- Email: [email protected]
Gas flow in constriction microdevices
Sensors and Actuators 83 Ž2000. 277–283 www.elsevier.nlrlocatersna
Gas flow in constriction microdevices Xinxin Li b
a,b
, Wing Yin Lee a , Man Wong b, Yitshak Zohar
a,)
a Department of Mechanical Engineering, Hong Kong UniÕersity of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China Department of Electrical and Electronic Engineering, Hong Kong UniÕersity of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China
Received 7 June 1999; received in revised form 20 October 1999; accepted 25 October 1999
Abstract Constriction devices contain an element inserted into the fluid stream, which either changes the local streamwise distribution of flow area or applied frictional resistance to the flow. Two such devices: a micro orifice plate and a micro Venturi tube have been successfully fabricated for the study of fundamental flow phenomena in microdomains. Each device was integrated with a set of pressure sensors, and fabricated using standard micromachining techniques. Nitrogen gas was passed through the microdevices under inlet pressure up to 50 psi. Mass flow rate was first measured as a function of the overall pressure drop, and compared with results for a straight microchannel. Then, the detailed pressure distribution along each device was measured to understand the flow pattern around the flow obstruction. The results demonstrate that flow separation may occur in a microchannel flow with a very small Reynolds number. It is very possible that a micro vortex, on the order of 10 mm in size, can develop upstream and downstream of the obstruction. q 2000 Elsevier Science S.A. All rights reserved. Keywords: Microfluidics; Orifice plate; Venturi tube; Micro constrictions; Flow separation
1. Introduction The field of MEMS is expanding rapidly, and new potential applications are continuously being discovered. Inevitably, these microdevices will include fluid flows either in a primary or in a secondary role. Since the ability to fabricate MEMS is relatively new, it is not surprising that very little is known about the flow of gases and liquids in such minute passages. The physics of fluid flows in microdomains is most likely different from flows in macrodomains, for which a widely accepted mathematical model exists, i.e., Navier–Stokes equations. The issues to be addressed include: the determination at what length scale the continuum assumption breaks down; the modification of the present theories to account for non-continuum effects; and the assessment to what extent the phenomena such as flow separation, transition to turbulence and compressible effects Žshock waves. still occur in microdomains w1x. Flow through a straight channel is the simplest but most common configuration in microfluidic systems. Microchannels with integrated pressure sensors were fabricated to study the flow field w2,3x. The measured mass ) Corresponding author. Tel.: q852-2358-7194; fax: q852-2358-1543. E-mail: [email protected]
flow rate and pressure distributions indicated the development of slip flow conditions. This flow field, however, presents a simple balance between pressure gradient and wall shear stress. Constriction devices, on the other hand, contain an element inserted into the fluid stream. Such an element, e.g., an orifice plate, either changes the local streamwise distribution of flow area or presents additional resistance to the flow, which can result in flow separation. Macro flow fields associated with separation and reattachment have received significant attention because of their importance in many engineering applications w4x. However, due to the complicated nature of the phenomenon, similar studies in microdevices have yet to be carried out. In all viscous flows the primary control parameter is the Reynolds number, Re s ULrn , where U is a velocity scale, L a characteristic length scale and n the fluid kinematic viscosity w5x. For Re 4 1, the viscous forces can often be neglected and the flow outside the boundary layer is considered to be inviscid. Both viscous and inertia forces are important when Re ; 1. On the other hand, for Re < 1, inertia forces are negligible resulting in a viscous-dominated, creeping flow, often called Stokes flow. A characteristic of rounded bodies in creeping flow is smooth streamlines near their surface with no separation. However, bodies with sharp corners or projecting ap-
0924-4247r00r$ - see front matter q 2000 Elsevier Science S.A. All rights reserved. PII: S 0 9 2 4 - 4 2 4 7 Ž 9 9 . 0 0 3 0 8 - 8
278
X. Li et al.r Sensors and Actuators 83 (2000) 277–283
pendages do show flow separation. A unique case of creeping flow is the flow between two parallel plates separated by a narrow gap, h. This flow, often called Hele–Shaw flow, is characterized by the reduced Reynolds number, ReU s ŽULrn .Ž hrL. 2 < 1, where L is the scale of a body inserted between the plates. Although the flow is highly viscous, the resulting pattern of streamlines around a body with sharp corners is similar to that in potential flow about the same shape with no separation w6x. In macro-scale flows, creeping flow is usually associated with low velocity and a length scale of order one. In micro-scale flows, on the other hand, the length scale is very small while the velocity can be of order one. Thus, flow in a microsystem, where a sharp-cornered obstacle is inserted between two walls separated by a very narrow gap, presents an intriguing case. Inherently, the Reynolds number is very small since any length scale is very small. However, the reduced Reynolds number is also very small since the height of a microchannel can be smaller than any other length scale. Thus, it is not clear whether the flow around the sharp corners is attached, like Hele–Shaw, or separated, like two-dimensional Stokes flow. Two such devices with sharp corners are a Venturi tube or an orifice plate. The Venturi tube has a shape that attempts to mimic the flow pattern through a streamlined obstruction, while the orifice plate is basically a back-to-back abrupt contraction and abrupt expansion. At present, it is still difficult to conduct flow visualizations in microsystems, and measurement of the pressure distribution is the only alternative to investigate the flow pattern. Hence, in this work, microchannels with orifice- and Venturi-like constrictions have been integrated with pressure sensors allowing a detail study of the flow field in the vicinity of the constriction elements.
2. Design and fabrication The microdevices were fabricated on silicon substrates. Either the orifice- or the Venturi-element is located at the center of a microchannel Ž1 mm high, 40 mm wide and
Fig. 2. Close-up view of the orifice plate located at the channel center.
4000 mm long., as shown in Fig. 1. The orifice ŽFig. 2. is realized by two constrictions, each 10 mm wide and 10 mm long. The Venturi ŽFig. 3. is similar except for the side walls being slanted at 458 rather than 908. The minimum cross-section area in each device is 1 = 20 mm2 . In order to provide reference data, a straight microchannel with identical dimensions, but without any obstruction element, was fabricated following an identical process flow. Pressure sensors are sparsely distributed along the straight sections of the microchannel for reference, and densely around the constriction element. They are used for detail measurement of the pressure distribution along and at the center of the microchannel. The pressure is measured at the side of the channel, and we assume that it is constant over the thickness. Along the straight portions of the microchannel, far from the inletroutlet and constrictions regions, the pressure is assumed to be constant over the width as well since the aspect ratio is large Žabout 1:40.. The microchannels integrated with pressure microsensors were fabricated using surface micromachining techniques, while the inlet and outlet were bulk micromachined. The ceiling of the microchannel was made of transparent low-stress silicon nitride film, 1 mm thick, to allow flow visualization in future studies.
Fig. 1. A photograph of an integrated microdevice.
X. Li et al.r Sensors and Actuators 83 (2000) 277–283
Fig. 3. Close-up view of the Venturi tube located at the channel center.
Schematic cross-sections of the main fabrication steps are shown in Fig. 4. The initial substrate is a Ž100. double-polished, 4-in. Si-wafer. A 0.8-mm thick thermal silicon dioxide was grown and patterned to form the channel and sensor chambers. This was followed by an APCVD deposition and patterning of a 0.25-mm thick PSG film for fast sacrificial-layer etching. The phosphorous content in the PSG determines the sacrificial layer etching rate, i.e., the higher the phosphorous concentration, the faster the etch rate w7x. In the present work, the phosphorous content was about 6%. The pattern of the PSG layer is similar to that of the oxide layer, except for the distributed pads along the sides of the patterns to be used as etching holes. Next, the structural layer of 1 mm, low-stress nitride was LPCVD deposited to form the channel walls and ceiling as well as the sensor membrane ŽFig. 4a.. Anisotropic etching was used to form the inletroutlet holes from wafer backside, using the oxidernitride double
279
layer as an etch mask. Following the opening of the etching holes, the sacrificial layer was etched in 49% HF ŽFig. 4b.. This step was very critical as the release time could not be too long, since concentrated HF also etches silicon nitride at a rate of 0.04 mmrmin. Therefore, the interval distance between adjacent etching holes should be designed properly. In the present work, the required time to release all the structures was about 40–45 min. The formation of the channel chambers was completed with the deposition of a thick LTO layer to seal the etching holes. Then, a poly-silicon layer was LPCVD deposited, boron doped and patterned to form the piezoresistors on the sensor membrane ŽFig. 4c.. This poly layer could be used to seal the holes. The LPCVD process resulted in very low pressure in the chambers, and the diaphragms were deflected downward under the ambient atmospheric pressure. Finally, the metal layer for interconnections was sputter deposited, patterned and sintered to complete the fabrication process ŽFig. 4d..
3. Experimental set-up A schematic of the experimental set-up is illustrated in Fig. 5. Nitrogen gas was passed through the microdevices under inlet pressure of up to 50 psi. The volume flow rate was measured using a glass syringe with a volume of 10 ml. The gas flow rate was measured optically as a meniscus of water traveled past the marked scale on the syringe as a function of time. Prior to the pressure distribution measurements, all sensors were calibrated and the sensitivity is about 0.03 mVrV kPa w8x. The inlet and outlet of each device were connected to the gas source, and the
Fig. 4. Cross-sections of the main fabrication steps.
X. Li et al.r Sensors and Actuators 83 (2000) 277–283
280
Fig. 5. An illustration of the experimental set-up.
pressure was adjusted. Once a steady state was reached, the voltage output of all sensors was recorded. The process was repeated 6–8 times, until satisfactory calibration curves were obtained. Then, pressure measurements were collected in both devices for different flow rates.
4. Results and discussion Flow rate measurements were first conducted to assess the effect of the constriction elements on the overall fluid flow as compared with a straight microchannel fabricated on a separate device. After the reliability of pressure measurements was established using a straight microchannel, pressure distribution around the obstructions were used to analyze the local flow pattern. 4.1. Flow rate measurements Nitrogen gas was passed through the microdevices under inlet pressure of up to 50 psi. Mass flow rates, Qm , were first measured as a function of the pressure drop. The mass flow rate in a straight channel under a given pressure drop, Pi y Po , is a cubic function of the height w9x: Qm s
h 3 wPo2 24 RTl m
Pi
2
žž / / Po
y 1 q 12 Kn o
ž
Pi Po
y1
/
Kn s 0 and small pressure drop, Eq. Ž1. is reduced to the two-dimensional, incompressible Poiseuille expression: Qm s
h 3 wr d P 12 m
ž / dx
s
h 3 wPo2 12 RTl m
ž
Pi Po
y1
/
Ž 2.
where the pressure gradient is constant along the channel. During the sacrificial etch to create the channel cavity, the nitride layer forming the ceiling is also slightly etched. This results in a channel height larger than the designed value. Since the flow rate is very sensitive to this parameter, it is very important to find out its exact value. Eq. Ž1. has been shown to provide good predictions of mass flow rate in a straight microchannel for low-pressure drop, Pi y Po - 50 psi, and it can be used to determine the actual height. The best fit of the calculated flow rate to the measured data in the straight microchannel, shown in Fig. 6, is obtained for h s 1.1 mm. All the devices were fabricated in an identical process flow. Therefore, the height of constriction microdevices should also be about
Ž 1.
where h, w and l are the channel height, width and length; Pi and Po are the inlet and outlet pressure; T, m and R are the fluid temperature, viscosity and specific gas constant, respectively; Kn o s lorh is the outlet Knudsen number based on the outlet mean free path and the channel height. In the present experiment, Kn o s 0.06 for the nitrogen outlet pressure of 1 atm. The model accounts for compressible and slip flow effects, but neglects acceleration and non-parabolic velocity profile effects w10x. At the limit for
Fig. 6. Measured mass flow rate of a straight channel compared with theoretical calculations.
X. Li et al.r Sensors and Actuators 83 (2000) 277–283
1.1 mm. The mass flow-rate provides an estimate for the velocity scale, U s Qm RTrPo hw, for the calculation of the Reynolds number. The highest pressure-drop used in this set of experiments, about 40 psi, resulted in Re s Uhrn ( 0.05 and ReU s ŽUhrn .Ž hrd . 2 ( 0.0005 for the microdevices, where d is the length of the constriction from the channel wall. Thus, the condition not only for Stokes but also for Hele–Shaw flow was met for the constriction devices as well. The measured flow-rate results for both constriction microdevices are compared in Fig. 7 with theoretical calculations for a straight channel with the same dimensions. The measured mass flow rate in either device is significantly smaller than the theoretical predictions of flow rates in straight channel due to the obstructions. Moreover, the ‘Venturi’ flow rate is about twice as large as the ‘orifice’ flow rate, indicating that the orifice presents a larger resistance to the flow in the microchannel. Introducing the concept of equivalent length, l e , where the resistance of an added section of the straight channel is equivalent to the resistance of the flow obstruction, l erl was experimentally found to be 0.2 for the Venturi and 1.25 for the orifice obstacle. The dashed lines are theoretical predictions based on a straight channel with the same width and height but with the modified length, l q l e , where l s 4000 mm is the original channel length. This means that slanting the perpendicular, 10 mm wall of the orifice element at 458, as in the Venturi element, resulted in doubling the flow rate through the device. The difference between the two devices has to be due to detailed flow pattern around each element at the mid-device, which suggests flow separation due to the sharp angle obstruction, and pressure measurements can shed some light into these flow patterns. 4.2. Pressure distribution along a straight microchannel Pressure distribution measurements start with calibration of the integrated pressure sensors, and a sample of the calibration curves is shown in Fig. 8. Then, the straight
Fig. 7. Measured mass flow rate of constriction microdevices compared with theoretical calculations.
281
Fig. 8. Calibration curves of sensors along the microchannel.
microchannel device was utilized again to establish the reliability of the pressure measurements. The analytical model used for calculating the flow rate can also provide the pressure distribution, P Ž x ., along a straight microchannel w9x: PŽ x. Po
sy6 Kn o
(ž
q
6 Kn o q
Pi2 Po2
/ ž q
Pi2 Po2
/
y1 q12 Kn o
ž
Pi Po
x
y1
/ž / l
.
Ž 3. The non-linear pressure distributions along the straight microchannel, measured by the integrated sensors, are compared in Fig. 9 with calculations based on Eq. Ž3.. The agreement between the experimental measurements and analytical calculations is satisfactory. Thus, pressure distributions along the constriction microdevices can be used to understand the flow pattern around the flow obstructions. The channel length upstream and downstream of the obstructions was selected to be large, about 2000 mm, to ensure the development of regular channel flow such that end effects can be neglected. Indeed the non-linear pres-
Fig. 9. Non-linear pressure distributions along the straight channel.
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X. Li et al.r Sensors and Actuators 83 (2000) 277–283
Fig. 10. Non-linear pressure distributions along the orifice-plate device.
sure distributions outside the obstruction zone, shown in Fig. 10 for the orifice and in Fig. 11 for the Venturi device, agree well with predictions based on Eq. Ž3.. However, the larger pressure drop across the Venturi constriction than the pressure drop across the orifice constriction is surprising and inconsistent with the flow rate measurements. Close observation of the data in Fig. 11 reveals that this result is mainly based on the output of a single sensor located at x s 2700 mm. Thus, more experiments are required to validate the pressure distributions before and after the constriction elements. 4.3. Flow patterns around the constriction elements A very limited number of pressure sensors, only four, can be integrated around the constriction elements ŽFigs. 2 and 3. due to the size of the membrane. This size, 100 = 100 mm2 , is required to ensure reasonable sensitivity of the pressure sensors. However, the reversal of the flow direction doubles the number of available data points if the sensors are asymmetrically positioned across the obstructions. In the present devices, one sensor is located at the mid-obstruction to indicate whether the forward and backward flow yield the same pressure at the same point, allowing the combination of the two data sets into one
Fig. 11. Non-linear pressure distributions along the Venturi-tube device.
Fig. 12. Pressure distributions and streamline pattern around the orifice obstruction.
pressure distribution. Consequently, seven pressure data points can be collected across the obstruction for any given mass flow rate. Interesting pressure distributions were measured within the obstruction zones, and are plotted in Figs. 12 and 13 for both devices. The static pressure just upstream of the orifice increases slightly ŽFig. 12., indicating low-speed flow. Further downstream, the pressure decreases smoothly through the orifice, suggesting that the streamlines converge with increasing flow speed. However, the static pressure at the throat, where the channel cross-section area is the smallest, is not the minimum. It is possible that a re-circulation zone exists at either side of the orifice, with
Fig. 13. Pressure distributions and streamline pattern around the Venturi obstruction.
X. Li et al.r Sensors and Actuators 83 (2000) 277–283
lower flow speed and higher pressure, due to flow separation as sketched in Fig. 12. The mainstream flow continues to accelerate from the orifice to form a vena contracta, and then decelerates again to fill the channel. At the vena contracta, the flow area is the smallest with essentially straight flow streamlines. Thus, the minimum pressure is uniform across the channel cross-section at that location. A vortex may then exist within each re-circulation zone with a lateral size on the order of the obstruction, 10 mm, and height of about 1 mm. It is also possible that the pressure extrema could indicate stagnation points, i.e., points of separation and reattachment of the flow, rather than the location of the vortex cores as suggested in Fig. 12. Furthermore, the flow pattern would then be symmetrical with respect to the orifice. In the Veturi device, not all the sensors around the obstruction functioned and only four data points are available instead of seven. Nevertheless, the static pressure just upstream and downstream the Venturi increases slightly, while the pressure at the throat is clearly lower as shown in Fig. 13. This indicates that, due to the slanted walls at 458, the flow separation is significantly reduced and localized by the sharp corners. The pressure variation is mainly due to the area change as for attached flow. Indeed, the measured pressure drop over the Venturi is much higher than the drop measured over the orifice obstruction. This pressure drop over such a small distance associated with the micro obstruction can be utilized to construct a micro flow meter, and the Venturi device clearly provides a higher sensitivity than the orifice device. Clearly, the spatial resolution for the pressure measurements around the constriction elements is not adequate for obtaining accurate flow patterns, due to the large size of the pressure-sensor membrane. Hence, the suggested flow patterns are still very tentative and more work need to be done to verify the occurrence of flow separation and the subsequent flow patterns.
5. Conclusions Two constriction microdevices, containing either an orifice or a Venturi obstruction, have been successfully
283
integrated with pressure microsensors. The measured mass flow rate through the Venturi was about twice the flow rate through the orifice and about 80% of the flow rate in a straight channel. The equivalent length of the Venturi resistance to the flow was found to be 20%, and that of the orifice was about 125%. These flow-rate measurements indicate that separation may occur in a microchannel flow with very small Reynolds number. It is plausible that a micro vortex, with a lateral scale smaller than 10 mm and height of about 1 mm, is developed adjacent to the orifice. The flow separation can significantly be reduced or eliminated with a Venturi design. Acknowledgements This work is supported by the Hong Kong Research Grant Council through RGC grant HKUST6012r98E. References w1x C.M. Ho, Y.C. Tai, Micro-electro-mechanical systems ŽMEMS. and fluid flows, Annu. Rev. Fluid Mech. 30 Ž1998. 579–612. w2x J.Q. Liu, Y.C. Tai, K.C. Pong, C.M. Ho, Micro-machined channelrpressure sensor systems for micro flow studies, Proc. of the 7th Int. Conf. on Solid-State Sensors and Actuators, Transducers’93, Japan, 1993, pp. 995–999. w3x S. Wu, J. Mai, Y. Zohar, Y.C. Tai, C.M. Ho, A suspended microchannel with integrated temperature sensors for high-pressure flow studies, Proc. of the 11th IEEE Workshop on Micro Electro Mechanical Systems, Germany, 1998, pp. 87–92. w4x P. Bradshaw, F.Y.F. Wong, The reattachment and relaxation of a turbulent shear layer, J. Fluid Mech. 52 Ž1972. 113–135. w5x F.M. White, Viscous Fluid Flow, 2nd edn., McGraw-Hill, 1991. w6x H. Schlichting, Boundary Layer Theory, 7th edn., McGraw-Hill, 1979. w7x J.Q. Liu, Y.C. Tai, J.J. Lee, K.C. Pong, Y. Zohar, C.M. Ho, In situ monitoring and universal modeling of sacrificial PSG etching using hydrofluoric acid, Proc. of the 6th IEEE Workshop on Micro Electro Mechanical Systems, USA, 1993, pp. 71–76. w8x X.X. Li, Y. Zohar, M. Wong, Improved piezoresistive sensor using novel nickel induced laterally crystallized polycrystalline silicon, Proc. of the 10th Int. Conf. on Solid-State Sensors and Actuators, Transducers’99, Japan, 1999, pp. 266–269. w9x E.B. Arkilic, M.A. Schmidt, K.S. Breuer, Gaseous slip flow in long microchannels, J. Microelectromech. Syst. 6 Ž1997. 167–178. w10x H.R. van den Berg, C.A. Seldam, P.S. Gulik, Compressible laminar flow in a capillary, J. Fluid Mech. 246 Ž1993. 1–20.
Gas flow in constriction microdevices Xinxin Li b
a,b
, Wing Yin Lee a , Man Wong b, Yitshak Zohar
a,)
a Department of Mechanical Engineering, Hong Kong UniÕersity of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China Department of Electrical and Electronic Engineering, Hong Kong UniÕersity of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China
Received 7 June 1999; received in revised form 20 October 1999; accepted 25 October 1999
Abstract Constriction devices contain an element inserted into the fluid stream, which either changes the local streamwise distribution of flow area or applied frictional resistance to the flow. Two such devices: a micro orifice plate and a micro Venturi tube have been successfully fabricated for the study of fundamental flow phenomena in microdomains. Each device was integrated with a set of pressure sensors, and fabricated using standard micromachining techniques. Nitrogen gas was passed through the microdevices under inlet pressure up to 50 psi. Mass flow rate was first measured as a function of the overall pressure drop, and compared with results for a straight microchannel. Then, the detailed pressure distribution along each device was measured to understand the flow pattern around the flow obstruction. The results demonstrate that flow separation may occur in a microchannel flow with a very small Reynolds number. It is very possible that a micro vortex, on the order of 10 mm in size, can develop upstream and downstream of the obstruction. q 2000 Elsevier Science S.A. All rights reserved. Keywords: Microfluidics; Orifice plate; Venturi tube; Micro constrictions; Flow separation
1. Introduction The field of MEMS is expanding rapidly, and new potential applications are continuously being discovered. Inevitably, these microdevices will include fluid flows either in a primary or in a secondary role. Since the ability to fabricate MEMS is relatively new, it is not surprising that very little is known about the flow of gases and liquids in such minute passages. The physics of fluid flows in microdomains is most likely different from flows in macrodomains, for which a widely accepted mathematical model exists, i.e., Navier–Stokes equations. The issues to be addressed include: the determination at what length scale the continuum assumption breaks down; the modification of the present theories to account for non-continuum effects; and the assessment to what extent the phenomena such as flow separation, transition to turbulence and compressible effects Žshock waves. still occur in microdomains w1x. Flow through a straight channel is the simplest but most common configuration in microfluidic systems. Microchannels with integrated pressure sensors were fabricated to study the flow field w2,3x. The measured mass ) Corresponding author. Tel.: q852-2358-7194; fax: q852-2358-1543. E-mail: [email protected]
flow rate and pressure distributions indicated the development of slip flow conditions. This flow field, however, presents a simple balance between pressure gradient and wall shear stress. Constriction devices, on the other hand, contain an element inserted into the fluid stream. Such an element, e.g., an orifice plate, either changes the local streamwise distribution of flow area or presents additional resistance to the flow, which can result in flow separation. Macro flow fields associated with separation and reattachment have received significant attention because of their importance in many engineering applications w4x. However, due to the complicated nature of the phenomenon, similar studies in microdevices have yet to be carried out. In all viscous flows the primary control parameter is the Reynolds number, Re s ULrn , where U is a velocity scale, L a characteristic length scale and n the fluid kinematic viscosity w5x. For Re 4 1, the viscous forces can often be neglected and the flow outside the boundary layer is considered to be inviscid. Both viscous and inertia forces are important when Re ; 1. On the other hand, for Re < 1, inertia forces are negligible resulting in a viscous-dominated, creeping flow, often called Stokes flow. A characteristic of rounded bodies in creeping flow is smooth streamlines near their surface with no separation. However, bodies with sharp corners or projecting ap-
0924-4247r00r$ - see front matter q 2000 Elsevier Science S.A. All rights reserved. PII: S 0 9 2 4 - 4 2 4 7 Ž 9 9 . 0 0 3 0 8 - 8
278
X. Li et al.r Sensors and Actuators 83 (2000) 277–283
pendages do show flow separation. A unique case of creeping flow is the flow between two parallel plates separated by a narrow gap, h. This flow, often called Hele–Shaw flow, is characterized by the reduced Reynolds number, ReU s ŽULrn .Ž hrL. 2 < 1, where L is the scale of a body inserted between the plates. Although the flow is highly viscous, the resulting pattern of streamlines around a body with sharp corners is similar to that in potential flow about the same shape with no separation w6x. In macro-scale flows, creeping flow is usually associated with low velocity and a length scale of order one. In micro-scale flows, on the other hand, the length scale is very small while the velocity can be of order one. Thus, flow in a microsystem, where a sharp-cornered obstacle is inserted between two walls separated by a very narrow gap, presents an intriguing case. Inherently, the Reynolds number is very small since any length scale is very small. However, the reduced Reynolds number is also very small since the height of a microchannel can be smaller than any other length scale. Thus, it is not clear whether the flow around the sharp corners is attached, like Hele–Shaw, or separated, like two-dimensional Stokes flow. Two such devices with sharp corners are a Venturi tube or an orifice plate. The Venturi tube has a shape that attempts to mimic the flow pattern through a streamlined obstruction, while the orifice plate is basically a back-to-back abrupt contraction and abrupt expansion. At present, it is still difficult to conduct flow visualizations in microsystems, and measurement of the pressure distribution is the only alternative to investigate the flow pattern. Hence, in this work, microchannels with orifice- and Venturi-like constrictions have been integrated with pressure sensors allowing a detail study of the flow field in the vicinity of the constriction elements.
2. Design and fabrication The microdevices were fabricated on silicon substrates. Either the orifice- or the Venturi-element is located at the center of a microchannel Ž1 mm high, 40 mm wide and
Fig. 2. Close-up view of the orifice plate located at the channel center.
4000 mm long., as shown in Fig. 1. The orifice ŽFig. 2. is realized by two constrictions, each 10 mm wide and 10 mm long. The Venturi ŽFig. 3. is similar except for the side walls being slanted at 458 rather than 908. The minimum cross-section area in each device is 1 = 20 mm2 . In order to provide reference data, a straight microchannel with identical dimensions, but without any obstruction element, was fabricated following an identical process flow. Pressure sensors are sparsely distributed along the straight sections of the microchannel for reference, and densely around the constriction element. They are used for detail measurement of the pressure distribution along and at the center of the microchannel. The pressure is measured at the side of the channel, and we assume that it is constant over the thickness. Along the straight portions of the microchannel, far from the inletroutlet and constrictions regions, the pressure is assumed to be constant over the width as well since the aspect ratio is large Žabout 1:40.. The microchannels integrated with pressure microsensors were fabricated using surface micromachining techniques, while the inlet and outlet were bulk micromachined. The ceiling of the microchannel was made of transparent low-stress silicon nitride film, 1 mm thick, to allow flow visualization in future studies.
Fig. 1. A photograph of an integrated microdevice.
X. Li et al.r Sensors and Actuators 83 (2000) 277–283
Fig. 3. Close-up view of the Venturi tube located at the channel center.
Schematic cross-sections of the main fabrication steps are shown in Fig. 4. The initial substrate is a Ž100. double-polished, 4-in. Si-wafer. A 0.8-mm thick thermal silicon dioxide was grown and patterned to form the channel and sensor chambers. This was followed by an APCVD deposition and patterning of a 0.25-mm thick PSG film for fast sacrificial-layer etching. The phosphorous content in the PSG determines the sacrificial layer etching rate, i.e., the higher the phosphorous concentration, the faster the etch rate w7x. In the present work, the phosphorous content was about 6%. The pattern of the PSG layer is similar to that of the oxide layer, except for the distributed pads along the sides of the patterns to be used as etching holes. Next, the structural layer of 1 mm, low-stress nitride was LPCVD deposited to form the channel walls and ceiling as well as the sensor membrane ŽFig. 4a.. Anisotropic etching was used to form the inletroutlet holes from wafer backside, using the oxidernitride double
279
layer as an etch mask. Following the opening of the etching holes, the sacrificial layer was etched in 49% HF ŽFig. 4b.. This step was very critical as the release time could not be too long, since concentrated HF also etches silicon nitride at a rate of 0.04 mmrmin. Therefore, the interval distance between adjacent etching holes should be designed properly. In the present work, the required time to release all the structures was about 40–45 min. The formation of the channel chambers was completed with the deposition of a thick LTO layer to seal the etching holes. Then, a poly-silicon layer was LPCVD deposited, boron doped and patterned to form the piezoresistors on the sensor membrane ŽFig. 4c.. This poly layer could be used to seal the holes. The LPCVD process resulted in very low pressure in the chambers, and the diaphragms were deflected downward under the ambient atmospheric pressure. Finally, the metal layer for interconnections was sputter deposited, patterned and sintered to complete the fabrication process ŽFig. 4d..
3. Experimental set-up A schematic of the experimental set-up is illustrated in Fig. 5. Nitrogen gas was passed through the microdevices under inlet pressure of up to 50 psi. The volume flow rate was measured using a glass syringe with a volume of 10 ml. The gas flow rate was measured optically as a meniscus of water traveled past the marked scale on the syringe as a function of time. Prior to the pressure distribution measurements, all sensors were calibrated and the sensitivity is about 0.03 mVrV kPa w8x. The inlet and outlet of each device were connected to the gas source, and the
Fig. 4. Cross-sections of the main fabrication steps.
X. Li et al.r Sensors and Actuators 83 (2000) 277–283
280
Fig. 5. An illustration of the experimental set-up.
pressure was adjusted. Once a steady state was reached, the voltage output of all sensors was recorded. The process was repeated 6–8 times, until satisfactory calibration curves were obtained. Then, pressure measurements were collected in both devices for different flow rates.
4. Results and discussion Flow rate measurements were first conducted to assess the effect of the constriction elements on the overall fluid flow as compared with a straight microchannel fabricated on a separate device. After the reliability of pressure measurements was established using a straight microchannel, pressure distribution around the obstructions were used to analyze the local flow pattern. 4.1. Flow rate measurements Nitrogen gas was passed through the microdevices under inlet pressure of up to 50 psi. Mass flow rates, Qm , were first measured as a function of the pressure drop. The mass flow rate in a straight channel under a given pressure drop, Pi y Po , is a cubic function of the height w9x: Qm s
h 3 wPo2 24 RTl m
Pi
2
žž / / Po
y 1 q 12 Kn o
ž
Pi Po
y1
/
Kn s 0 and small pressure drop, Eq. Ž1. is reduced to the two-dimensional, incompressible Poiseuille expression: Qm s
h 3 wr d P 12 m
ž / dx
s
h 3 wPo2 12 RTl m
ž
Pi Po
y1
/
Ž 2.
where the pressure gradient is constant along the channel. During the sacrificial etch to create the channel cavity, the nitride layer forming the ceiling is also slightly etched. This results in a channel height larger than the designed value. Since the flow rate is very sensitive to this parameter, it is very important to find out its exact value. Eq. Ž1. has been shown to provide good predictions of mass flow rate in a straight microchannel for low-pressure drop, Pi y Po - 50 psi, and it can be used to determine the actual height. The best fit of the calculated flow rate to the measured data in the straight microchannel, shown in Fig. 6, is obtained for h s 1.1 mm. All the devices were fabricated in an identical process flow. Therefore, the height of constriction microdevices should also be about
Ž 1.
where h, w and l are the channel height, width and length; Pi and Po are the inlet and outlet pressure; T, m and R are the fluid temperature, viscosity and specific gas constant, respectively; Kn o s lorh is the outlet Knudsen number based on the outlet mean free path and the channel height. In the present experiment, Kn o s 0.06 for the nitrogen outlet pressure of 1 atm. The model accounts for compressible and slip flow effects, but neglects acceleration and non-parabolic velocity profile effects w10x. At the limit for
Fig. 6. Measured mass flow rate of a straight channel compared with theoretical calculations.
X. Li et al.r Sensors and Actuators 83 (2000) 277–283
1.1 mm. The mass flow-rate provides an estimate for the velocity scale, U s Qm RTrPo hw, for the calculation of the Reynolds number. The highest pressure-drop used in this set of experiments, about 40 psi, resulted in Re s Uhrn ( 0.05 and ReU s ŽUhrn .Ž hrd . 2 ( 0.0005 for the microdevices, where d is the length of the constriction from the channel wall. Thus, the condition not only for Stokes but also for Hele–Shaw flow was met for the constriction devices as well. The measured flow-rate results for both constriction microdevices are compared in Fig. 7 with theoretical calculations for a straight channel with the same dimensions. The measured mass flow rate in either device is significantly smaller than the theoretical predictions of flow rates in straight channel due to the obstructions. Moreover, the ‘Venturi’ flow rate is about twice as large as the ‘orifice’ flow rate, indicating that the orifice presents a larger resistance to the flow in the microchannel. Introducing the concept of equivalent length, l e , where the resistance of an added section of the straight channel is equivalent to the resistance of the flow obstruction, l erl was experimentally found to be 0.2 for the Venturi and 1.25 for the orifice obstacle. The dashed lines are theoretical predictions based on a straight channel with the same width and height but with the modified length, l q l e , where l s 4000 mm is the original channel length. This means that slanting the perpendicular, 10 mm wall of the orifice element at 458, as in the Venturi element, resulted in doubling the flow rate through the device. The difference between the two devices has to be due to detailed flow pattern around each element at the mid-device, which suggests flow separation due to the sharp angle obstruction, and pressure measurements can shed some light into these flow patterns. 4.2. Pressure distribution along a straight microchannel Pressure distribution measurements start with calibration of the integrated pressure sensors, and a sample of the calibration curves is shown in Fig. 8. Then, the straight
Fig. 7. Measured mass flow rate of constriction microdevices compared with theoretical calculations.
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Fig. 8. Calibration curves of sensors along the microchannel.
microchannel device was utilized again to establish the reliability of the pressure measurements. The analytical model used for calculating the flow rate can also provide the pressure distribution, P Ž x ., along a straight microchannel w9x: PŽ x. Po
sy6 Kn o
(ž
q
6 Kn o q
Pi2 Po2
/ ž q
Pi2 Po2
/
y1 q12 Kn o
ž
Pi Po
x
y1
/ž / l
.
Ž 3. The non-linear pressure distributions along the straight microchannel, measured by the integrated sensors, are compared in Fig. 9 with calculations based on Eq. Ž3.. The agreement between the experimental measurements and analytical calculations is satisfactory. Thus, pressure distributions along the constriction microdevices can be used to understand the flow pattern around the flow obstructions. The channel length upstream and downstream of the obstructions was selected to be large, about 2000 mm, to ensure the development of regular channel flow such that end effects can be neglected. Indeed the non-linear pres-
Fig. 9. Non-linear pressure distributions along the straight channel.
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Fig. 10. Non-linear pressure distributions along the orifice-plate device.
sure distributions outside the obstruction zone, shown in Fig. 10 for the orifice and in Fig. 11 for the Venturi device, agree well with predictions based on Eq. Ž3.. However, the larger pressure drop across the Venturi constriction than the pressure drop across the orifice constriction is surprising and inconsistent with the flow rate measurements. Close observation of the data in Fig. 11 reveals that this result is mainly based on the output of a single sensor located at x s 2700 mm. Thus, more experiments are required to validate the pressure distributions before and after the constriction elements. 4.3. Flow patterns around the constriction elements A very limited number of pressure sensors, only four, can be integrated around the constriction elements ŽFigs. 2 and 3. due to the size of the membrane. This size, 100 = 100 mm2 , is required to ensure reasonable sensitivity of the pressure sensors. However, the reversal of the flow direction doubles the number of available data points if the sensors are asymmetrically positioned across the obstructions. In the present devices, one sensor is located at the mid-obstruction to indicate whether the forward and backward flow yield the same pressure at the same point, allowing the combination of the two data sets into one
Fig. 11. Non-linear pressure distributions along the Venturi-tube device.
Fig. 12. Pressure distributions and streamline pattern around the orifice obstruction.
pressure distribution. Consequently, seven pressure data points can be collected across the obstruction for any given mass flow rate. Interesting pressure distributions were measured within the obstruction zones, and are plotted in Figs. 12 and 13 for both devices. The static pressure just upstream of the orifice increases slightly ŽFig. 12., indicating low-speed flow. Further downstream, the pressure decreases smoothly through the orifice, suggesting that the streamlines converge with increasing flow speed. However, the static pressure at the throat, where the channel cross-section area is the smallest, is not the minimum. It is possible that a re-circulation zone exists at either side of the orifice, with
Fig. 13. Pressure distributions and streamline pattern around the Venturi obstruction.
X. Li et al.r Sensors and Actuators 83 (2000) 277–283
lower flow speed and higher pressure, due to flow separation as sketched in Fig. 12. The mainstream flow continues to accelerate from the orifice to form a vena contracta, and then decelerates again to fill the channel. At the vena contracta, the flow area is the smallest with essentially straight flow streamlines. Thus, the minimum pressure is uniform across the channel cross-section at that location. A vortex may then exist within each re-circulation zone with a lateral size on the order of the obstruction, 10 mm, and height of about 1 mm. It is also possible that the pressure extrema could indicate stagnation points, i.e., points of separation and reattachment of the flow, rather than the location of the vortex cores as suggested in Fig. 12. Furthermore, the flow pattern would then be symmetrical with respect to the orifice. In the Veturi device, not all the sensors around the obstruction functioned and only four data points are available instead of seven. Nevertheless, the static pressure just upstream and downstream the Venturi increases slightly, while the pressure at the throat is clearly lower as shown in Fig. 13. This indicates that, due to the slanted walls at 458, the flow separation is significantly reduced and localized by the sharp corners. The pressure variation is mainly due to the area change as for attached flow. Indeed, the measured pressure drop over the Venturi is much higher than the drop measured over the orifice obstruction. This pressure drop over such a small distance associated with the micro obstruction can be utilized to construct a micro flow meter, and the Venturi device clearly provides a higher sensitivity than the orifice device. Clearly, the spatial resolution for the pressure measurements around the constriction elements is not adequate for obtaining accurate flow patterns, due to the large size of the pressure-sensor membrane. Hence, the suggested flow patterns are still very tentative and more work need to be done to verify the occurrence of flow separation and the subsequent flow patterns.
5. Conclusions Two constriction microdevices, containing either an orifice or a Venturi obstruction, have been successfully
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integrated with pressure microsensors. The measured mass flow rate through the Venturi was about twice the flow rate through the orifice and about 80% of the flow rate in a straight channel. The equivalent length of the Venturi resistance to the flow was found to be 20%, and that of the orifice was about 125%. These flow-rate measurements indicate that separation may occur in a microchannel flow with very small Reynolds number. It is plausible that a micro vortex, with a lateral scale smaller than 10 mm and height of about 1 mm, is developed adjacent to the orifice. The flow separation can significantly be reduced or eliminated with a Venturi design. Acknowledgements This work is supported by the Hong Kong Research Grant Council through RGC grant HKUST6012r98E. References w1x C.M. Ho, Y.C. Tai, Micro-electro-mechanical systems ŽMEMS. and fluid flows, Annu. Rev. Fluid Mech. 30 Ž1998. 579–612. w2x J.Q. Liu, Y.C. Tai, K.C. Pong, C.M. Ho, Micro-machined channelrpressure sensor systems for micro flow studies, Proc. of the 7th Int. Conf. on Solid-State Sensors and Actuators, Transducers’93, Japan, 1993, pp. 995–999. w3x S. Wu, J. Mai, Y. Zohar, Y.C. Tai, C.M. Ho, A suspended microchannel with integrated temperature sensors for high-pressure flow studies, Proc. of the 11th IEEE Workshop on Micro Electro Mechanical Systems, Germany, 1998, pp. 87–92. w4x P. Bradshaw, F.Y.F. Wong, The reattachment and relaxation of a turbulent shear layer, J. Fluid Mech. 52 Ž1972. 113–135. w5x F.M. White, Viscous Fluid Flow, 2nd edn., McGraw-Hill, 1991. w6x H. Schlichting, Boundary Layer Theory, 7th edn., McGraw-Hill, 1979. w7x J.Q. Liu, Y.C. Tai, J.J. Lee, K.C. Pong, Y. Zohar, C.M. Ho, In situ monitoring and universal modeling of sacrificial PSG etching using hydrofluoric acid, Proc. of the 6th IEEE Workshop on Micro Electro Mechanical Systems, USA, 1993, pp. 71–76. w8x X.X. Li, Y. Zohar, M. Wong, Improved piezoresistive sensor using novel nickel induced laterally crystallized polycrystalline silicon, Proc. of the 10th Int. Conf. on Solid-State Sensors and Actuators, Transducers’99, Japan, 1999, pp. 266–269. w9x E.B. Arkilic, M.A. Schmidt, K.S. Breuer, Gaseous slip flow in long microchannels, J. Microelectromech. Syst. 6 Ž1997. 167–178. w10x H.R. van den Berg, C.A. Seldam, P.S. Gulik, Compressible laminar flow in a capillary, J. Fluid Mech. 246 Ž1993. 1–20.