Patent Publication Number: US-2011073188-A1

Title: Microvalve for control of compressed fluids

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     Reference is made to commonly-assigned, U.S. patent application Ser. No. ______(Docket 94230), entitled “MICROVALVE FOR CONTROL OF COMPRESSED FLUIDS” filed concurrently herewith. 
    
    
     FIELD OF THE INVENTION 
     The present invention relates generally to micro-electromechanical devices and, more particularly, to micro-electromechanical valves that control flow of compressed fluids through fluid channels. 
     BACKGROUND OF THE INVENTION 
     Micro Electro Mechanical Systems (MEMS) are a relatively recent development. They are used in many mass-market commercial devices such as accelerometers, pressure sensors, ink jet printer heads, and digital mirror arrays for projectors. They are also used as alternatives to conventional electromechanical devices as actuators, valves, and position locaters. They are potentially low cost due to use of microelectronic fabrication techniques. G. Stemme provides a useful review of techniques and principles that can be used to fabricate MEMS liquid flow control devices in a paper entitled “Micro fluid sensors and actuators” in IEEE Proceedings of Sixth International symposium on Micro Machines and Human Sciences, pp. 45-52 (1995). 
     MEMS microvalves are characterized by their geometry, actuation mechanism, whether they are active or passive, normally open or closed, and whether they contain external or integrated actuators. Additionally, their membrane material can also be used to characterize them. Membrane materials are typically divided into silicon-based and non silicon-based. “Normally open” (“closed”) simply means that the valve is open (closed) when no power is applied. Most MEMS microvalves are silicon-based since they are created using existing silicon chip fabrication methods established by the electronics industry. Newer MEMS fabrication techniques such as Lithographic Galvanoformung Abformung (LIGA), LIGA-like and Deep Reactive Ion Etching (DRIE), etc. permit mass fabrication, including non-silicon parts, with high aspect ratios. Other materials previously incorporated into microvalve designs include Titanium, Nickel, Copper, Aluminum, and Silicon. Stainless steel is also often used for these purposes. 
     The actuation mechanism in active microvalves includes a means to open and close an orifice and regulate the flow. This classification can be further divided into external and integrated actuators. External actuators include solenoid plungers, piezoelectric stack actuators, and pneumatic devices. Integrated actuators provide an intrinsic mechanism to actuate the valve such as electrostatic attraction, heating of bimetallic strips, thermo-pneumatic (heating/expansion), shape memory alloy (SMA), and electromagnetic. Each type of mechanism offers advantages and disadvantages in terms of cost, complexity, speed, performance, and reliability. These factors need to be optimized for the given applications. 
     The number and variety of application areas for microvalves for flow control have been increasing rapidly due to their small size, low-power consumption and relatively large flow rates. These include micro-propulsion, refrigeration, fuel injection, liquid chromatographic separations, and chemical synthesis. An interesting emerging application is compressed fluid based printing. Compressed fluids are fluids that contain at least one component in substantial amount that is gas at ambient temperature and pressure. 
     In a paper entitled “Leak-tight piezoelectric microvalve for high-pressure gas micro-propulsion” published in  J. of Microelectromechanical Systems,  13, p. 799 (2004), E. Yang et al. describe the development of a normally-closed piezoelectric microvalve that operated successfully up to inlet pressure of about 68 bar and an actuation repetition frequency of 1 KHz. Similarly, in a paper entitled “piezoelectric microvalve for compact high-frequency, high differential pressure hydraulic micro-pumping systems” published in  J. of Microelectromechanical Systems,  12, p. 81 (2003), D. C. Roberts et al. describe the development of a piezoelectrically driven hydraulic amplification microvalve. The microvalve operated successfully at pressure differentials of 4-10 bar and actuation repetition frequency of 1-10 KHz, with a large stroke (20-30 μm). B. J. Kirby et al. describe “Voltage-addressable on/off microvalves for high-pressure microchip operations” in a paper published in  J. of Chromatography  A, 979, p. 147 (2002). They demonstrate that the glass substrates and cross-linked polymer monoliths can operate in water-acetonitrile mixtures and hold-off pressures up to 350 bar with open/closed flow ratios of 10 4  to 10 6  over the pressure range of 1.5-70 bar and operates at a frequency of 1 Hz. In a paper published in  Sensors and Actuators  A, 134, p. 257 (2007), D. G. Lee et al. describe “Large flow rate/high frequency microvalve array for high performance actuators”. They use silicon-on-insulator wafer to simplify the fabrication process. Their microvalves have an analytical resonant frequency of 50 KHz and operate at pressure differentials of up to 1.4 bar. A useful comparison of various microvalves for gas flow is also available in a paper entitled “Design, fabrication and characterization of a novel gas microvalve using micro- and fine machining” by I. Fazal et al. published in  J. of Micromechanics and Microengineering,  16, p. 1207 (2006). Most of the microvalves included in this review did not exhibit an ability to control flows for pressure differentials exceeding 25 bar. Microvalves with thermal or thermo-pneumatic actuation provide large force through large stroke but slow response time (&gt;300 ms). 
     The microvalves described above represent a range of options available in terms of differential pressures, frequency, response time, stroke, size, and complexity of fabrication. However, none of the published valve designs appear to be capable of providing a way to control flow of compressed fluids to meet combined requirements such as being able to operate at the required pressure (for example, &gt;30 Bar), in a leak-proof manner (for example, open/closed flow ratio&gt;1000), at the desired high actuation frequency (for example, &gt;10 KHz) and of desired compactness (for example, that enables making a nozzle array that permits printing at resolutions exceeding 150 dots per inch). It would be desirable to have microvalve architectures providing these improved operating characteristics. As such, there is a need for new valve designs that solve the problem of simultaneously satisfying such requirements for the control of compressed fluid flows. 
     Commonly assigned U.S. Pat. No. 6,464,341 entitled “Dual Action Thermal Actuator and Method of Operating Thereof” issued Oct. 15, 2002 to Furlani et al., describes a method and apparatus for operating a thermal actuator as a liquid drop emitter in an inkjet print head. The disclosed thermal actuator includes a base element and a cantilevered element extending from the base element, and normally residing at a first position before actuation. The cantilevered element includes a bather layer, constructed of a low thermal conductivity material bonded between a first deflector layer and a second deflector layer, both of which are constructed of electrically resistive materials having substantially equal coefficients of thermal expansion. The thermal actuator also includes a first pair of electrodes connected to the first deflector layer and a second pair of electrodes connected to the second deflector layer for applying electrical pulses to cause resistive heating of the first or second deflector layers, resulting in thermal expansion of the first or second deflector layer relative to each other. Application of an electrical pulse to either pair of electrodes causes deflection of the cantilevered element away from its first position, and, alternately, causes a positive or negative pressure in the liquid at the nozzle of a liquid drop emitter. The actuator never needs to close fully in order to control the formation of ink droplets. 
     Commonly assigned U.S. Pat. No. 6,588,884, entitled “Tri-Layer of Thermal Actuator and Method of Operating” issued Jul. 8, 2003 to Furlani et al., describes an apparatus and method of operating a thermal actuator for a liquid drop emitter such as an inkjet print head. The disclosed thermal actuator includes a base element and a cantilevered element extending from the base element and normally residing at a first position before actuation. The cantilevered element includes a barrier layer constructed of a low thermal conductivity material, bonded between a deflector layer and a restorer layer, both of which are constructed of materials having substantially equal coefficients of thermal expansion. The thermal actuator also includes an apparatus adapted to apply a heat pulse directly to the deflector layer, causing a thermal expansion of the deflector layer relative to the restorer layer and deflection of the cantilevered element to a second position, followed by restoration of the cantilevered element to the first position as heat diffuses through the bather layer to the restorer layer and the cantilevered element reaches a uniform temperature. When used as a thermal actuator for liquid drop emitters, the cantilevered element resides in a liquid filled chamber that includes a nozzle for ejecting liquid. Application of a heat pulse to the cantilevered element causes deflection of a free end forcing liquid from the nozzle. It is not necessary to close a valve for successful operation of this device. 
     Commonly assigned U.S. Pat. No. 7,033,000, issued Apr. 25, 2006 to Delametter et al., and U.S. Pat. No. 7,029,101, issued Apr. 18, 2006 to Delametter et al., both entitled “Tapered Multi-Layer Thermal Actuator And Method Of Operating Same” disclose different embodiments of apparatus for and method of operating a thermal actuator for a micromechanical device, especially a liquid drop emitter for use in an ink jet printhead. The disclosed thermal actuator includes a base element and a cantilevered element including a thermo-mechanical bender portion extending from the base element to a free end tip. The thermo-mechanical bender portion includes a bather layer constructed of a dielectric material having low thermal conductivity, a first deflector layer constructed of a first electrically resistive material having a large coefficient of thermal expansion, and a second deflector layer constructed of a second electrically resistive material having a large coefficient of thermal expansion wherein the barrier layer is bonded between the first and second deflector layers. 
     US Patent Application Publication No. 2009/0079783 A1, published Mar. 26, 2009, by Mehta et al., discloses a MEMS print head based printing apparatus. It is used for delivering a mixture of compressed fluid and marking material and depositing the marking material in a pattern on to a substrate. The print head includes individually controlled microvalves positioned along each micro-nozzle, with typical turn on- and off-times in the range 10 −5  to 10° sec. For control of flow of supercritical gases, such microvalves have to operate at input side pressures exceeding the critical pressure of the gas. For example, the use of supercritical carbon dioxide typically requires the microvalve to operate at input pressure exceeding 73 bar. 
     The design and fabrication of microvalves for use in environments that have high operating pressures and high actuation frequencies present new challenges. Accordingly, there is an ongoing need for microvalves that operate adequately in these types of environments. 
     SUMMARY OF THE INVENTION 
     The abovementioned thermal cantilever based designs are be attractive for compressed fluid flow control if they can be used as valves instead of drop emitters. However, we have found through calculations that for a desired temperature increase, a cantilever element that is exposed to net pressure across its entire length (i.e., when it is uniformly loaded) bends progressively less as operating pressure is increased. Hence, for sufficiently high pressures, such as those required for compressed fluids, a cantilever beam with, for example, thermal stimulation will have zero deflection across its length and will not open sufficiently. It is not apparent that any known modifications serve to ameliorate the situation. The results of trial-and-error computational experiments have unexpectedly revealed features of the present invention that should be present in designs of microvalves, for example, cantilever based microvalves, in order to make them suitable for use in compressed fluid flow control applications. 
     According to one aspect of the present invention, a micro-electromechanical device for controlling compressed fluid flow is provided. A chamber includes a fluid flow inlet port, a high pressure region exceeding 30 bar, and a fluid flow outlet port. A moveable micro-electromechanical valve is positioned to contact the fluid flow outlet port when the moveable micro-electromechanical valve is in a first position. An electrical connection to the moveable micro-electromechanical valve provides an electrical pulse train to the moveable micro-electromechanical valve to actuate the valve at a rate of 10 KHz or more to move the valve in order to control fluid communication between the high pressure region and a low pressure region downstream from the fluid flow outlet port. 
     According to another aspect of the present invention, a method of controlling compressed fluid flow includes providing a source of compressed fluid, the compressed fluid being under a pressure of at least 30 bar; providing a micro-electromechanical device including: a chamber including a fluid flow inlet port, a high pressure region, and a fluid flow outlet port, the fluid flow inlet port being in fluid communication with the source of compressed fluid; a moveable micro-electromechanical valve positioned to contact the fluid flow outlet port when the moveable micro-electromechanical valve is in a first position; and an electrical connection to the moveable micro-electromechanical valve; and actuating the moveable micro-electromechanical valve at a rate of 10 KHz or more by providing an electrical pulse train to the moveable micro-electromechanical valve using the electrical connection to control fluid communication between the high pressure region and a low pressure region downstream from the fluid flow outlet port. 
     According to another aspect of the present invention, a compressed fluid microvalve for controlling flow of compressed fluid from a region of high pressure to a region of low pressure is provided. A chamber includes an inlet port, a region of high pressure, and an outlet port leading to a region allow pressure. A cantilever beam includes a first portion, a second portion, and a third portion. The cantilever beam is anchored to a portion of the chamber and is suspended in the chamber such that the first portion and third portion of the cantilever beam are exposed to the region of high pressure on all sides. The second portion of the cantilever beam overlaps the outlet port. The cantilever beam includes a first position in contact with the outlet port to prevent fluid flow from the chamber through the outlet port and a second position removed from contact with the outlet port to permit fluid flow from the chamber through the outlet port. A controller is in electrical communication with the cantilever beam and is configured to provide an actuation pulse to the cantilever beam to move the cantilever beam from the first position in contact with the outlet port to the second position removed from contact with the outlet port. 
     According to another aspect of the present invention a method of controlling compressed fluid flow includes providing a source of compressed fluid; providing a compressed fluid microvalve including: a chamber including an inlet port, a region of high pressure, and an outlet port leading to a region of low pressure, the inlet port being in fluid communication with the source of compressed fluid; and a cantilever beam including a first portion, a second portion, and a third portion, the cantilever beam being anchored to a portion of the chamber and being suspended in the chamber such that the first portion and third portion of the cantilever beam are exposed to the region of high pressure on all sides, and the second portion of the cantilever beam overlaps the outlet port, the cantilever beam including a first position in contact with the outlet port to prevent fluid flow from the chamber through the outlet port and a second position removed from contact with the outlet port to permit fluid flow from the chamber through the outlet port; providing a controller in electrical communication with the cantilever beam; and actuating the cantilever beam using the controller to move the cantilever beam from the first position in contact with the outlet port to the second position removed from contact with the outlet port. 
     According to another aspect of the present invention, a normally closed or a normally open micro-electromechanical valve unit for controlling flow of compressed fluids from a region of high pressure to a region of low pressure is provided. A microfluidic chamber includes an inlet and an outlet for fluid. The chamber accommodates a valve element. The valve element includes a base element that provides an anchor and a valve seat defining an outlet conduit. The outlet conduit provides fluid communication between a high pressure region and a low pressure region. A deflectable cantilevered element including a bender portion extends from the anchor on the base element to a free end tip residing either at a first position in sealing contact with the valve seat or at a second position spaced apart or removed from contact with the valve seat. When in the first position, the cantilevered element experiences an unbalanced force only on the portion of the cantilevered element circumscribed by the valve seat such that the fluid communication between the high pressure region and the low pressure region is restricted. When in the second position, the cantilevered element permits fluid communication between the high pressure region and the low pressure region. A pair of electrodes are electrically connected to the deflectable cantilevered element to apply an electrical pulse to the deflectable cantilevered element, the application of which results in deflection of the cantilevered element to the second position, followed by restoration of the cantilevered element to the first position. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       In the detailed description of the preferred embodiments of the invention presented below, reference is made to the accompanying drawings, in which: 
         FIG. 1A  is a schematic view of a bi-layer microvalve in its closed position according to a first embodiment of this invention; 
         FIG. 1B  is a schematic view of a bi-layer microvalve in its open position according to a first embodiment of this invention; 
         FIG. 2A  is a schematic view of a tri-layer microvalve in its closed position according to a second embodiment of this invention; 
         FIG. 2B  is a schematic view of a tri-layer microvalve in its open position according to a second embodiment of this invention; 
         FIG. 3A  is a schematic view of the bottom surface of the bi-layer microvalve shown in  FIG. 1A ; 
         FIG. 3B  is a schematic view of the bottom surface of the tri-layer microvalve shown in  FIG. 2A ; 
         FIG. 4  is the geometry used for calculating the resonance frequency of a bimorph beam; 
         FIG. 5  is a schematic view of a uniformly loaded bi-layer microvalve in its closed position; 
         FIG. 6  plots defection of a uniformly loaded bi-layer microvalve versus position along the beam at different loading pressures for a 200 degree C. temperature difference; 
         FIG. 7  plots defection of a partially loaded bi-layer microvalve versus position along the beam at different loading pressures for a 200 C degree C. temperature difference; 
         FIG. 8  plots deflection of a partially loaded bi-layer microvalve as a function of the location of the microvalve seat along the length of the microvalve at different loading pressures for a 200 degree C. temperature difference; 
         FIG. 9  plots deflection of a partially loaded tri-layer microvalve as a function of position along the beam as described in Example 1; 
         FIG. 10  plots the maximum temperature in the partially loaded tri-layer microvalve as a function of time as described in Example 1; 
         FIG. 11  plots deflection of a partially loaded bi-layer microvalve as a function of position along the beam as described in Example 2; and 
         FIG. 12  plots the maximum temperature in the partially loaded bi-layer microvalve as a function of time as described in Example 2. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     The present description will be directed in particular to elements forming part of, or cooperating more directly with, apparatus in accordance with the present invention. It is to be understood that elements not specifically shown or described can take various forms well known to those skilled in the art. Figures shown and described herein are provided in order to illustrate key principles of operation of the present invention and are not drawn with intent to show actual size or scale. Some exaggeration may be necessary in order to emphasize relative spatial relationships or principles of operation. 
     As used herein, the term “compressed fluid” is defined to include a liquid having a density equal to greater than 0.1 g per cubic centimeter; or a supercritical fluid having density equal to or greater than 0.1 g per cubic centimeter; or a compressed gas having a density equal to or greater than 0.1 g per cubic centimeter or any combination thereof. Materials that are above their critical point, defined by a critical temperature and a critical pressure, are known as supercritical fluids. The critical temperature and critical pressure typically define a thermodynamic state in which a fluid or a material becomes supercritical and exhibits gas like and liquid like properties. Ambient conditions are preferably defined as temperature in the range from −100 to +100° C., and pressure in the range from 1×10 3 −100 bar for this application. 
     It is well known that the shape of the thermo-mechanical bender portion of a cantilevered thermal actuator influences its performance. Similarly, the shape of the piezoelectric bender portion of a cantilevered piezoelectric actuator influences its performance. The cantilevered element is designed to have a length sufficient to result in an amount of deflection sufficient to meet the requirements of the microvalve application. The details of thermal expansion differences, stiffness, modulus of elasticity, density, thickness, piezoelectric coefficients and other factors associated with the layers of the thermo-mechanical or piezoelectric bender portion are considered in determining an appropriate length for the cantilevered element. The length is also limited by the desired maximum frequency of operation. It is preferable that the cantilever element includes two or more layers, thus forming a multilayered thermo-mechanical or piezoelectric device. 
     The width of the cantilevered element is important in determining the force that is achievable during actuation. The actuation moves a fluid mass and overcome counter forces. In order to operate as a leak proof microvalve, the actuator compresses materials at the seat of the valve to achieve good contact or sealing. In general, for a given length and material layer construction, the force that can be generated is proportional to the width of the thermo-mechanical or piezoelectric bender portion of the cantilevered element. A straightforward design for a thermo-mechanical or piezoelectric bender is therefore a rectangular beam of width w 0  and length L, wherein L is selected to produce adequate actuator deflection and w 0  is selected to produce adequate force of actuation, for a given set of thermo-mechanical materials and layer constructions. 
     It is also known that the straightforward rectangular shape mentioned above is not the most energy efficient shape for the thermo-mechanical or piezoelectric bender. In fact, a thermo-mechanical or piezoelectric bender portion that reduces in width from the anchored end of the cantilevered element to a narrower width at the free end produces more force for a given area of the bender. 
       FIG. 1A  shows a schematic view of a compressed fluid flow control system  100  utilizing a bi-layer cantilever beam  30  as a microvalve actuator shown in its closed position according to a first embodiment of this invention. The compressed fluid control system  100  includes a compressed fluid source  90 , a compressed fluid inlet control valve  80 , a microvalve enclosure  70  and a chamber  180  defined as the interior of microvalve enclosure  70 . The fluid contained in the compressed fluid source may include any solvent or mixture of solvents that are miscible with the supercritical fluids and/or compressed liquids. 
     The microvalve enclosure  70  includes a microvalve enclosure top  200  with a high pressure inlet port  110  in fluid communication with the compressed fluid source  90  and the chamber  180 , a microvalve enclosure base  140  with a low pressure outlet port  130  and a controller interface conduit  20  used to provide control signals to actuate the bi-layer cantilever beam  30 . In one embodiment of the invention, the bi-layer cantilever beam  30  includes a first layer  34  of a material having a high coefficient of thermal expansion and a second layer  32  of a material having a low coefficient of thermal expansion. The components of microvalve enclosure  70  are sealed together so that chamber  180  maintains a high pressure differential with respect to the outside environment when the cantilever beam  30  is in its closed position as shown in  FIG. 1A . 
     The compressed fluid flow control system  100  can include additional fluid flow channels. When included, the fluid channels that the compressed fluid flows through are, typically, very small in size and are commonly referred to as micro-channels. Either the inlet port, the outlet port, or both ports can be fluidically connected to one or more micro-channels. When the fluid system includes micro-sized channels, actuation of the microvalve actuator, for example, the bi-layer cantilever beam  30 , controls compressed fluid flow through the micro-sized channels. 
     The bi-layer cantilever beam  30  is suspended in the chamber  180  and is supported and bonded to a microvalve anchor  150  and supported by a microvalve seat  160  when in the closed position. We call the closed position a first position which is in contact with the outlet port and prevents the flow of compressed fluid from the chamber through the outlet port. The microvalve anchor  150  is composed of a thermally conductive material and acts as a heat sink. The microvalve anchor  150  and the microvalve seat  160  are attached to the microvalve enclosure base  140  or the microvalve substrate. Alternatively, the microvalve substrate can be a separate part (not shown) that is in intimate contact with the microvalve enclosure base  140 . The microvalve seat  160  has the same inner size and shape as the size and shape of the opening in the low-pressure outlet port  130 . At the top of the microvalve seat  160  is a microvalve seat interface  60 , which makes a tight seal with the bottom surface  38  of the first layer  34  of the bi-layer cantilever beam  30  when the microvalve is in its closed position. The valve seat thus provides a fluid seal when in contact with the cantilever beam in its closed position. The plane labeled  0  or pivot position is located at the right edge of the anchor  150 . The bi-layer cantilever beam  30  is attached to the anchor  150  at locations to the left of plane  0 . The left end of the cantilever beam  30  is defined as Plane C. The length of attachment of the cantilever to the anchor is thus C which is typically between 5 and 30 μm. The width of the cantilever beam  30  is w (shown in  FIG. 3A ). The anchor overlap area of the cantilever bimorph microvalve  30  defined by the product wC acts as a heat sink during actuation of the microvalve. Plane L describes the right edge of the cantilever beam  30  of length L with respect to the pivot position of the cantilever beam  30 . Plane A is the location of the left edge of microvalve seat  160  and plane B is the location of the right edge of microvalve seat  160 . When the bi-layer cantilever beam  30  is in its closed position as shown in  FIG. 1A , there is an unbalanced force region  170  located between planes A and B. The pressure P in the unbalanced force region is equal to the pressure of the compressed fluid in the chamber. There is also an unbalanced force on the beam in the region of the beam from C to  0 . The unbalanced force in this region has no bearing on the performance of the bi-layer cantilever beam since the beam does not deflect in this region and it serves as an anchor location. It is preferred that the microvalve seat  160  is composed of a thermally conductive material so that the microvalve seat  160  can also act as heat sink when the microvalve  30  is in its closed position. 
     The microvalve cantilever beam  30  is suspended in the chamber  180  such that it includes a first portion from plane  0  to plane A, a second portion from plane A to plane B, and a third portion from plane B to plane L. The cantilever beam  30  is anchored to a portion of the chamber at one end of the cantilever beam (also referred to as an anchor or anchor portion, the region from plane C to plane  0 ). The first portion of the cantilever beam  30  extends from the pivot point of the cantilever beam  30  to the second portion of the cantilever beam  30 . The second portion of the cantilever beam  30  overlaps the outlet port  130  and includes the microvalve seat  160  and the third portion of the cantilever beam is suspended in the chamber and ends at plane L. The first and third portions of the cantilever beam are subjected to the region of high pressure on all sides at all times. The cantilever beam  30  has a first position in contact with the outlet port  130  to prevent fluid flow from the chamber through the outlet port. As shown in  FIG. 1A  and a second position as shown in  FIG. 1B  removed from contact with the outlet port  130  to permit fluid flow from the chamber through the outlet port. 
     The microvalve cantilever beam  30  has a cantilever electrode contact region  120  located at the interface of the bi-layer cantilever beam  30  and anchor  150 . The controller interface conduit  20  is located at the top surface of the microvalve anchor  150  and extends into the cantilever electrode contact region  120  of the microvalve  30 .  FIG. 3A  shows further detail of the bi-layer cantilever beam  30  by showing a bottom surface view of surface  38 . The electrode surface of cantilever first layer,  38  includes electrode contact pads  40 , electrode  36 , and an electrode gap  50 . The electrode contact pads  40  are aligned with the cantilever electrode contact region  120  at the top surface of microvalve anchor  150 . During manufacturing of the microvalve  30  electrical leads in the controller interface conduit  20  are contacted to the electrode contact pads  40  of electrode  36 . A controller  24  provides electrical current to the electrical leads in the in the controller interface conduit  20  which in turn applies current to the electrode surface of the cantilever first layer  38 . 
     The controller  24  is in electrical communication with the first layer  34  of the cantilever beam, the controller being configured to provide an actuation pulse to the first layer of the cantilever beam  34  which moves the cantilever beam  30  from a first closed position in contact with the outlet port  160  through the microvalve seat  160  as shown in  FIG. 1A  to a second position removed from contact with the outlet port  160  as shown in  FIG. 1B . When the actuation pulse is removed from the first layer of the cantilever beam  34 , the pressure in the region of high pressure is sufficient to move the cantilever beam  30  from the second position back to the first position. 
     During operation of microvalve  30  a rapid voltage pulse from the controller  24  via conduit  20  through contact pads  40  is supplied to electrode  36  of the cantilever beam first layer  34 . A current flows through the electrode  36  and through the electrical conducting material of first layer  34  creating resistive heating in the layer. This results in a rapid increase in the temperature of the first layer  34 . When the first layer is composed of a material with both a high thermal coefficient of expansion and thermal conductivity, this layer will expand in both length and width causing the material to bend upward as the voltage is applied to the electrodes. When the voltage is removed from the electrode  36  of the first layer  34  there will be no more temperature rise in the first layer. As the heat diffuses into the second layer  34  the temperatures of the two layers will equilibrate and the valve will close. Cooling of the bottom layer will occur as heat is lost through the heat sink at the anchor  150  and the valve seat  160  of the microvalve when contact is restored as the microvalve closes. 
       FIG. 2A  and  FIG. 2B  shows a schematic view of a compressed fluid flow control device  100  using a tri-layer cantilever beam  190  as an alternative embodiment of this invention. Tri-layer cantilever beam  190  includes a cantilever first layer  196  of a material having a high coefficient of thermal expansion, a cantilever second layer or middle layer  194  of a material having a low coefficient of thermal expansion and a cantilever third layer  192  of a material having a high coefficient of thermal expansion.  FIG. 2A  shows the tri-layer cantilever beam  190  in its closed position while  FIG. 2B  shows the tri-layer cantilever beam  190  in its open position.  FIG. 3B  shows further detail of the tri-layer cantilever beam  190 . The second layer  194  is constructed of a low thermal conductivity and electrically insulating material bonded between a first layer  196  and a third layer  192 , both of which are constructed of electrically conductive materials having substantially equal coefficients of thermal expansion. The third layer  192  can have an optional electrode on its top surface (not shown) in order to use this as a second deflection layer as described in co-assigned U.S. Pat. No. 6,464,341 which is incorporated by reference. 
     During operation of microvalve  190  a rapid voltage pulse from the controller  24  via conduit  20  through contact pads  40  is supplied to electrode  36  of the cantilever beam first layer  196 . A current flows through the electrode  36  and through the electrical conducting material of first layer  34  creating resistive heating in the layer. This results in a rapid increase in the temperature of the first layer  196 . When the first layer is composed of a material with both high thermal coefficient of expansion and thermal conductivity this layer will expand in both length and width causing the material to bend upward as the voltage is applied to the electrodes. When the voltage is removed from the electrode  36  of the first layer  34  there will be no more temperature rise in the first layer. As the heat diffuses into the second layer  194  and then the third layer  192  the temperatures of the three layers will equilibrate and the valve will close. Applying a voltage to the top layer  192  will cause the beam to bend downward thus ensuring the closing of the valve. The controller is used to provide an actuation pulse to the third layer of the cantilever beam when the cantilever beam is in the second position removed from contact with the outlet port to move the cantilever beam to the first position in contact with the outlet port. This offers a second mechanism to enable valve closing. Cooling of the bottom layer can occur as heat is lost through the heat sink at the anchor  150  and the valve seat  160  of the microvalve when contact is restored as the microvalve closes. 
     The thermal deflection Y(x,T) of a cantilever bi-layer or bimorph beam of length L from a pivot point defined as  0  as a function of distance x along the length of the beam. The cantilevered element includes a barrier layer, constructed of a low thermal conductivity material bonded between a first deflector layer and a second deflector layer, both of which are constructed of electrically resistive materials having substantially equal coefficients of thermal expansion can be shown to be 
         Y ( x,T )= Y   M ( x,T )− Y   P ( x )  (1)
 
     where Y M (x,T) is the bending due to thermal moment and Y P (x) is the bending due to unbalanced pressure. The first term of equation 1 is given by 
     
       
         
           
             
               
                 
                   
                     
                       
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                             ) 
                           
                         
                          
                         
                           x 
                           2 
                         
                       
                       
                         2 
                          
                         
                             
                         
                          
                         EI 
                       
                     
                   
                   ) 
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
     where EI is the flexural rigidity of the beam and M(T) is the thermal moment of the beam. The flexural rigidity of the beam is the product of the moment of inertia I and the modulus of elasticity E in a single layer beam. For a 2 layer beam EI is given by 
     
       
         
           
             
               
                 
                   EI 
                   = 
                   
                     w 
                      
                     
                         
                     
                      
                     
                       
                         
                           
                             E 
                             1 
                           
                            
                           
                             E 
                             2 
                           
                            
                           
                             h 
                             1 
                           
                            
                           
                             h 
                             2 
                             3 
                           
                         
                         
                           12 
                            
                           
                             ( 
                             
                               
                                 
                                   h 
                                   1 
                                 
                                  
                                 
                                   E 
                                   1 
                                 
                               
                               + 
                               
                                 
                                   h 
                                   2 
                                 
                                  
                                 
                                   E 
                                   2 
                                 
                               
                             
                             ) 
                           
                         
                       
                        
                       
                         [ 
                         
                           4 
                           + 
                           
                             6 
                              
                             
                                 
                             
                              
                             
                               
                                 h 
                                 1 
                               
                               
                                 h 
                                 2 
                               
                             
                           
                           + 
                           
                             4 
                              
                             
                               
                                 ( 
                                 
                                   
                                     h 
                                     1 
                                   
                                   
                                     h 
                                     2 
                                   
                                 
                                 ) 
                               
                               2 
                             
                           
                           + 
                           
                             
                               
                                 E 
                                 1 
                               
                               
                                 E 
                                 2 
                               
                             
                              
                             
                               
                                 ( 
                                 
                                   
                                     h 
                                     1 
                                   
                                   
                                     h 
                                     2 
                                   
                                 
                                 ) 
                               
                               3 
                             
                           
                           + 
                           
                             
                               
                                 E 
                                 2 
                               
                               
                                 E 
                                 1 
                               
                             
                              
                             
                               ( 
                               
                                 
                                   h 
                                   2 
                                 
                                 
                                   h 
                                   1 
                                 
                               
                               ) 
                             
                           
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
     where w is the width of the beam, E 1  and E 2  are the moduli of elasticity of the first and second layers and h 1  and h 2  are the thicknesses of the 2 layers. The thermal moment of the beam M(T) is given by 
     
       
         
           
             
               
                 
                   
                     M 
                      
                     
                       ( 
                       T 
                       ) 
                     
                   
                   = 
                   
                     w 
                      
                     
                         
                     
                      
                     
                       
                         
                           E 
                           1 
                         
                          
                         
                           
                             E 
                             2 
                           
                            
                           
                             ( 
                             
                               
                                 h 
                                 1 
                               
                               + 
                               
                                 h 
                                 2 
                               
                             
                             ) 
                           
                         
                          
                         
                           h 
                           1 
                         
                          
                         
                           
                             h 
                             2 
                           
                            
                           
                             [ 
                             
                               
                                 
                                   α 
                                   1 
                                 
                                  
                                 
                                   ( 
                                   
                                     
                                       T 
                                       1 
                                     
                                     - 
                                     
                                       T 
                                       0 
                                     
                                   
                                   ) 
                                 
                               
                               - 
                               
                                 
                                   α 
                                   2 
                                 
                                  
                                 
                                   ( 
                                   
                                     
                                       T 
                                       2 
                                     
                                     - 
                                     
                                       T 
                                       0 
                                     
                                   
                                   ) 
                                 
                               
                             
                             ] 
                           
                         
                       
                       
                         2 
                          
                         
                           ( 
                           
                             
                               
                                 h 
                                 1 
                               
                                
                               
                                 E 
                                 1 
                               
                             
                             + 
                             
                               
                                 h 
                                 2 
                               
                                
                               
                                 E 
                                 2 
                               
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
     where α 1  and α 2  are the coefficients of thermal expansion of the first and second layers respectively. 
     For a uniformly loaded bimorph beam the relationship 
     
       
         
           
             
               
                 
                   
                     
                       Y 
                       P 
                     
                      
                     
                       ( 
                       x 
                       ) 
                     
                   
                   = 
                   
                     
                       - 
                       
                           
                       
                        
                       
                         
                           Pwx 
                           2 
                         
                         
                           24 
                            
                           
                               
                           
                            
                           EI 
                         
                       
                     
                      
                     
                       ( 
                       
                         
                           6 
                            
                           
                             L 
                             2 
                           
                         
                         - 
                         
                           4 
                            
                           Lx 
                         
                         + 
                         
                           x 
                           2 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
     can be derived where P is the force per unit area on the beam or the pressure of the compressed fluid. 
     For a partially loaded bimorph beam the total unbalanced load force is Pw(B-A). The relationship for Y P (x) can be shown to be 
     
       
         
           
             
               
                 
                   
                     
                       Y 
                       P 
                     
                      
                     
                       ( 
                       
                         x 
                         
                           0 
                           - 
                           A 
                         
                       
                       ) 
                     
                   
                   = 
                   
                     
                       - 
                       
                           
                       
                        
                       
                         
                           Pw 
                            
                           
                             ( 
                             
                               B 
                               - 
                               A 
                             
                             ) 
                           
                         
                         
                           12 
                            
                           
                               
                           
                            
                           EI 
                         
                       
                     
                      
                     
                       ( 
                       
                         
                           3 
                            
                           
                             ( 
                             
                               A 
                               + 
                               B 
                             
                             ) 
                           
                            
                           
                             x 
                             2 
                           
                         
                         - 
                         
                           2 
                            
                           
                             x 
                             3 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       Y 
                       P 
                     
                      
                     
                       ( 
                       
                         x 
                         
                           A 
                           - 
                           B 
                         
                       
                       ) 
                     
                   
                   = 
                   
                     
                       - 
                       
                           
                       
                        
                       
                         
                           Pw 
                            
                           
                             ( 
                             
                               B 
                               - 
                               A 
                             
                             ) 
                           
                         
                         
                           24 
                            
                           
                               
                           
                            
                           EI 
                         
                       
                     
                      
                     
                       ( 
                       
                         
                           6 
                            
                           
                             ( 
                             
                               A 
                               + 
                               B 
                             
                             ) 
                           
                            
                           
                             x 
                             2 
                           
                         
                         - 
                         
                           4 
                            
                           
                             x 
                             3 
                           
                         
                         + 
                         
                           
                             
                               ( 
                               
                                 x 
                                 - 
                                 A 
                               
                               ) 
                             
                             4 
                           
                           
                             B 
                             - 
                             A 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       Y 
                       P 
                     
                      
                     
                       ( 
                       
                         x 
                         
                           B 
                           - 
                           L 
                         
                       
                       ) 
                     
                   
                   = 
                   
                     
                       - 
                       
                           
                       
                        
                       
                         
                           Pw 
                            
                           
                             ( 
                             
                               B 
                               - 
                               A 
                             
                             ) 
                           
                         
                         
                           24 
                            
                           
                               
                           
                            
                           EI 
                         
                       
                     
                      
                     
                       
                         ( 
                         
                           
                             4 
                              
                             
                               ( 
                               
                                 
                                   A 
                                   2 
                                 
                                 + 
                                 AB 
                                 + 
                                 
                                   B 
                                   2 
                                 
                               
                               ) 
                             
                              
                             x 
                           
                           - 
                           
                             A 
                             3 
                           
                           - 
                           
                             AB 
                             2 
                           
                           - 
                           
                             
                               A 
                               2 
                             
                              
                             B 
                           
                           - 
                           
                             B 
                             3 
                           
                         
                         ) 
                       
                       . 
                     
                   
                 
               
               
                 
                     
                 
               
             
           
         
       
     
     The relationships above for the deflection of bimorph beams are for the case when the beams are driven below the first or fundamental resonance frequency. Resonance frequencies for cantilever beams can be calculated from the theory for the transverse vibrations of a bar fixed at one end from as described in L. Kinsler, A. Frey, Q. Coppens and J Sanders, “Fundamental of Acoustics, Third Edition”, 1982 John Wiley and Sons, pp 72-75. The resonance frequencies f of a beam of a homogeneous material is given by 
     
       
         
           
             
               
                 
                   f 
                   = 
                   
                     
                       
                         π 
                          
                         
                             
                         
                          
                         c 
                          
                         
                             
                         
                          
                         κ 
                       
                       
                         8 
                          
                         
                             
                         
                          
                         
                           L 
                           2 
                         
                       
                     
                      
                     
                       ( 
                       
                         
                           1.194 
                           2 
                         
                         , 
                         
                           2.988 
                           2 
                         
                         , 
                         
                           5 
                           2 
                         
                         , 
                         
                           7 
                           2 
                         
                         , 
                         … 
                       
                        
                       
                           
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
     where c is the speed of sound in the material given by 
     
       
         
           
             
               
                 
                   c 
                   = 
                   
                     
                       E 
                       ρ 
                     
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
     where E is the modulus of elasticity and ρ is the density of the material and κ is the radius of gyration. For a beam of rectangular cross section the radius of gyration is given by 
     
       
         
           
             
               
                 
                   κ 
                   = 
                   
                     h 
                     
                       12 
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
     where h is the thickness of the beam. For the uniform material cantilever beam the fundamental resonance frequency is given by 
     
       
         
           
             
               
                 
                   
                     f 
                     o 
                   
                   = 
                   
                     0.162 
                      
                     
                       
                         E 
                         ρ 
                       
                     
                      
                     
                       
                         h 
                         
                           L 
                           2 
                         
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
           
         
       
     
     The article by Lee and Marcus titled, “The Deflection Bandwidth Product of Poly(Vinylidene Fluoride) Benders and Related Structures in Ferroelectrics Vol. 32, pp 93-101, 1981 describe the fundamental relationships for deflection and resonance in unimorph, bimorph and multimorph beams.  FIG. 4  shows the geometry used for calculating the resonance frequency of a bimorph beam. The variable b defines the location of the neutral axis. The location of the neutral axis is given by the expression 
     
       
         
           
             
               
                 
                   b 
                   = 
                   
                     
                       1 
                       2 
                     
                      
                     
                       [ 
                       
                         
                           
                             
                               a 
                               2 
                             
                              
                             C 
                           
                           - 
                           
                             
                               ( 
                               
                                 1 
                                 - 
                                 a 
                               
                               ) 
                             
                             2 
                           
                         
                         
                           aC 
                           + 
                           1 
                           - 
                           a 
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
     where C is given by 
     
       
         
           
             
               
                 
                   C 
                   = 
                   
                     
                       
                         E 
                         2 
                       
                       
                         E 
                         1 
                       
                     
                     . 
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
     The resonance frequencies are given by 
     
       
         
           
             
               
                 
                   f 
                   = 
                   
                     
                       
                         π 
                          
                         
                             
                         
                          
                         h 
                       
                       
                         8 
                          
                         
                             
                         
                          
                         
                           L 
                           2 
                         
                       
                     
                      
                     
                       
                         
                           E 
                           1 
                         
                         
                           ρ 
                           1 
                         
                       
                     
                      
                     
                       
                         
                           
                             
                               
                                 
                                   [ 
                                   
                                     
                                       - 
                                       
                                         b 
                                         3 
                                       
                                     
                                     - 
                                     
                                       
                                         ( 
                                         
                                           a 
                                           - 
                                           b 
                                           - 
                                           1 
                                         
                                         ) 
                                       
                                       3 
                                     
                                   
                                   ] 
                                 
                                 + 
                               
                             
                           
                           
                             
                               
                                 C 
                                  
                                 
                                   [ 
                                   
                                     
                                       
                                         ( 
                                         
                                           a 
                                           - 
                                           b 
                                         
                                         ) 
                                       
                                       3 
                                     
                                     + 
                                     
                                       b 
                                       3 
                                     
                                   
                                   ] 
                                 
                               
                             
                           
                         
                         
                           3 
                            
                           
                             [ 
                             
                               1 
                               - 
                               a 
                               + 
                               Da 
                             
                             ] 
                           
                         
                       
                     
                      
                     
                       ( 
                       
                         
                           1.194 
                           2 
                         
                         , 
                         
                           2.988 
                           2 
                         
                         , 
                         
                           5 
                           2 
                         
                         , 
                         
                           7 
                           2 
                         
                         , 
                         … 
                       
                        
                       
                           
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
           
         
       
     
     where D is given by 
               D   =       ρ   2       ρ   1         ,           h=h   1   +h   2  and 
     
       
         
           
             
               
                 
                   a 
                   = 
                   
                     
                       
                         h 
                         2 
                       
                       h 
                     
                     . 
                   
                 
               
               
                 
                   ( 
                   14 
                   ) 
                 
               
             
           
         
       
     
     Resonance frequency relationships for tri-layer and multi-layer beams are also derived in the Lee and Marcus reference. Table 1 shows a compilation of materials that are useful for the construction of thermally actuated microvalves according to various embodiments of this invention along with their relevant materials coefficients. 
     
       
         
           
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                 Properties of Materials Useful in Beam Structures 
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                 Thermal 
                   
                   
                   
                 Young&#39;s 
                   
               
               
                   
                 expansion 
                 Thermal 
                 Specific 
                   
                 Modulus 
                 Intrinsic 
               
               
                   
                 coefficient 
                 Conductivity 
                 Heat 
                 Density 
                 (10{circumflex over ( )}11 
                 Resistivity 
               
               
                 Material 
                 (10-6 K-1) 
                 (W/m-K) 
                 (J/g-K) 
                 (g/cm3) 
                 N/m2) 
                 (ohm-cm) 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 Au 
                 14.2 
                 317 
                 0.129 
                 19.3 
                 0.8 
                 2.27E−08 
               
               
                 Al 
                 25 
                 237 
                 0.897 
                 2.7 
                 0.7 
                 2.65E−08 
               
               
                 Si 
                 2.6 
                 149 
                 0.705 
                 2.33 
                 1.5 
                 2.20E+02 
               
               
                 Zn 
                 35 
                 116 
                 0.388 
                 7.13 
                 0.79 
                 5.50E−08 
               
               
                 Si 3 N 4   
                 0.8 
                 19 
                 0.17 
                 3.17 
                 3.85 
                 1.00E+14 
               
               
                 Ta 
                 6.3 
                 57.5 
                 0.14 
                 16.69 
                 1.86 
                 1.35E−05 
               
               
                 Pb 
                 28.9 
                 35 
                 0.129 
                 11.3 
                 0.16 
                 2.00E−07 
               
               
                 PolySilicon ins 
                 4.7 
                 33.2 
                 0.702 
                 2.33 
                 1.9 
                 1.00E+05 
               
               
                 TI 
                 8.6 
                 21.9 
                 0.523 
                 4.51 
                 1.2 
                 3.90E−07 
               
               
                 nichrome 
                 10 
                 12 
                 0.445 
                 8.5 
                 2.1 
                 1.10E−07 
               
               
                 SiO2 
                 0.55 
                 1.4 
                 0.17 
                 2.65 
                 0.73 
                 1.00E+15 
               
               
                   
               
            
           
         
       
     
     For example, a 200 μm long by 30 μm wide bi-layer beam including 10 μm thick Aluminum (Al) and 10 μm thick silicon nitride (Si 3 N 4 ) has a fundamental resonance frequency of 567 kHz. Similarly, a 200 μm long by 30 μm wide tri-layer beam including 7 μm thick first Aluminum (Al), a 7 μm thick silicon nitride (Si 3 N 4 ) layer and a second 7 μm thick Aluminum (Al) layer has a fundamental resonance frequency of 586 kHz. 
       FIG. 5  shows a uniformly loaded cantilever beam flow control system. The figure is similar to that of  FIG. 1A  except that the unbalanced pressure region  170  extends the entire length of bimorph cantilever beam  30 . As shown below when the unbalanced pressure region  170  acting on the cantilever beam  30  extends over its entire length L, the valve to function at pressures above 30 bar. 
       FIG. 6  shows curves of the deformation of a 200 μm long, 30 pin wide uniformly loaded bi-layer cantilever beam (mounted in the system shown in  FIG. 5  and including 10 μm thick Aluminum (Al) and 10 μm thick silicon nitride (Si 3 N 4 )) as a function of position along the beam at 4 different loading pressures of 1 bar, 10 bar, 20 bar and 30 bar for a 200 degree temperature differential. The x axis is the position along the cantilever beam in microns, and the y axis is the deflection (deformation) in microns at position x. In order for a microvalve to open, the deflection should be positive over the position of the hole, otherwise it can not open. It has been determined that a micro-valve of this construction and dimensions functions suitably at pressures up to and including 28.4 bar (approximately 30 bar). 
       FIG. 7  shows curves of the deformation of the same type of cantilever beam  30  used in the discussion of  FIG. 6  (mounted in the compressed fluid flow control system shown in  FIG. 1  and including 200 μm long, 30 μm wide bi-layer of 10 μm thick Aluminum (Al) and 10 μm thick silicon nitride (Si 3 N 4 )) as a function of position along the beam at 5 different loading pressures of 1 bar, 30 bar, 100 bar, 150 bar and 200 bar for a 200 degree temperature differential. The position of A is at 150 μm and B is at 165 μm for the data shown in  FIG. 7 . The microvalve seat interface  60  is 5 μm long at A and B and the dimensions of the opening in the low pressure outlet port  130  is 5 μm by 20 μm. In order for the micro valve  30  to open, the deformation needs to be positive at the location of the opening in the microvalve seat interface  60 . The micro valve of this design is suitable for use in environments including pressures of up to and including 180 bar (greater than or exceeding 30 bar). 
       FIG. 8  shows curves of the deformation of the same type of cantilever beam  30  at the location of the opening in the microvalve seat interface  60  used in the discussion of  FIGS. 6 and 7  (mounted in the compressed fluid flow control system shown in  FIG. 1  and including 200 μm long, 30 μm wide bi-layer of 10 μm thick Aluminum (Al) and 10 μm thick silicon nitride (Si 3 N 4 )) as a function of the location of the microvalve seat  60  at 5 different loading pressures of 1 bar, 30 bar, 100 bar, 150 bar and 200 bar for a 200 degree temperature differential. The position of the opening for the data shown in  FIG. 8  is defined as the point of the opening farthest from the pivot point  0 . Thus for a 5 μm wide microvalve seat interface  60  the largest possible position of the opening would be 195 μm from the pivot point  0  for a 200 μm long beam. It is observed that moving point A closer to the pivot point  0  enables operation at higher pressures. For a pressure of 200 bar it is observed that this design will function as a valve if the position of the opening is less than 142 μm from the pivot point. Increasing the dimensions of the second portion of the cantilever beam results in lower maximum operating pressures for a given position of plane A. It is thus desirable that the length dimension of the second portion of the cantilever beam be less than 30% of the total length L. 
     The dynamics of thermally actuated cantilever beam microvalve operation depends on a number of time constants associated with various internal and external heat flows. The internal heat flows of the cantilever beam are driven by the temperature differential among layers. For the purpose of understanding the present invention, heat flow from a first layer to a second layer can be viewed as a heating process for the second layer and a cooling process for the first layer. For a tri-layer cantilever beam the middle layer can be viewed as establishing a time constant τ B  for heat transfer in both heating and cooling processes. 
     The time constant τ B  is approximately proportional to the square of the thickness of the middle layer and inversely proportional to the thermal conductivity of the materials used to construct this layer. The heat pulse input to the first layer should be shorter in duration than the heat transfer time constant τ B , otherwise the potential temperature differential and deflection magnitude will be dissipated by excessive heat loss through the central layer. 
     A second heat flow path, from the cantilevered element to the surroundings, is also present. The details of the external heat flows will depend importantly on the application of the thermal actuator. Heat can flow from the actuator to substrate, or other adjacent structural elements, by conduction. Since the actuator is operating in a compressed fluid, it will lose heat via convection and conduction to the fluid. Heat will also be lost via radiation. For purpose of understanding the present invention, heat lost to the surroundings can be characterized as a single external cooling time constant τ S  that integrates the many processes and pathways that are operating. 
     Another timing parameter of importance is the desired repetition period τ C  for operating the thermal actuator. Since the heat transfer time constant τ B  governs the time required for the cantilevered element to restore to a first position, it is preferred that τ B &lt;&lt;τ C  for energy efficiency and rapid operation. Uniformity in actuation performance from one pulse to the next will improve as the repetition period τ C  is chosen to be several units of τ B  or more. That is, if τ C &gt;5τ B  then the cantilevered element will have fully equilibrated and returned to the first or nominal position. If, instead τ C &lt;2τ B , then there will be some significant amount of residual deflection remaining when a next deflection is attempted and the microvalve will not close. 
     The time constant of heat transfer to the surround, τ S , can also influence the actuator repetition period τ C . For an efficient design, τ S  will be significantly longer than τ B . Therefore, even after the cantilevered element has reached internal thermal equilibrium after a time of 3 to 5τ B , the cantilevered element will be above the ambient temperature or starting temperature, until a time of 3 to 5τ S . A new deflection can be initiated while the actuator is still above ambient temperature. However, to maintain a constant amount of mechanical actuation, higher and higher peak temperatures for the layers of the cantilevered element will be required. Repeated pulsing at periods τ C &lt;3τ S  will cause continuing rise in the maximum temperature of the actuator materials until some failure mode is reached unless a heat sink is included in the design as a portion of the substrate. When a semiconductor or metallic material such as silicon is used for substrate, the indicated heat sink portion can be simply a region of the substrate designated as a heat sinking location. Alternatively, a separate material can be included within the substrate to serve as an efficient sink for heat conducted away from the cantilevered element at the anchor portion. 
     Another important aspect of the dynamic behavior of a thermally actuated microvalve is the flow of compressed fluid through the microvalve as a function of the deflection of the microvalve at the outlet port. The initial deflection of a cantilever beam creates a flow that is restricted by the dimensions of the outlet port and the magnitude of the deflection. The phenomenon of choked flow in compressed fluids occurs when the flow velocity through the outlet port of the microvalve reaches the sonic velocity. The mass flow rate of compressed fluid through the microvalve is a maximum under this condition. The pressure at the choke point is also fixed. As a result the unbalanced pressure across the cantilever beam will be less than when in the closed position. The cantilever beam will then deflect more than that expected from the initial unbalanced pressure across the cantilever beam. This is a novel and unanticipated feature of this invention. The amplification of deflection is a result of the initial deflection itself. The flow rate of the compressed fluid will thus depend on the restricting area of the opening at the outlet port. The total compressed fluid flow will thus be modulated by the frequency of operation of the microvalve. 
     Example 1 
     The operation of a 200 μm long by 30 μm wide tri-layer thermo-mechanical micro-valve designed according to the teachings of this invention was mathematically modeled. The tri-layer valve had a 7 μm thick silicon nitride (Si 3 N 4 ) layer sandwiched between two 7 μm thick aluminum layers. The part of the tri-layer valve in constant contact at the anchor was 20 μm long and it served as a heat sink. Also, the valve seat opening was 10 μm long by 20 μm wide and was located at 145 μm from the anchor. Initially, the valve was at 40 degree C. and 100 bar pressure in the high pressure chamber, forcing it in a closed position on the valve seat. Then a voltage pulse was applied to raise the temperature of the bottom aluminum layer 200 degree C. above the ambient (40 degree C) in 1 μsec. The solid curve in  FIG. 9  shows the calculated static deflection profile of the cantilever beam under these conditions. The pressure drop across the cantilever beam at the outlet port is calculated to be 46 bar for the choked flow condition. The dotted curve in  FIG. 9  shows the expected deflection profile of the cantilever beam under the choked flow condition. As seen in  FIG. 9  this results in about a 2 μm deflection above the valve seat due to the differential expansion between the bottom aluminum layer and the silicon nitride layer. The heated layer then conducted heat through the silicon nitride layer to the top aluminum layer and the temperature of the thermo-mechanical valve became more uniform. As shown in the dot-dashed curve of  FIG. 9 , when the temperature differential decreased to 57 degrees C, the stresses due to the differential expansion are sufficiently reduced and the thermo-mechanical valve is restored to its closed position. 
       FIG. 10  shows the peak temperature rise of the cantilever beam as a function of time for periodic actuation at 50 KHz. The data show that after a few such successive initial voltage pulses, the peak temperature rise of the cantilever beam becomes stable around 238 C above the ambient. For 50 KHz pulse repetition frequency, computed mass flow rate delivered through the micro-valve was about 20 mg/sec for compressed carbon dioxide in its supercritical state. Operation at lower frequencies such as 10 kHz will result in lower peak temperature rise of the cantilever beam microvalve. 
     Example 2 
     The operation of a 200 μm long by 30 μm wide bi-layer thermo-mechanical micro-valve designed according to the teachings of this invention was mathematically modeled. The bi-layer valve had 10 μm thick silicon nitride (Si 3 N 4 ) top layer and a 10 μm thick aluminum bottom layer. The part of the bi-layer valve in constant contact at the anchor was 20 μm long and it served as a heat sink. Also, the valve seat was 10 μm long by 20 μm wide and was located at 110 μm from the anchor. Initially, the valve was at 40 degree C. and 150 bar pressure in the high pressure chamber, forcing it in a closed position on the valve seat. Then a voltage pulse was applied to raise the temperature of the bottom aluminum layer 200 degree C. above the ambient (40 degree C) in 1 μsec. The solid curve in  FIG. 11  shows the calculated static deflection profile of the cantilever beam under these conditions. The pressure drop across the cantilever beam at the outlet port is calculated to be 69 bar for the choked flow condition. The dotted curve in  FIG. 11  shows the expected deflection profile of the cantilever beam under the choked flow condition. As seen in  FIG. 11  this results in about a 1.6 μm deflection above the valve seat due to the differential expansion between the bottom aluminum layer and the silicon nitride layer. The heated layer then conducted heat through the silicon nitride and the temperature of the thermo-mechanical valve became more uniform. As shown in the dot-dashed curve of  FIG. 11 , when the temperature differential decreased to 51 degrees C, the stresses due to the differential expansion are sufficiently reduced and the thermo-mechanical valve is restored to its closed position. 
       FIG. 12  shows the peak temperature rise of the cantilever beam as a function of time for periodic actuation at 50 KHz. The data show that after a few such successive initial voltage pulses, the peak temperature rise of the cantilever beam becomes stable around 280 C above the ambient. For 50 KHz pulse repetition frequency, computed mass flow rate delivered through the micro-valve was about 6 mg/sec for compressed carbon dioxide. 
     Table 2 below shows computational results of the microvalve operation described in Example 1 for different outlet port positions for a periodic actuation of 50 KHz. 
     
       
         
           
               
               
               
               
               
               
             
               
                 TABLE 2 
               
               
                   
               
               
                   
                 Outlet Port 
                   
                   
                   
                   
               
               
                   
                 Position 
                   
                   
                   
                 Max T 
               
               
                 H 
                 (μm from 
                 P 
                 Initial temp pulse, 
                 Flow_rate 
                 rise 
               
               
                 (μm) 
                 pivot) 
                 (bar) 
                 dT (deg C.) 
                 (mg/s) 
                 (deg C.) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 777 
                 80-90 
                 100 
                 200 
                 9.41 
                 350 
               
               
                 777 
                  90-100 
                 100 
                 200 
                 11.4 
                 330 
               
               
                 777 
                 110-120 
                 100 
                 200 
                 14.9 
                 275 
               
               
                 777 
                 120-130 
                 100 
                 200 
                 16.7 
                 260 
               
               
                 777 
                 130-140 
                 100 
                 200 
                 18.0 
                 240 
               
               
                 777 
                 145-155 
                 100 
                 200 
                 19.7 
                 235 
               
               
                 777 
                 160-170 
                 100 
                 200 
                 21.2 
                 250 
               
               
                 777 
                 180-190 
                 100 
                 200 
                 21.7 
                 260 
               
               
                 777 
                 185-195 
                 100 
                 200 
                 21.6 
                 270 
               
               
                   
               
            
           
         
       
     
     Two or more cantilever microvalves can also be placed in the same chamber described in  FIGS. 1 and 2 . Each microvalve would have its own outlet port so that each of the cantilevers could be controlled individually. A microfluidic device including arrays of microvalves as described in Examples 1 and 2, placed in a common chamber can be constructed into linear arrays with a center to center spacing of &lt;200 μm, and preferably 42 μm corresponding to a printing density of 600 dpi. 
     While the previous discussions have been described in terms of thermally actuated micro cantilever beams, it is known that the same underlying principles can also apply to piezoelectric cantilever beams. Systems that incorporate piezoelectric devices have been described, for example, by Kyser et. al. in U.S. Pat. No. 3,946,398; Zolten in U.S. Pat. No. 3,683,212; Stemme in U.S. Pat. No. 3,747,120; Howkins in U.S. Pat. No. 4,459,601; and Fischbeck in U.S. Pat. No. 4,584,590. Piezoelectric tri-morph actuation mechanisms and optimization of actuator dimensions have been described, for example, by Gemmen et al. in U.S. Pat. No. 7,159,841. Additionally, Kluge discloses a piezoelectrically actuated microvalve in U.S. Pat. No. 6,142,444. 
     The invention has been described in detail with particular reference to certain preferred embodiments thereof, but it will be understood that variations and modifications can be effected within the scope of the invention. 
     PARTS LIST 
     
         
           10  Uniformly loaded cantilever beam flow control system 
           20  Controller interface conduit 
           24  Controller 
           30  Bi-Layer cantilever beam microvalve 
           32  Cantilever second layer 
           34  Cantilever first layer 
           36  Electrode 
           38  Electrode surface of cantilever first layer 
           40  Electrode contact pads 
           50  Electrode gap 
           60  Microvalve seat interface 
           70  Microvalve enclosure 
           80  Compressed fluid inlet control valve 
           90  Compressed fluid source 
           100  Compressed fluid flow control system 
           110  Compressed fluid Inlet port 
           120  Cantilever electrode contact region 
           130  Low pressure outlet port 
           140  Microvalve enclosure base 
           150  Microvalve anchor 
           160  Microvalve seat 
           170  Unbalanced force region 
           180  Chamber 
           190  Tri-layer cantilever beam microvalve 
           192  Cantilever third layer 
           194  Cantilever second layer 
           196  Cantilever first layer 
           200  Microvalve enclosure top