Microvalve and mass flow meter using the same

Abstract

The present invention relates to the art of microvalves and provides a microvalve and a mass flow meter using the same. The microvalve includes a first substrate, a second substrate and an intermediate layer, the intermediate layer being disposed between the first substrate and the second substrate and including an array formed by a plurality of actuators, the actuators including a throttle hole having a throttle gas inlet and a throttle gas outlet, the throttle hole through which gas flows from the throttle gas inlet to the throttle hole and then from the throttle gas outlet to the second substrate, and a cantilever that moves relative to the throttle gas inlet, the cantilever adjusting the opening area of ​​the throttle gas inlet by adjusting the distance between the cantilever and the throttle gas inlet. The present invention improves the valve flux by adjusting the opening area of ​​the throttle gas inlet by moving the cantilever relative to the throttle gas inlet. The actuator array can achieve proportional control and diffuse gas discharge, or form a mass flow meter. Furthermore, the flow rate can be further improved by joining a plurality of microvalves together.

Description

[Technical Field]

[0001] This invention generally relates to the technical field of microvalves. More specifically, this invention relates to microvalves and mass flow meters using the same. [Background technology]

[0002] The structure of conventional microvalves, or micro-electromechanical system valves (MEMS valves), is similar to that of diaphragm valves (diaphragm / membrane valves). Figures 1A and 1B show schematic diagrams of conventional microvalves. As shown in Figures 1A and 1B, an operable diaphragm is provided at the top of the microvalve, and a valve seat is provided below the diaphragm. An actuator moves the diaphragm (or the diaphragm is also the actuator) upward to open the orifice, or downward to close the orifice. The flux size of the microvalve is determined by the circumference of the orifice multiplied by the stroke (displacement) of the diaphragm.

[0003] Conventional microvalves are typically manufactured using a base substrate (silicon or quartz glass), with channels etched into the substrate for horizontal gas or liquid flow, and a diaphragm and / or actuator bonded to the channels to form a complete microvalve. If the channels are complex or require deep etching, channels may be created in two separate substrates, which are then aligned and bonded to form the complete channels.

[0004] Due to the micron-level, and even nano-level, processing characteristics of MEMS processes, the thickness of the substrate used for processing is typically only 625 μm, the deposition thickness of lead zirconate titanate (PZT) is typically a maximum of 5 μm, the depth and hole diameter of deep groove etching do not exceed 1 mm, and the movement stroke on the diaphragm is typically on the micron scale (for example, the stroke of a 25 mm PZT ceramic cantilever beam is typically only 250 μm, and MEMS micro-nano structures can typically only achieve movement at the 10 μm level). In other words, conventional microvalves can only achieve flow control at the microliter level. Taking a 1 / 8 inch orifice as an example, if the orifice diameter is 1.78 mm and combined with a diaphragm with a stroke of 10 μm, the stroke would be 1.78 × 0.01 × 3.14 = 0.055892 mm 2 It can generate only the flux of 0.56 mm even when the diaphragm stroke reaches 100 μm. 2 It is possible to generate only the flux. Furthermore, in conventional technology, it remains difficult to realize a diaphragm with a 1 / 8-inch orifice and a 100 μm stroke, and typically the stroke of the diaphragm in a microvalve is only about 10 μm to 20 μm.

[0005] Therefore, there is a need to provide novel microvalves that can achieve a larger valve flux. [Overview of the Initiative]

[0006] To solve at least some of the above problems in the prior art, the microvalve according to the present invention is: A first substrate having a substrate gas inlet, wherein the gas flows from the substrate gas inlet to the intermediate layer, The device includes an intermediate layer disposed between the first substrate and the second substrate, which includes an array formed by a plurality of actuators, and a second substrate having a substrate gas outlet from which gas flows out, wherein the actuators are A throttle hole having a throttle gas inlet and a throttle gas outlet, wherein the gas flows from the throttle gas inlet into the throttle hole and then flows from the throttle gas outlet to the second substrate, The system includes a cantilever configured to be movable relative to the throttle gas inlet, which adjusts the opening area of ​​the throttle gas inlet by adjusting the distance between the cantilever and the throttle gas inlet.

[0007] In one embodiment of the present invention, the microvalve is The present invention further includes a housing that surrounds the first substrate, the intermediate layer, and the second substrate, and has a housing gas inlet and a housing gas outlet, and includes a metal housing, a ceramic housing, or a resin housing.

[0008] In one embodiment of the present invention, the microvalve is A throttle hole step connected to the second substrate, in which the throttle gas outlet is located, The device includes a throttle hole enclosure in which the throttle gas inlet is located, the first end of which is connected to the first substrate and the second end facing away from the first end is connected to the throttle hole step.

[0009] In one embodiment of the present invention, the substrate 1 is The throttle hole enclosure further includes a substrate step connected to the first end, wherein the substrate step and / or the throttle hole step are configured to suppress short-circuit airflow generated in the gap between the cantilever and the second substrate and / or the first substrate.

[0010] In one embodiment of the present invention, the cantilever has a wet material coating and / or The cantilever includes an electrostatically driven cantilever, an electromagnetically driven cantilever, a piezoelectrically driven cantilever, or an electrically heated cantilever.

[0011] In one embodiment of the present invention, the cantilever is configured to be horizontally movable relative to the throttle gas inlet, or The cantilever is configured to be vertically movable relative to the throttle gas inlet.

[0012] In one embodiment of the present invention, the microvalve is The system further includes an outer frame positioned around the intermediate layer to restrict airflow.

[0013] In one embodiment of the present invention, the throttle hole enclosure includes a first throttle gas inlet and a second throttle gas inlet facing away from the first throttle gas inlet. The cantilever includes a first cantilever configured to be movable relative to the first throttle gas inlet and a second cantilever configured to be movable relative to the second throttle gas inlet.

[0014] In one embodiment of the present invention, a grid is provided at one or more of the substrate gas inlet, substrate gas outlet, and throttle gas outlet to form a laminar flow component.

[0015] In one embodiment of the present invention, the cantilever is connected to one or more throttle holes.

[0016] In one embodiment of the present invention, a plurality of microvalves are configured to be joined together to improve flow rate.

[0017] In one embodiment of the present invention, the throttle port gas outlets of multiple actuators achieve diffused gas discharge by discharging gas individually or by combining them into multiple groups and then discharging the grouped gas.

[0018] In one embodiment of the present invention, the microvalve is The system further includes a control circuit connected to multiple actuators, each configured to control the opening degree of the multiple actuators.

[0019] Here, the term "opening degree" refers to the ratio at which the actuator is turned on and may be any numerical value between 0 and 100%.

[0020] In one embodiment of the present invention, the control circuit performs an operation of setting the flow rate Q that needs to be controlled, setpoint an operation of determining the maximum accurate measurement value max(Q ) of a single actuator, actr an operation of calculating the integer i = {Q / max(Q setpoint )}, actr an operation of turning on i actuators whose sum of flow rates is i × max(Q ), actr and an operation of turning on the (i + 1)-th actuator and setting the flow rate of the (i + 1)-th actuator to Q - i × Max(Q setpoint ) actr ) and is configured to execute.

[0021] In one embodiment of the present invention, the control circuit further when the flow rate of the (i + 1)-th actuator is lower than the threshold value, sets the flow rates of a total of j + 2 actuators from the (i - j)-th to the (i + 1)-th to (Q setpoint - j × max(Q actr )) / (j + 2) and is configured to execute the operation.

[0022] Also, another microvalve according to the present invention includes a first substrate having a substrate gas inlet through which gas flows from the substrate gas inlet to an intermediate layer, an intermediate layer disposed between the first substrate and a second substrate and including an array formed by a plurality of actuators, and a second substrate having a substrate gas outlet through which gas flows out, and the actuator A throttle hole having a throttle gas inlet and a throttle gas outlet, wherein the gas flows from the throttle gas inlet into the throttle hole and then flows from the throttle gas outlet to the second substrate, The system includes a diaphragm configured to control the opening degree of the throttle gas inlet.

[0023] In one embodiment of the present invention, the first substrate is configured to restrict airflow, and the second substrate has a substrate gas inlet and a substrate gas outlet, the gas flows from the substrate gas inlet to the intermediate layer, returns to the second substrate, and then flows out from the substrate gas outlet.

[0024] Furthermore, the mass flow meter according to the present invention is Microvalves and The microvalve includes a sensing member disposed on at least one of the plurality of actuators of the microvalve.

[0025] In one embodiment of the present invention, the sensing member includes a pressure sensor and a temperature sensor, and the microvalve, the pressure sensor and the temperature sensor form a pressure-type mass flow meter and / or The sensing member includes a heater and a temperature sensor, and the microvalve, heater, and temperature sensor form a thermal mass flow meter.

[0026] In one embodiment of the present invention, for choke flow, the flow rate Q passing through the i-th actuator on the microvalve is defined as the flow rate Q. i Adjust according to the following formula, Q i =C×P UPi Here, C represents the first correlation coefficient, and P UPi The first side pressure of the i-th actuator is shown, and the first correlation coefficient C is the opening area A of the i-th actuator. i It is positively correlated with and / or For non-choked flow, the flow rate Q passing through the i-th actuator on the microvalve is... i Adjust according to the following formula,

number

[0027] The present invention has at least the following beneficial effects. The microvalve according to the present invention includes an array formed by a plurality of actuators, and the valve flux can be effectively improved by adjusting the opening area of ​​the throttle gas inlet by moving the cantilever in the actuator relative to the throttle gas inlet. The plurality of actuators can form an actuator array, which can achieve proportional control and diffused gas discharge, or form a mass flow meter. Furthermore, the flow rate can be further improved by joining a plurality of microvalves together. [Brief explanation of the drawing]

[0028] To further illustrate the above and other advantages and features of each embodiment of the present invention, each embodiment will be described in more detail with reference to the accompanying drawings. Note that these drawings only show typical embodiments of the present invention and should not be considered to limit the scope of the invention. For clarity, identical or corresponding components are denoted by the same or similar reference numerals in the drawings.

[0029] [Figure 1A] A schematic diagram of a conventional microvalve is shown. [Figure 1B] A schematic diagram of a conventional microvalve is shown. [Figure 2] This shows a perspective view of a microvalve and its package housing according to one embodiment of the present invention. [Figure 3] A schematic diagram of a microvalve in one embodiment of the present invention is shown. [Figure 4] This shows a schematic perspective view of a microvalve in one embodiment of the present invention. [Figure 5] This shows a plan view of a microvalve in one embodiment of the present invention. [Figure 6] This shows a schematic diagram of an exploded view of a microvalve in one embodiment of the present invention. [Figure 7A] This shows a schematic diagram of the bottom of the first substrate in one embodiment of the present invention. [Figure 7B] A schematic diagram of the second substrate and throttle hole in one embodiment of the present invention is shown. [Figure 8A] This shows a plan view of the intermediate layer when the actuator in one embodiment of the present invention is turned on. [Figure 8B] This shows a plan view of the intermediate layer when the actuator in one embodiment of the present invention is turned off. [Figure 9] A schematic diagram of a microvalve having a double cantilever and a double opening in another embodiment of the present invention is shown. [Figure 10] A plan view of a microvalve having a double cantilever and a double opening in another embodiment of the present invention is shown. [Figure 11] This shows a schematic exploded view of a microvalve having a double cantilever and a double opening in another embodiment of the present invention. [Figure 12] This is a schematic diagram of the bottom of the first substrate in another embodiment of the present invention. [Figure 13] A schematic diagram of the second substrate and throttle hole of a microvalve having a double cantilever and double opening in another embodiment of the present invention is shown. [Figure 14] This diagram shows a schematic configuration of a microvalve in which the cantilever operates vertically, according to one embodiment of the present invention. [Figure 15A] This diagram shows a schematic of the intermediate layer of a microvalve in which the cantilever operates vertically, according to one embodiment of the present invention. [Figure 15B] This diagram shows a schematic of the intermediate layer of a microvalve in which the cantilever operates vertically, according to one embodiment of the present invention. [Figure 16A]This diagram shows a schematic representation of the airflow direction of a microvalve in which the cantilever operates vertically, according to one embodiment of the present invention. [Figure 16B] This diagram shows a schematic representation of the airflow direction of a microvalve in which the cantilever operates vertically, according to one embodiment of the present invention. [Figure 17] This diagram shows a schematic arrangement of sensors on a microvalve in one embodiment of the present invention. [Figure 18] A schematic diagram of a conventional thermal mass flow meter is shown. [Figure 19] This is a schematic diagram of the actuator structure on a die in one embodiment of the present invention. [Figure 20A] A schematic diagram of the grid below the cantilever in one embodiment of the present invention is shown. [Figure 20B] This shows a side view of the lower grid of the cantilever in one embodiment of the present invention. [Figure 21] This diagram shows a schematic of the control logic for an actuator array in one embodiment of the present invention. [Figure 22] This is a schematic diagram of a microvalve in another embodiment of the present invention. [Figure 23] This shows a schematic diagram of the airflow in an actuator according to one embodiment of the present invention. [Figure 24] A schematic diagram showing the changes in pressure and flow rate of a choke flow in one embodiment of the present invention is shown. [Modes for carrying out the invention]

[0030] Please note that the components in each drawing are exaggerated for illustrative purposes and are not necessarily accurate in scale. In each drawing, the same component or component with the same function is denoted by the same reference numeral.

[0031] In this invention, unless otherwise specified, "placed above," "placed above," and "placed above" do not exclude the case where an intermediate object exists between them. Furthermore, "...placed above or above" only indicates the relative positional relationship between two members, and in some cases, for example, after reversing the orientation of the product, it can be converted to "...placed below or below," and vice versa.

[0032] In this invention, each embodiment is merely for illustrating the technical means of the present invention and is not limiting.

[0033] In this invention, unless otherwise specified, the classifiers "one" and "1" do not exclude scenes with multiple elements.

[0034] Furthermore, for clarity and brevity, only some parts or components may be shown in the embodiments of the present invention, but those skilled in the art will understand that necessary parts or components can be added as needed for specific scenarios based on the teachings of the present invention. Also, unless otherwise specified, features of different embodiments of the present invention can be combined with each other. For example, a feature in a second embodiment may replace a corresponding feature or function in a first embodiment that is the same or similar, and the resulting embodiment will similarly be included within the scope of disclosure or description of this application.

[0035] Within the scope of this invention, expressions such as "same," "identical," and "equal" do not mean that the two numerical values ​​are absolutely equal, but rather allow for a certain reasonable error; in other words, these expressions also include "substantially the same," "substantially identical," and "substantially equal." By analogy, in this invention, terms indicating direction such as "perpendicular to" and "parallel to" similarly include the meanings of "substantially perpendicular" and "substantially parallel."

[0036] Furthermore, the step numbers of each method of the present invention do not limit the order in which the method steps are performed. Unless otherwise specified, the method steps may be performed in a different order.

[0037] The present invention will be further described below with reference to specific embodiments.

[0038] Figure 2 shows a perspective view of a microvalve and its package housing in one embodiment of the present invention. As shown in Figure 2, the microvalve is packaged inside a housing 201, and gas can flow in or out through vents in the housing 201, and the housing 201 can use common metal, ceramic, or resin packaging processes. The microvalve may include a plurality of actuators, including a first substrate 202, a second substrate 203, and an intermediate layer 204. The intermediate layer 204 is disposed between the first substrate 202 and the second substrate 203, and the first substrate 202 and the second substrate 203 are provided with intake holes and / or vent holes, and gas may flow in from the first substrate 202 or the second substrate 203, flow through the intermediate layer 204 and flow out from different sides of the second substrate 203 or the first substrate 202, or gas may flow in from the first substrate 202 or the second substrate 203, flow through the intermediate layer 204 and flow out from the same side of the first substrate 202 or the second substrate 203.

[0039] The intermediate layer 204 is provided with an orifice and a horizontally positioned cantilever, the cantilever also serving as the diaphragm in the microvalve, and the cantilever may be coated with a wetting material to protect it. An outer frame that restricts airflow may be provided around the intermediate layer 204. In the intermediate layer 204, the cantilever can move relative to the orifice to adjust the distance between the cantilever and the orifice, and further change the opening / flux of the orifice to achieve proportional control of the microvalve. A step may be provided near the first substrate 202 and the second substrate 203 of the orifice to reduce, and ultimately eliminate, the short-circuit airflow generated in the gap between the cantilever and the first substrate 202 and the second substrate 203. The cantilever may be an electrostatically driven cantilever, an electromagnetically driven cantilever, a piezoelectric driven cantilever, or an electrothermal driven cantilever.

[0040] Also, for better understanding, in FIG. 2 and other drawings of the specification, the curvature of the cantilever is exaggeratedly shown for the purpose of explaining the principle and may not be proportional to the actual situation.

[0041] FIG. 3 shows a schematic view of a microvalve in an embodiment of the present invention. FIG. 3 shows the structure of the microvalve with the package housing removed, hiding the outer frame disposed around the intermediate layer 204. As shown in FIG. 3, a plurality of pores 301 are provided in the first substrate 202 processed by the MEMS process, and a cantilever 302 is provided in the intermediate layer 204.

[0042] FIG. 4 shows a perspective schematic view of a microvalve in an embodiment of the present invention. FIG. 5 shows a plan view of a microvalve in an embodiment of the present invention. As shown in FIGS. 4 and 5, the intermediate layer 204 includes a plurality of actuators including a cantilever 302 and a throttle hole 401, and the throttle hole 401 includes a throttle hole gas outlet 4011 and an enclosure 4012 disposed around the throttle hole gas outlet 4011.

[0043] In the present invention, the microvalve may be a matrix array formed by a plurality of small microvalves (actuators). In the present invention, the microvalve may include n×m outlets in the outer frame, and each outlet corresponds to i (i = 1 or 2) throttle holes 401 respectively, so the microvalve can be regarded as an array of m×n×i actuators. In the packaging process, if the n×m outlets in the outer frame are not merged or merged into x×y outlets (x < m, y < n), the gas can be evenly discharged from the microvalve on the plane.

[0044] In this invention, a microvalve typically packages one die on a single wafer into a package. The packaged package may be connected to a Vacuum Coupling Radius Seal (VCR) fitting or surface mounted on a piping module. Since the die size is limited by the exposure area (short size) of the mask aligner, multiple dies may be packaged in a single package to increase the flow rate of the microvalve, and each die may be configured with an array of multiple actuators. The cantilever 302 of the actuator may be fixed at one or two points, and each cantilever 302 corresponds to one or more throttle holes 401. By providing a grid within the throttle holes 401, the Reynolds number of the throttle holes 401 can be reduced, and the throttle holes 401 can further constitute a laminar flow component.

[0045] Figure 6 shows an exploded schematic diagram of a microvalve in one embodiment of the present invention. As shown in Figure 6, the intermediate layer 204 includes a plurality of actuators, each actuator including a throttle hole 401 and a cantilever 302, and the first substrate 202 and the second substrate 203 are provided with pores 301, and the first substrate 202, the intermediate layer 204 and the second substrate 203 can be bonded together to form a microvalve.

[0046] Figure 7A shows a schematic diagram of the bottom of the first substrate in one embodiment of the present invention. Figure 7B shows a schematic diagram of the second substrate and throttle hole in one embodiment of the present invention. As shown in Figures 7A and 7B, the first substrate 202 may be provided with a first step 701, and the second substrate 203 may be provided with a second step 702. As the cantilever 302 moves, there is a gap between the cantilever 302 and the first substrate 202 and the second substrate 203, and a gap also exists between the cantilever 302 and the throttle hole 401. By setting the step higher than the gap in the cantilever 302, the gap between the cantilever 302 and the throttle hole 401 can be sealed. The first substrate 202 and the second substrate 203 may be a quartz substrate, a silicon substrate, an SOI substrate, or a silicon carbide substrate. Because the cantilever 302 may have deflection, the step located below the throttle hole 401 may be shallower than the step located above the throttle hole 401. The step also needs to have a certain height so that the airflow can flow into the throttle hole 401 along the upper or lower edge of the step and increase the flux.

[0047] Figures 8A and 8B show plan views of the intermediate layer in one embodiment of the present invention, when the actuator is turned on and when the actuator is turned off, respectively. As shown in Figures 8A and 8B, proportional control of the flux can be achieved by controlling the distance between the cantilever 302 and the throttle hole 401 during the movement of the cantilever 302. Flux (opening area) = circumference of throttle hole 401 × distance between the cantilever 302 and the throttle hole 401. After flowing through the throttle hole 401, the gas can flow out downwards along a 90-degree bend through the pores 301 on the second substrate 203. To maximize the flow rate of the microvalve, the maximum opening area of ​​each throttle hole 401 must be less than or equal to the area of ​​the corresponding gas-releasing pore 301, and the sum of the maximum opening areas of all throttle holes 401 must be less than the sum of the areas of all pores 301.

[0048] Figure 9 shows a schematic diagram of a microvalve having a double cantilever and double openings in another embodiment of the present invention. Figure 10 shows a plan view of a microvalve having a double cantilever and double openings in another embodiment of the present invention. As shown in Figures 9 and 10, a bidirectional opening is provided in the throttle hole 401 of the actuator, and a first cantilever 901 and a second cantilever 902 are provided at the two opening locations, respectively. In this embodiment, the throttle hole 401 may be formed by front and rear vertical baffle plates and upper and lower steps, and the flux of the throttle hole 401 is the sum of the fluxes of the two openings, and the sum of the fluxes of the bidirectional openings is less than or equal to the sum of the fluxes of the corresponding gas-releasing holes 301. The symmetry of the microvalve having a double cantilever and double openings is more preferable and is advantageous for integrated manufacturing using MEMS processes.

[0049] Figure 11 shows an exploded schematic view of a microvalve having a double cantilever and a double opening in another embodiment of the present invention. Figure 12 shows a schematic view of the bottom of the first substrate in another embodiment of the present invention. As shown in Figure 12, the bottom of the first substrate 202 of the microvalve having a double cantilever and a double opening may be provided with a first step 701 that shields the gap between the first cantilever 901 and the second cantilever 902 in the throttle hole 401 and the first substrate 202.

[0050] Figure 13 shows a schematic diagram of the second substrate and throttle hole of a microvalve having a double cantilever and double opening in another embodiment of the present invention. As shown in Figure 13, the throttle hole 401 is located on the second substrate 203, and a second step 702 is provided between the throttle hole 401 and the second substrate 203.

[0051] In this embodiment, the microvalve processing process may include the following steps.

[0052] The second substrate 203 and throttle holes 401 are formed in the oxide layer of the SOI wafer by an etching process.

[0053] A first cantilever 901 and a second cantilever 902 can be formed in the oxide layer of another SO1 wafer, and double-sided processing can be performed on the PZT layer or electrostatic actuator layer on the bimorph. Examples of processing methods for the actuator layer include chemical vapor deposition (CVD), reactive physical vapor deposition (RPVD), physical vapor deposition (PVD), and sol-gel method (SolgelJI).

[0054] The first substrate 202 can be configured on another SO1 wafer.

[0055] The above-mentioned SOI wafers can be doped with boron and thinned to a thickness of 100 μm to 200 μm. Furthermore, a low dielectric constant passivation layer (e.g., nitrogen-oxygen organic polymer) can be applied to the through-holes and the surface of each device by CVD or other methods to protect them and prevent corrosion of the devices and contamination by high-purity gases.

[0056] Figure 14 shows a schematic configuration of a microvalve with a vertically operating cantilever in one embodiment of the present invention. As shown in Figure 14, the cantilever is movable up and down, and gas flows in from above or below. Figures 15A and 15B show schematic diagrams of the intermediate layer of a microvalve with a vertically operating cantilever in one embodiment of the present invention. As shown in Figure 15A, the cantilever may be fixed on both sides. As shown in Figure 15B, the cantilever may be fixed on one side. The stroke of a cantilever fixed on one side is greater.

[0057] Figures 16A and 16B show schematic diagrams of the airflow direction of a microvalve with a vertically operating cantilever in one embodiment of the present invention. As shown in Figures 16A and 16B, the gas inlet may be located on the first substrate 202 or on the second substrate 203. In the embodiment shown in Figure 16A, both the gas inlet and gas outlet are located on the second substrate 203, which allows for both distribution of incoming gas and collection and focusing of outgoing gas, and the gas inlet and gas outlet passages are staggered or finger-staggered.

[0058] A microvalve with vertically operating cantilevers can achieve a packing density of approximately 2 / 3 in the X-axis direction and approximately 1 / 1 in the Y-axis direction, for a total packing density of approximately 50%. Assuming that gas can be discharged over 75% of the length in each Y-axis direction, with a width of 70 μm for each cantilever, a distance of 30 μm between cantilevers, and an average stroke of 5 μm (the stroke at the highest point of the cantilever may be 10 μm, and the lower flow channel cross-section may be approximately triangular). Assuming that the length and width of the die on the wafer are both 10 mm, an effective size of 7.5 mm can be obtained in the length direction of the die, and 100 rows of cantilevers may be provided. The total flux area of ​​the microvalve with vertically operating cantilevers is 7.5 mm × 0.005 × 100 × 2 = 7.5 mm 2 This may also be the case. That is, the flux area of ​​a 2cm x 1cm die may be equivalent to a 1 / 4 inch pipe, and the flux area of ​​a 2cm x 3cm die may be equivalent to a 3 / 4 inch pipe. Furthermore, since microvalves can withstand greater pressure drops and flow velocities than pipes, 1cm 2 or 2cm 2 The MEMS process area can meet the current application demand for proportional control valves (MFCs) in semiconductor devices.

[0059] Figure 17 shows a schematic diagram of the sensor arrangement on a microvalve in one embodiment of the present invention. A pressure-type mass flow meter can be formed by arranging pressure sensors at the gas inlet and gas outlet, and also by arranging a temperature sensor. A thermal-type mass flow meter can also be formed by providing a heater and thermometer in the throttle hole 401, in which case this throttle hole 401 may correspond to the thermal flow measurement passage in the thermal-type mass flow meter. Figure 18 shows a schematic diagram of a conventional thermal-type mass flow meter. As shown in Figure 18, measurement is performed in a bypass passage. In the embodiment of the present invention shown in Figure 17, the heater and thermometer may be arranged upstream of or within one throttle hole 401, and this throttle hole 401 corresponds to the measurement bypass in Figure 18. Laminar flow components can be formed by etching grids at the throttle hole 401, gas inlet, and gas outlet locations. In fact, in the embodiment of the present invention, because the size of the throttle hole 401 is sufficiently small, the flow path between the throttle hole 401 and the first substrate 202 and second substrate 203 can form a natural laminar flow component. Figure 20A shows a schematic diagram of the grid below the cantilever in one embodiment of the present invention. Figure 20B shows a side view of the grid below the cantilever in one embodiment of the present invention. As shown in Figures 20A to 20B, the grid below the cantilever can reduce the characteristic size of the conduit, reduce the Reynolds number, and form a laminar flow component (LFE), and as described above, laminar flow components can also be formed by adding grids in other intake circuits.

[0060] In embodiments of the present invention, by assembling and packaging multiple dies, it is possible to achieve increased flow rate and diffused gas discharge. Figure 19 is a schematic diagram of the actuator structure on a die in one embodiment of the present invention. As shown in Figure 19, a 4×2 actuator structure may be provided on one die, with four throttle holes 401 provided in each actuator, with bidirectional openings in the throttle holes 401, and cantilevers provided at each of the two openings. Assume that the length of the cantilevers is 2 mm and the distance between the cantilevers is 100 μm. A 10×100 actuator array can be constructed on a single 20 mm × 10 mm die, and by controlling each actuator, very accurate flow rate control can be achieved. In Figure 19, after four 2×2 dies are packaged, one larger mass flow meter is formed, i.e., a flow rate × 4 can be obtained. The gas outlets of each throttle hole do not need to be assembled (or assembled into several groups), and each gas outlet (or gas outlet of each group) can discharge gas independently, enabling independent and uniform gas discharge from the mass flow meter.

[0061] The area flux of the actuator is min(A). inlet ,A orifice ,A outlet ) depends, and here, A inlet This indicates the area of ​​the gas inlet of the actuator, A outlet This indicates the area of ​​the gas outlet of the actuator, A orifice This indicates the area of ​​the throttle hole. The total flux of the actuator array is determined by the area flux of the multiple actuators. inlet , A orifice , A outlet Since they are proportional to each other, A inlet , A orifice , A outlet and the total area A of the MEMS process total This can be determined by determining the ratio (i.e., the fill-in factor) of the die used in the MEMS process. total Once the ratio between feature sizes is determined, the actuator Ainlet , A orifice and A outlet By determining the following, the flux area of ​​the actuator array can also be determined. Once the flow velocity, temperature, and pressure are determined, the flow rate of the actuator array can be determined.

[0062] Below, we can calculate the actuator's gas inlet and outlet as rectangles, and then set factor = 3.14 / 4, taking into account the rounded corners of the gas inlet and outlet.

[0063] A inlet =W inlet ×L inlet , A outlet =W outlet ×L outlet , A total = W × L, where L inlet , W inlet L indicates the length and width of the gas inlet of the actuator. outlet , W outlet The length and width of the actuator's gas outlet are indicated, while L and W indicate the length and width of the die.

[0064] Regarding actuators having a single cantilever and a single opening, A orifice =2 × (L open +H open )×Δ open For an actuator that satisfies the following conditions and has a double cantilever and a double opening, A orifice =4 × (L open +H open )×Δ open Satisfying the condition, where L open H open Δ indicates the length and height of the throttle opening. open This indicates the distance the cantilever travels. open , L inlet L outlet It approximates A. orifice is A inlet and A outlet It is necessary to approximate H open Assuming that we can ignore A orifice = 2 × L open ×Δopen It satisfies the condition.

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[0065] Typically, the distance Δ the cantilever travels. open Since it's not that big, W outlet , W inlet Approximately 2 times or 4 times Δ open This improves the filling rate, and a more precise method is further H open The calculation involves determining a value slightly smaller than the height the cantilever moves. Furthermore, as can be seen from the above calculation, when the sizes of the throttle hole, gas inlet, and gas outlet are matched, the conventional microvalve has a significant limitation on the flux Δ open The effect of this invention on the flux is not significant.

[0066] In one embodiment of the present invention, the height of the cantilever is close to the thickness of the SOI wafer, approximately 80 μm to 100 μm, the length is approximately 200 μm to 3 mm, and the width is approximately 20 μm to 50 μm, Δ open The size ranges from 1.5 μm to 22 μm. open The larger the value, the more advantageous it is for machining the throttle hole, and the more the filling rate can be improved.

[0067] As mentioned above, A after optimization inlet , A orifice , A outlet Because their sizes are similar, A inlet , A outlet When calculating the filling rate, A totalcan be determined. In the length direction of the die, the orthographic projections of the gas inlet and the gas outlet do not overlap. After removing the enclosure of the throttle hole, the filling rate in the optimized length direction of the die is about 1 / 3. In the width direction of the gas outlet and the die, the sum of the width of the cantilever, the enclosure of the throttle hole, and Δ open or the sum of the widths of two cantilevers and 2 times Δ open can achieve a filling rate of 2 / 5. Furthermore, when adding other filling rates (such as chamfers) of 2 / 3, the total filling rate is 1 / 3×2 / 3×2 / 5 = 8.9%. Therefore, the size of the flow area in a 30mm 2 die is larger than that of a 1 / 8-inch pipeline, and the size of the flow area in a 250mm 2 die is larger than that of a 1 / 4-inch pipeline. Also, by joining the dies, a larger flow rate can be realized. Compared with conventional pipelines, the microvalve according to the present invention can withstand higher flow velocities. Usually, the flow velocity of gas in a pipeline is 12m / s to 15m / s. If the flow velocity is tripled, that is, if the flow velocity of the gas is increased to 30m / s to 45m / s, the flow area in a 250mm 2 die may be not less than that of a 3 / 8-inch pipeline.

[0068] In the present invention, a plurality of actuators can form an actuator array. FIG. 21 shows a schematic diagram of the control logic of an actuator array in an embodiment of the present invention. As shown in FIG. 21, a plurality of actuators are connected to a digital control circuit through metal through-holes or bonded to a substrate provided with a control circuit, and the control circuit can control the opening degree of any actuator. In an embodiment of the present invention, the number of actuators turned on by a bonding bit line can be selected to more accurately control the flow rate.

[0069] Taking an actuator array with 100 actuators as an example, the actuators can be arranged so that the flow rate when each actuator is fully turned on approaches the same, meaning that a 1% increase in flow rate can be achieved when a single actuator is fully turned on. Assuming that the proportional opening accuracy of a single actuator itself is 5%, the actuator array can achieve a control accuracy of 0.05%.

[0070] Furthermore, by arranging actuators redundantly in the actuator array, the service life can be extended. In one embodiment of the present invention, 120 actuators are arranged, and each actuator has multiple throttle holes and gas outlets. Each gas outlet has an independent bit line for selecting its operating state. When the total flux of the actuator array is calibrated to 100 actuators, the flux of the actuator array is 120% of the nameplate value. If an actuator fails, the valve array can continue to obtain sufficient flux by accessing a new backup actuator via the circuit, effectively extending the service life of the equipment. In addition, the total number of on / off cycles and total stroke of each actuator can be recorded by the firmware. The service life of an actuator is related to the number of on / off cycles, and recording the number of valve openings and closings is a method for determining its service life loss. Alternatively, the stroke (distance) can be recorded, and in the present invention, the excitation voltage (voltage excitation) or excitation current (current excitation) can be integrated with respect to time, and the temperature of the electric thermo actuator read for a thermal MEMS actuator can be integrated. In operation, by preferentially turning on the actuator with the lowest integrated value, the losses of each actuator can be equalized, thereby avoiding prematurely reaching the designed service life due to excessive wear on individual actuators.

[0071] A proportional valve refers to a valve in which a valve control factor such as pressure or flow rate is proportional to the input signal or shows a high linear relationship. For example, a valve driven by a piezoelectric actuator generally has phenomena such as creep and hysteresis loop in the piezoelectric actuator, and has low linearity. A common method is to attach a piezoelectric sensor to the side of the actuator to measure the deformation of the actuator and form a closed-loop control to ensure linearity and achieve proportional control. Multiple actuators have more or less a certain linearity problem.

[0072] Conventionally, it has been difficult to measure the operating distance of a cantilever and diaphragm actuator. Therefore, the linearity of valve opening control is low, and it is difficult to improve the accuracy of flow control. In an embodiment of the present invention, the number of actuators turned on by a bonding bit line can be selected to more accurately control the flow rate. Taking an actuator array having 100 actuators as an example, the actuators can be arranged so that the flow rates when each actuator is fully turned on approach the same, that is, when a single actuator is fully turned on, a 1% increase in flow rate can be realized. Assuming that the accuracy of the proportional opening of a single actuator itself is 5%, the actuator array can obtain a control accuracy of 0.05%.

[0073] In an embodiment of the present invention, the process of flow control includes setting the flow rate Q to be controlled, determining the maximum accurate measurement value that a single actuator can drive as max(Q), calculating the integer of i = {Q / max(Q)}, turning on i actuators whose sum of flow rates is i×max(Q), turning on the (i + 1)-th valve, and setting the flow rate of the (i + 1)-th actuator to Q - i×Max(Q), which may be included. setpoint to set, and determining the maximum accurate measurement value that a single actuator can drive as max(Q actr ), calculating the integer of i = {Q setpoint / max(Q actr ), turning on i actuators whose sum of flow rates is i×max(Q actr ), turning on the (i + 1)-th valve, and setting the flow rate of the (i + 1)-th actuator to Q setpoint -i×Max(Q actr ), which may be included.

[0074] If the flow rate of the (i+1)th actuator is lower than the threshold, the flow rates of the (i-2nd), (i-1st), (ith), and (i+1th)th actuators are set to (Q setpoint -i × max(Q) actr ) + 3 × max(Q actr )) / 4 simultaneously, or further set the flow rate of the ijth, i-j+1th, ...ith, i+1th actuators, totaling j+2 actuators, to (Q setpoint -j × max(Q) actr It can be set to )) / (j+2).

[0075] In one embodiment of the present invention, multi-zone pressure control is added, and more pressure sensors are attached to the actuator (for thermal MFCs, a heater and corresponding temperature sensors must be added accordingly), allowing for more precise control of the flow rate by having each group of sensors independently detect the pressure (and temperature) in each region.

[0076] In one embodiment of the present invention, the total area of ​​three cantilevers, each with a length of 1 mm and a width of 100 μm, is 0.3 mm². 2 Therefore, the arch opening of the cantilever is simplified so that the cantilever is lifted horizontally by 10 μm. As can be seen from the calculation, when the pressure difference between the inlet and outlet is 1 bar, the amount of air that can pass through is 1.0516903e~5 kg / s, which is equivalent to approximately 524 ml / min of air (different gas types, different densities, different flow rates at the same operating pressure), i.e., 0.3 mm 2 This valve is designed to handle a flow rate of 500 sccm and has an area of ​​10 mm². 2 The valve may accommodate a flow rate of 16 slm (100 actuators) and have an area of ​​100 mm². 2 The valve may accommodate a flow rate of 160 slm (1000 actuators).

[0077] In another embodiment of the present invention, the total area of ​​three cantilevers, each 1 mm in length and 100 μm in width, is 0.3 mm². 2The arch opening of the cantilever is 15 μm. As can be seen from the calculation, when the inlet / outlet pressure difference is 1 bar, the passable air volume flow rate is 4.41 × 10⁻¹⁰ -6 m 3 This is equal to / s, which is equal to 264.6 sccm, i.e., 0.3 mm 2 This valve is designed to handle a flow rate of 264 sccm and has an area of ​​10 mm². 2 The valve is compatible with a flow rate of 8.7 slm (100 actuators) and has an area of ​​100 mm². 2 The valve is compatible with a flow rate of 87 slm (1000 actuators).

[0078] Figure 22 is a schematic diagram of a microvalve in another embodiment of the present invention. As shown in Figure 22, the microvalve has an actuator array formed by 2x2 actuators, the actuator array including circular diaphragms 2201 and corresponding throttle holes, each diaphragm 2201 may be driven by piezoelectricity or by other means. Each diaphragm 2201 may correspond to one or more throttle holes (for example, in Figure 22, one diaphragm 2201 corresponds to one throttle hole), and if each diaphragm 2201 corresponds to multiple throttle holes, the flux of a single diaphragm can be increased. The diaphragms 2201 are connected upstream and downstream of the throttle holes, and the total flow rate of the microvalve is Q total =ΣQ i Satisfying Q i This indicates the flow rate of the i-th actuator.

[0079] As described above, in the embodiments of the present invention, a mass flow meter can be formed by arranging a pressure sensor, a temperature sensor, a heater, and another temperature sensor in a microvalve. In the mass flow meter, the flow rates passing through different actuators may be calculated using different calculation methods depending on whether the airflow is a choke flow or not.

[0080] The choke phenomenon refers to the phenomenon where, when the flow velocity at a certain cross-section of a pipe reaches the speed of sound, the flow velocity, pressure, and flow rate of the airflow ahead of the sound-speed cross-section remain unchanged regardless of how much the pressure outside the pipe outlet decreases. Choke flow is easily formed in many situations, such as the startup choke in a supersonic wind tunnel (see Wind Tunnel), the intake choke in an aircraft, friction tube choke, and heated tube choke.

[0081] Taking choking in an aircraft's air intake as an example, if the Mach number Ma00 < 1 of the airflow far ahead of the intake, the airflow velocity ahead of the intake increases, the flow velocity in the throat within the inlet increases, and the flow rate increases. If the Mach number Ma00 = 1 in the throat, even if the airflow velocity ahead of the intake increases, the flow rate does not increase, and only a supersonic flow and shock wave appear after the throat. If the Mach number Ma00 > 1 of the airflow far ahead, the supersonic airflow flows directly into the intake without any turbulence in front of the inlet. If the throat area is sufficiently large and all the incoming gas can pass through, the intake is not choked. If the throat area is too small and the flow rate that can pass through is less than the flow rate that directly enters, the throat is choked, gas accumulates in front of the throat, the pressure increases, a separation shock wave is formed in front of the inlet, some excess airflow overflows from the outlet, and a supersonic region and shock wave appear after the throat. A choke in an aircraft's air intake increases the drag the aircraft experiences and significantly reduces engine thrust.

[0082] Figure 23 shows a schematic diagram of the airflow in an actuator in one embodiment of the present invention. To ensure clarity, Figure 23 merely illustrates the airflow direction and pressure in the actuator and does not represent the actual structure of the actuator. As shown in Figure 23, for a compressible fluid, if the pressure P1 at the gas inlet of the actuator is kept constant and the pressure P2 at the gas outlet gradually decreases, the mass flow rate flowing through the actuator gradually increases to its maximum value, and in this case, the further decreasing P2 flow rate also stops increasing. This situation is called choke flow. To form choke flow, it is usually necessary to have P1 ≥ 2P2 (the specific ratio is related to the specific heat of the gas), in which case the flow rate passing through the actuator is related only to P1 and is directly proportional to the absolute value of P1.

[0083] Figure 24 shows a schematic diagram of the pressure and flow rate changes in a choke flow in one embodiment of the present invention. The choke point of the fluid is determined by the liquid pressure recovery factor F L And the critical differential pressure ratio coefficient X when there is no gas connecting pipe T Determined by the process, the liquid is formed by vapor, and the gas reaches the speed of sound at the contraction neck. The choke critical pressure can be calculated using the following formula.

number

[0084] Choke critical pressure P in actuator choked The ratio of to P1 can be expressed by the following formula.

number

number

[0085] For air, the critical pressure ratio can be calculated using the following formula.

number

[0086] The mass flow rate of a choke flow passing through an actuator, i.e., a sonic flow whose minimum pressure is equal to the critical pressure, can be expressed by the following equation.

number

[0087] For non-choke flow, the pressure function upstream and downstream of the actuator is:

number

number

number

[0088] In non-choked flow, the flow rate is limited by the speed of sound at the actuator outlet, and the upstream pressure P UP After that is determined, flow rate Q i This is directly proportional to the orifice area A in non-choke flow. By arranging multiple actuators 402i, the upstream pressure P of the actuators 402i can be controlled. UPi By maintaining it nearly constant, the impact on back pressure can be minimized. When the upstreams of multiple actuators 402i are connected to each other, and the flow rate (flow velocity) is large and the pipe diameter is small, a differential pressure Δ(P) can be maintained between the actuators. UPi ,P UPi+1 )=v 2 fLρ / 2D is generated. By adjusting the actuator according to the present invention, P UPi Without substantially changing the orifice area A, the differential pressure between the upstream parts of multiple actuators 402i is received. i By fine-tuning, it is possible to achieve accurate proportional control without the need to install a pressure control valve. In pressure flow control equipment, if the opening area of ​​the MFC is constant and the downstream pressure is constant, P UPi The flow rate needs to be controlled by increasing P. If the flow rate proportionality changes, UPi As Q increases, i It will also increase.

[0089] Regarding the choke flow, Q i When it doubles, P UPi It also doubles, and typically, in this case, the flow rate Q in other actuators. j P decreases UPj P also decreased,UPi and P UPj Because these factors are interrelated, back pressures can interfere with each other, leading to contradictions and over-limitations. If the flow rate difference is too large, precise control becomes difficult. The same applies to non-choked flows.

[0090] If the airflow through actuator 402i is a choked flow, then the flow rate Q in actuator 402i i =C×P UPi Therefore, C exhibits the first correlation coefficient and is positively correlated with the opening area of ​​the i-th actuator.

[0091] While various embodiments of the present invention have been described above, it should be understood that these are merely illustrative and not limiting. It will be apparent to those skilled in the art that various combinations, modifications, and alterations can be made without departing from the spirit and scope of the invention. Therefore, the scope and width of the invention disclosed herein should not be limited by the exemplary embodiments disclosed above, but should be defined solely by the appended claims and their equivalents.

Claims

1. A first substrate having a substrate gas inlet, wherein gas flows from the substrate gas inlet to an intermediate layer, An intermediate layer is disposed between the first substrate and the second substrate and includes an array formed by a plurality of actuators, A second substrate having a substrate gas outlet from which gas flows out, The actuator is A throttle hole having a throttle gas inlet and a throttle gas outlet, wherein the gas flows from the throttle gas inlet into the throttle hole and then flows from the throttle gas outlet to the second substrate, A cantilever configured to be movable relative to the throttle gas inlet, the cantilever adjusting the opening area of ​​the throttle gas inlet by adjusting the distance between the cantilever and the throttle gas inlet, A microvalve characterized by the following features.

2. The first substrate, the intermediate layer, and the second substrate are surrounded by a housing which has a housing gas inlet and a housing gas outlet, and the housing further includes a metal housing, a ceramic housing, or a resin housing. The microvalve according to feature 1.

3. The throttle hole is, A throttle hole step connected to the second substrate, in which the throttle gas outlet is located, A throttle hole enclosure is provided, the first end of which is connected to the first substrate and the second end facing away from the first end is connected to the throttle hole step, and the throttle gas inlet is located therein. The microvalve according to feature 1.

4. The first substrate is, The throttle hole enclosure further includes a substrate step connected to the first end, The substrate step and / or the throttle hole step are configured to suppress short-circuit airflow generated in the gap between the cantilever and the second substrate and / or the first substrate. The microvalve according to feature 3.

5. The cantilever has a wet material coating and / or The cantilever includes an electrostatically driven cantilever, an electromagnetically driven cantilever, a piezoelectrically driven cantilever, or an electrically heated cantilever. The microvalve according to feature 1.

6. The cantilever is configured to be horizontally movable relative to the throttle gas inlet, or The cantilever is configured to move vertically relative to the throttle gas inlet. The microvalve according to feature 1.

7. Further including an outer frame positioned around the intermediate layer to restrict airflow, The microvalve according to feature 1.

8. The throttle port enclosure includes a first throttle gas inlet and a second throttle gas inlet facing the first throttle gas inlet. The cantilever includes a first cantilever configured to be movable relative to the first throttle gas inlet, and a second cantilever configured to be movable relative to the second throttle gas inlet. The microvalve according to feature 3.

9. A grid is provided at one or more of the substrate gas inlet, substrate gas outlet, and throttle gas outlet to form a laminar flow component. The microvalve according to feature 1.

10. The cantilever is connected to one or more throttle holes. The microvalve according to feature 1.

11. Multiple microvalves are configured to be joined together to improve flow rate. The microvalve according to feature 1.

12. The throttle gas outlets of multiple actuators achieve diffused gas discharge by discharging gas individually or by combining gas into multiple groups and then discharging the gas as a group. The microvalve according to feature 1.

13. The control circuit further includes a control circuit connected to a plurality of actuators, each configured to control the opening degree of the plurality of actuators. The microvalve according to feature 1.

14. The aforementioned control circuit is The flow rate that needs to be controlled is Q ｓｅｔｐｏｉｎｔ The actions to be set, The maximum accurate metering value of a single actuator is max(Q). ａｃｔｒ The action that determines as, i = {Q ｓｅｔｐｏｉｎｔ / max(Q ａｃｔｒ The operation of calculating an integer in )}, The sum of the flow rates is i × max (Q) ａｃｔｒ The operation of turning on i actuators, Turn on the (i+1)th actuator and set the flow rate of the (i+1)th actuator to Q ｓｅｔｐｏｉｎｔ -i × Max (Q) ａｃｔｒ The actions to be set to ) and configured to perform, The microvalve according to feature 13.

15. The control circuit further, If the flow rate of the (i+1)th actuator is lower than the threshold, then the (i-j)th and (i-j+1)th actuators... ,..., the flow rates of the j + 2 actuators of the i-th and i + 1-th are set to (Q ｓｅｔｐｏｉｎｔ - j × max(Q ａｃｔｒ )) / (j + 2) and configured to execute an operation The microvalve according to feature 14.

16. A first substrate having a substrate gas inlet, wherein the gas flows from the substrate gas inlet to the intermediate layer, An intermediate layer is disposed between the first substrate and the second substrate and includes an array formed by a plurality of actuators, A second substrate having a substrate gas outlet from which gas flows out, The actuator is A throttle hole having a throttle gas inlet and a throttle gas outlet, wherein the gas flows from the throttle gas inlet into the throttle hole and then flows from the throttle gas outlet to the second substrate, A diaphragm configured to control the opening degree of the throttle gas inlet, A microvalve characterized by the following features.

17. The first substrate is configured to restrict airflow, The second substrate has a substrate gas inlet and a substrate gas outlet, The gas flows from the substrate gas inlet to the intermediate layer, returns to the second substrate, and then flows out from the substrate gas outlet. The microvalve according to feature 1 or 16.

18. A microvalve according to any one of claims 1 to 17, The microvalve includes a sensing member disposed in at least one of the plurality of actuators, A mass flow meter characterized by the following features.

19. The sensing member includes a pressure sensor and a temperature sensor, and the microvalve, the pressure sensor and the temperature sensor form a pressure-type mass flow meter and / or The sensing member includes a heater and a temperature sensor, and the microvalve, heater, and temperature sensor form a thermal mass flow meter. The mass flow meter according to feature 18.

20. Regarding choke flow, the flow rate Q passing through the i-th actuator on the microvalve is... ｉ Adjust according to the following formula, Q ｉ =C×P ＵＰｉ Here, C represents the first correlation coefficient, and P ＵＰｉ The first side pressure of the i-th actuator is shown, and the first correlation coefficient C is the opening area A of the i-th actuator. ｉ It is positively correlated with and / or For non-choked flow, the flow rate Q passing through the i-th actuator on the microvalve is... ｉ Adjust according to the following formula, [Math 1] Here, C' represents the second correlation coefficient, which is a constant, and A ｉ This indicates the opening area of ​​the i-th actuator, and P ＤＯＷＮｉ θ represents the pressure on the second side of the i-th actuator, R represents the ubiquitous gas constant, T represents the temperature, M represents the molecular mass, and γ represents the specific heat ratio. The mass flow meter according to feature 19.

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