aid in growing the volume of the bubble. In embodiment  1100  the bubble is generated by generator  1114 , is introduced into the downstream gate  1108  by upstream ABC  1102 , is maintained by element  1116 , and is then increased in volume by the same element  1116 . Thus the above embodiments illustrate instances of unitary and separated bubble controlling functions, and illustrate instances of thermal, pneumatic, hydraulic, optical, electrolytic, and microfluidic mechanisms which may be used for bubble generation, introduction, maintenance, growth, and movement. Other mechanisms for bubble generation, introduction, maintenance, growth, and movement will occur to those skilled in the art without departing from the scope of the present invention, for example the generation of gas bubbles by ultrasonic agitation. 
     The above examples are related to embodiments that are either fluiphilic to fluid  1  or fluiphobic to fluid  1 . However, embodiments that mix fluiphilic portions with fluiphobic portions can be implemented by one skilled in the art based on the present disclosure. 
     Various geometries, various materials, and various combinations of fluids can be used to embody the present invention. Table 1 below describes examples of a few possible ABC embodiments. These embodiments are not to be taken as limiting but rather are illustrative. 
     In Table 1, the “fluiphilic” geometry is similar to that of embodiment  300  above in which the equilibrium contact angle taken within fluid  1  is less than ninety degrees and in which the pressure relationships of Eq. 12 are satisfied. The “fluiphobic” geometry is similar to that of embodiment  700  in which the equilibrium contact angle taken within fluid  1  is greater than ninety degrees and in which the pressure relationships of Eq. 17 are satisfied. The “wetting” geometry is similar to that of embodiment  800  in which variations in wall material wetting properties rather than geometry variations achieve the energy potential relationships of Eq. 13. It should be appreciated that in all embodiments of the present invention, wetting properties are important to the functionality of the ABC. 
     All of the embodiments illustrated above have placed the source, gate, barrier, and drain regions in a single plane for purposes of illustration, and because fabrication of elements in a single plane is easy using lithrographic techniques familiar to the microelectronics world. However, co-planarity of the regions is not a requirement of s the invention. For example, it would be a simple matter to modify embodiment  300  as shown in FIG. 3 so that the source was defined in material  315  rather than material  304 . FIGS. 13A and 13B illustrate such an embodiment. In FIG. 13A a source is not seen connected to the gate  1306  because the gate is at a different plane in the switching device  1300 . Position  1330  (which corresponds to the position of a source in embodiments such as position  406  of FIG. 4) is just solid material. In embodiment  1300 , the source  1350  is connected to the gate  1306  at right angle to the orientation of the gate  1306  and the downstream channel. The space  1315  on the other side of the gate  1350  opposite to the source  1350  is plugged with solid material. FIG. 14 shows an embodiment  1400  similar to embodiment  1300  but in which no separate source region is present at location  1430 . In contrast to embodiment  1300  in which the separate source region  1350  is present, in embodiment  1400  layer  1408  exists on either side of the capillary. In this extreme case, refill of fluid  1  is provided by leakage flow past the moving bubble. As bubble  1402  flows from gate  1404  to drain  1406 , fluid  1  is able to slowly refill gate  1404  by flowing in blow-by paths  1410 ,  1412 ,  1414 , and  1416  in an upstream direction from the drain to the gate. 
     Applications of the present invention other than those considered herein will occur to those skilled in the art without departing from the scope of the invention. It is anticipated that such applications will arise in the fields of genomics, proteomics, chemical analysis, biomedicine, optics, and microfluidics, among others. Such applications can also use other energy potential sources, for example inertial means such as acceleration or centrifugation, to aid, oppose, or modify the energy potentials present in the ABC. Centrifugation, for example, can increase the energy of a trapped bubble without increasing its volume. An example of hydrophobic wall material that can be used in a fluiphobic system is polytetrafluoroethylene (PTFE), e.g., TEFLON made by DuPont Company. 
     
       
         
               
             
               
               
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                 Various fluid and materials combinations for 
               
               
                 example ABC embodiments. 
               
             
          
           
               
                   
                 Filling fluid 
                 Bubble fluid 
                   
               
               
                 Wall materials 
                 (fluid 1) 
                 (fluid 2) 
                 Geometry 
               
               
                   
               
               
                 Glass 
                 Water 
                 Water vapor 
                 Fluiphilic 
               
               
                 Glass 
                 Water 
                 Mercury 
                 Fluiphilic 
               
               
                 Glass 
                 Air 
                 Mercury 
                 Fluiphilic 
               
               
                 Glass 
                 Mercury 
                 Air 
                 Fluiphobic 
               
               
                 Glass 
                 Oil (easily wets walls) 
                 Air 
                 Fluiphilic 
               
               
                 Glass 
                 Oil (wets walls more 
                 Water 
                 Fluiphilic 
               
               
                   
                 easily than does Water) 
               
               
                 PTFE 
                 Water 
                 Air 
                 Fluiphobic 
               
               
                 Glass, 
                 Water 
                 Air 
                 Wetting 
               
               
                 polyethylene, 
               
               
                 polypropylene, and 
               
               
                 PTFE 
               
               
                   
               
             
          
         
       
     
     Although the above embodiments of the present invention have been described and illustrated in detail, it is to be understood that a person skilled in the art can make modifications within the scope of the invention. Furthermore, although the scientific theory of bubble movement has been described in the above, the application of the present invention is not dependent on any particular theory and can be practiced by one skilled in the art.