Microchannel Pressure Measurements Using Molecular ... - IEEE Xplore

JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 16, NO. 4, AUGUST 2007

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Microchannel Pressure Measurements Using Molecular Sensors Chihyung Huang, James W. Gregory, and John P. Sullivan

Abstract—Fluid mechanics on the microscale is an important subject for researchers who are interested in studying microdevices since physical phenomena change from macroscale to microscale. Channel flow is a fundamental topic for fluid mechanics. By using a molecular sensor known as pressure-sensitive paint (PSP), detailed pressure data can be obtained inside the microchannel and at the channel entrance. The achievable spatial resolution of the acquired pressure map can be as high as 5 µm. PSP measurements are obtained for various pressure ratios from 1.76 to 20, with Knudsen number (Kn) varying from 0.003 to 0.4. Compressibility and rarefaction effects can be seen in the pressure data inside the microchannel and at the channel entrance. [2006-0152] Index Terms—Fluid flow measurement, microchannel, microsensors, pressure-sensitive paint (PSP).

I. I NTRODUCTION

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ICROELECTROMECHANICAL systems (MEMS) have been studied and extensively applied in general life for the past few decades. The advantages of small size, low power consumption, high accuracy and low cost make MEMS one of the greatest techniques in the 21st century. In aerospace engineering, MEMS devices have been used in many fields, such as aerodynamics, heat transfer, and propulsion. For example, small-scale actuators can be placed inside the flow field to achieve active flow control. They can be used as control devices for triggering or suppressing boundary layer separation in a turbulent flow or as a mixing mechanism in a combustion chamber. Physical phenomena at the microscale can be quite different compared with those at the macroscale because of the size. Especially at small scales, issues such as viscous effects, compressibility effects, slip boundary conditions, and rarified gas effects become dominant. For example, when the characteristic length of a MEMS device gets smaller and closer to the mean

free path of gas molecules inside the MEMS device, the fluid will change from a slip-flow regime to a transition regime and a free-molecule flow regime. At the free-molecule flow regime, the gas molecules do not move one after another, as in a continuum flow. Instead, they exhibit particle-like movement due to the large space between each molecule. The Reynolds number in the MEMS flow is relatively smaller compared with the macroscale. For fluid mechanics, scientists are interested in the flow field in microdevices and the capability to measure and understand it. Experimental techniques have been developed for pressure measurements in micro devices, but most of them are limited to discrete data points, and the sensors are difficult to construct and embed in MEMS devices. It is necessary to find alternative ways to collect the detailed information inside the micro flow field. The molecular sensor is a novel technique that has been studied and used by researchers since the early 1980s. The sensor known as pressure-sensitive paint (PSP) or temperaturesensitive paint (TSP) can be used for pressure or temperature measurement. It has been successfully applied in aerospace engineering to obtain surface global pressure and temperature maps of the flow field either in wind tunnel experiments or in flight-test measurements. Liu and Sullivan provide a comprehensive background on the theory and practice of PSP and TSP [1], [2]. These techniques have the advantages of low cost, ease of use, and the potential for application to complicated geometries such as a sharp tip or corner. Furthermore, for the small size of molecular sensors, the general luminophore size is as small as a few nanometers; the molecules can be put inside the MEMS devices and are the best candidates for the MEMS measurements. Furthermore, the molecular sensor has its greatest sensitivity at the low pressure range below 1 psi, where standard pressure transducers usually have difficulty making measurements. II. B ACKGROUND

Manuscript received July 26, 2006; revised November 1, 2006. This paper was presented in part at the 21st Internal Congress on Instrumentation in Aerospace Simulation Facilities, Sendai, Japan, 2005. Subject Editor Y. Zohar. C. Huang was with the School of Aeronautics and Astronautics, Purdue University, West Lafayette, IN 47906 USA. He is now with the School of Industrial Engineering, Purdue University, West Lafayette, IN 47906 USA (e-mail: [email protected]). J. W. Gregory was with the School of Aeronautics and Astronautics, Purdue University, West Lafayette, IN 47906 USA. He is now with the Department of Aeronautics, U.S. Air Force Academy, Colorado Springs, CO 80840 USA (e-mail: [email protected]). J. P. Sullivan is with School of Aeronautics and Astronautics, Purdue University, West Lafayette, IN 47906 USA (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JMEMS.2007.892914

A. Literature Review of the Microchannel The physical behaviors in microfluidics are different from what they are at a continuum regime and a slip-flow or transition regime. For example, the pressure distribution along a microchannel has been measured with micro pressure sensors, and the nonlinear pressure distribution was found due to the viscous dissipation and compressibility effects at a small scale [3], [4]. Numerical simulations of the gas flow in MEMS devices have been performed with the compressible Navier–Stokes algorithm and compared with experimental results by Beskok et al. [5]. Similar results have been obtained by

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Jie et al. [6] with the same Navier–Stokes simulation. When the characteristic length in the microchannel decreases to an even smaller size as at the nanometer scale, or when the operating pressure decreases to as low as a few torr, the molecules of the fluid inside the microchannel do not behave according to the continuum theory. Instead, the particle motions more closely resemble the molecular dynamics theory. The Navier–Stokes equation is invalid in this situation. The investigation of the molecule behavior in microdevices needs another approach for the high Knudsen number (Kn) condition. Beskok [7] has performed a numerical simulation with Direct Simulation Monte Carlo (DSMC) for the microchannel flow at a high Knudsen number regime and found that the curvature of the pressure distribution inside the microchannel will be reduced due to the rarefaction effect. This means that the curvature of pressure distribution in microchannels depends on the combination of compressibility and rarefaction effect. The entrance effect in a microchannel shows a sudden pressure drop in the pressure distribution near microchannel inlets and has been studied by Jang et al. [8]. The entrance effect in a microchannel is quite different from that in a macroscale and needs more effort to investigate. The behavior of fluid flow in microchannels should be studied, and the characteristics can be used for medical purposes such as delivering drugs or for designing mechanical sensors for gas leakage detection. B. PSP Sensor The PSP sensor is an optical–chemical sensor. It is constructed by embedding luminescent molecules into a binder, which can be a polymer material or a porous surface. The luminophore is dissolved in the polymer material with a solvent and then sprayed on the model surface like regular paint or dissolved in the solvent then sprayed on a porous model surface. The binder can help the luminophore attach to the model surface and survive intact at different flow speeds. With the excitation of a particular wavelength illumination, such as a UV lamp or a blue/green LED, the luminescent molecules will absorb photons and be raised to a higher energy level. To return to the original energy state, the luminophore will emit luminescence through a radiative process at a longer wavelength. There are two different reactions of the radiative process: fluorescence and phosphorescence. In general, the luminescence measured from the PSP sensors includes intensity levels from both fluorescence and phosphorescence. Because of the different wavelength between excitation and emission, the excitation light and emission light can be separated by using a low-pass optical filter in front of the light source and a highpass optical filter in front of the photodetector. The schematic of the operation of PSP sensors is shown in Fig. 1. However, the luminescent intensity related to the energy transfer process will be affected not only by radiation processes but also by radiationless processes. The radiationless processes that will affect the emission intensity include oxygen quenching if oxygen molecules are present. Oxygen quenching is a process in which the emission intensity is quenched by the existence of oxygen molecules in the nearby environment. The interaction between oxygen mole-

Fig. 1.

Schematic of PSP measurement.

cules and luminescent molecules will consume the excitation energy in the luminescent molecules. Therefore, as the oxygen concentration increases, the luminescent intensity decreases. Because of the fixed portion of oxygen in the air, the relation of luminophore and oxygen molecules can be used to measure the static pressure in the air. The Stern–Volmer equation can be used for calibration with pressure and luminescent intensity and described as follows: P Iref = A(T ) + B(T ) I Pref

(1)

where I is the luminescent intensity, P is the static pressure, and ref is the reference taken before the test. Coefficients A and B are the temperature-dependent coefficients that can be obtained through calibration. However, in most instances, the calibration curve is not a simple linear equation; a power term is often added to the pressure ratio in the Stern–Volmer equation, or a second-order or higher order polynomial equation may be used to fit nonlinear calibration data. After collecting the intensity of emission from the luminescent molecules with a photodetector, the luminescent intensity can be converted to pressure for pressure measurement. This is the intensity-based measurement technique for PSP sensors. Similar to intensity-based measurement, the lifetime or phase shift of PSP sensors can also be calibrated like the intensity signal for lifetime measurement or phase-shift measurement. In this paper, the intensity-based technique is used for pressure measurement. PSP can be used for the application with the pressure range from 0.001 to 30 psia with accuracy around 0.001 psia. For different binders used in the PSP sensor, the response time can be varied from a couple of seconds to a tenth of a microsecond for steady flow measurements and unsteady flow measurements [1], [2]. C. Surface Roughness and Tangential Momentum Accommodation Coefficient (TMAC) Value for PSP The PSP Pt(II)meso-tetra(pentafluorophenyl) porphine (PtTFPP) was used as the sensor in this paper, and the surface condition of the PSP sensor was examined. The PSP sensor was coated on a glass slide with a surface roughness of 0.07 µm rms and thickness of 1.2 µm measured by an Alpha

HUANG et al.: MICROCHANNEL PRESSURE MEASUREMENTS USING MOLECULAR SENSORS

Fig. 2.

Surface roughness and thickness for PSP PtTFPP/TMSP.

Fig. 3. Mass flow rate and pressure data for calculating the TMAC value.

step 500 stylus profilometer, as shown in Fig. 2. The PSP sensor is coated from 0 to 500 µm, and the glass slide surface starts from 950 µm, where it was covered by a piece of tape. There are some spikes around the edge of the PSP sensor due to delamination of the tape. For microdevice measurements, it is important to know the fluid-to-surface interaction. The tangential momentum accommodation coefficient (TMAC) σv can help researchers decide when the slip-flow condition is needed instead of the no-slip condition. TMAC is defined by σv =

τi − τr τi − τw

(2)

where τi , τr , and τw are the momentum of the incoming, reflected, and re-emitted molecules, respectively. To measure the TMAC value for the PSP PtTFPP/1trimethysilypropyne (TMSP), another glass microchannel is made with PSP coated on the upper and lower glass slides, and two pieces of double sided tape are put in between the glass slide and used as left and right side sealing. The channel height is 76 µm, the length is 25 mm, and the width is 6 mm. The aspect ratio for the channel is relatively high to ensure a 2-D flow inside the channel, i.e., there is no 3-D effect in the flow field. Fig. 3 shows the normalized mass flow rate with the inverse mean pressure between the channel inlet and the exit. The TMAC value for the PSP PtTFPP/TMSP is calculated as 0.90, with Kn equal to 0.018. It is calculated by measuring the mass flow rate passing through the microchannel and the pressure change between the channel inlet and the exit. After substituting the mass flow rate and pressure data, the slope of the curve fit can be used to extract the TMAC value by using the following equation:

Pi2

H 3 w 2 − σm 1 H 3w m ˙ + = ko Po ¯ 2 − Po 24µLRT 4µLRT σm P

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(3)

where m ˙ is the mass flow rate through the microchannel, Pi is the inlet pressure, Po is the outlet pressure, H is the

Fig. 4. Schematic of microchannel.

channel height, w is the channel width, µ is the dynamic viscosity of air, L is the channel length, R is the gas constant, T is the temperature, ko is the Knudsen number calculated at the channel exit, Po is the pressure at channel exit, P¯ is the mean pressure between the inlet and exit pressures, and σm is the TMAC value. The TMAC value depends on the surface roughness of the binder of the PSP sensor. The other PSP sensor, namely, Pd(II)meso-tetra(pentafluorophenyl) porphine (PdTFPP)/TMSP, which is also used in this paper for a different pressure range, will have the same TMAC value as PtTFPP/TMSP because it has the same binder (i.e., TMSP). III. E XPERIMENTAL S ETUP A. Microchannel Device For PSP measurements in the microchannel flow, two 12.7 mm long, 235 µm wide, and 112 µm deep microchannel devices were fabricated with a micro CNC machine at the Aerospace Sciences Laboratory, Purdue University, West Lafayette, IN. Two channels were made with aluminum blocks to investigate the pressure distribution inside the microchannel at different flow regimes from the continuum flow to the slip flow to the transition flow. A schematic of the microchannel device is shown in Fig. 4. The hydraulic diameter for the microchannel device is calculated as 151.70 µm. The roughness of the channel surface was measured by an Alpha step 500 stylus profilometer and is plotted in Fig. 5. The depth of the channel is 112 µm, with a roughness of 2.29 µm rms at the bottom of the channel.

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Fig. 7.

Fig. 5. Bottom surface roughness and microchannel depth for microchannel A.

Experimental setup of microchannel measurement.

the microchannel. The pressure inside the channel varied from 0.05 to 14.5 psia, with different pressure ratios used to study the compressibility and rarefaction effects in the channel flow. A 10-gal vacuum tank was connected between the microchannel exit and the vacuum pump to maintain the pressure in the channel. Two Omega absolute pressure transducers (PX142) were also connected to the cavities at the channel inlet and exit to monitor the pressure at both ends. An MKS Instruments absolute pressure transducer (MKS690A) was used for lowpressure measurement. An Omega rotameter (FL3213ST) was connected at the channel inlet before the pressure regulator to measure the volume flow rate. The overall setup can be seen in Fig. 7. C. Calibration

Fig. 6. Microchannels A and B with PSP sensors PdTFPP and PtTFPP coated on glass slides.

B. Experimental Setup The pressure-sensitive paint PtTFPP/TMSP was chosen as the pressure sensor to cover a pressure range from 0.3 to 14.5 psia for the continuum and slip-flow regimes. For the transition-flow condition, PdTFPP/TMSP was used for pressure measurement because of its better sensitivity in the lower pressure range of 0.01–2.3 psia. PtTFPP/TMSP is made by mixing 5 mg PtTFPP (Porphyrin Products, Inc.) and 15 ml TMSP (Gelest, Inc.). PdTFPP/TMSP is made by mixing 5 mg PdTFPP (Frontier Scientific, formerly Porphyrin Products, Inc.), 0.5 g polymer powder poly(methylsisesquioxane) (Gelest, Inc.), and 15 ml TMSP. The PSP sensors coated on glass slides can be seen in Fig. 6. The glass slide with the PSP sensor was then bonded to the top of the microchannel device as a cover glass by cyanoacrylate glue. A 12-bit charge-coupled device (CCD) camera (SenSYS) with 512 × 768 pixels and a 55-mm Nikon nikkor microlens with extension tubes were used to obtain the pressure map inside the channel with spatial resolution up to 5 µm. A 2-in UV LED lamp from Innovative Scientific Solutions Inc. irradiated the PSP sensor from the left side of

In order to provide accurate pressure measurements in the microchannel, an in situ calibration process was carried out for each measurement. For the in situ calibration, images were taken with the same measurement setup while holding the pressure inside the channel steady and constant throughout the channel and cavities. A calibration curve was determined for each pixel inside the image as a pixel-by-pixel calibration, treating each pixel on the CCD chip as an individual PSP sensor. The pixel-by-pixel calibration can eliminate error due to variations in the intensity response at different locations imaged by the CCD sensor, which has been observed as one of the sources of error in PSP measurements at the micro scale. The calibration curves for each pixel inside the image can be obtained and the pressure map can be calculated from the calibrations. A typical calibration for PtTFPP with a reference pressure of 14.5 psia is shown in Fig. 8. A second-order polynomial equation is used to fit the calibration data. IV. P RESSURE M EASUREMENT W ITH THE PSP S ENSOR A. Intensity Images With PSP Measurement The intensity ratio image of PSP in the microchannel at a pressure ratio of 4.7 is shown in Fig. 9. The spatial resolution is about 20 µm to obtain the intensity data covering the whole microchannel, including part of the inlet and exit cavities. A


Fig. 8.

Typical calibration curve of PtTFPP/TMSP.

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Fig. 11. Pressure distribution inside microchannels A and B. TABLE I TEST CONDITIONS FOR COMPRESSIBILITY EFFECT MEASUREMENTS

B. Pressure Distribution in Microchannel Devices

Fig. 9. Image of the intensity ratio for a pressure ratio of 4.74 in the microchannel.

To verify the PSP measurements in different microchannel devices, two identical microchannel devices with the same design are tested with the same pressure condition and flow rate. Repeatability and consistency for the microchannel experiments must be demonstrated, even with different channel devices. The pressure data are calculated from the pixel row at the centerline of the channel. The pressure inside the channel shows almost the same trend with less than 10% difference for different channels for the same condition as seen in Fig. 11. V. C OMPRESSIBILITY E FFECT

Fig. 10. Pressure map inside the microchannel for the pressure ratio of 4.74.

pressure map of the microchannel at a pressure ratio of 4.7 is shown in Fig. 10. It can be seen that the pressure changes from 14 pisa at the channel inlet to 3 pisa at the channel exit.

It has been suggested that the pressure change inside a microchannel has a curvature distribution due to compressibility [3]. To investigate the compressibility effects in the microchannel flow, the PSP sensor was applied inside the microchannel, and the pressure data were obtained by holding the Knudsen number constant at the channel exit and varying the pressure ratio between the channel inlet and the channel exit. The pressure ratio changes from 1.76 to 4.74, with a Knudsen number of 0.003. The Reynolds number in the test condition varies from 5 to 89. The pressure condition and Knudsen number for each case are listed in Table I. After calibration, the pressure data along the centerline of the microchannel can be plotted from the inlet to the exit as shown in Fig. 12. It can also be plotted with a normalized

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Fig. 12. effects.


Pressure distribution inside the microchannel with compressibility

Fig. 13. Normalized pressure distribution inside the microchannel for compressibility effects.

scale between the inlet pressure P1 and the exit pressure P2 as shown in Fig. 13. The pressure data are averaged by the nearest ten points along the longitudinal axis. The Knudsen number is calculated based on the channel exit condition, exit pressure, and channel hydraulic diameter. Fig. 14 shows the deviation of the pressure data from the continuum theory. However, there are some entrance effects shown in the pressure data as a pressure drop at the inlet. It is difficult to compare the pressure data with the combined entrance effects, compressibility effect, and rarefaction effect. The entrance length for the microchannel is 0.6 hydraulic diameters at a low Reynolds number, which is about 3% of the channel length. To separate the entrance effect, it is assumed that the entrance length is within the first 10% of the channel length. The pressure data are replotted by shifting the starting point by 10% of the channel length using x/L − 0.1 x∗ = . L 0.9

(4)

Fig. 14. Pressure deviation inside the microchannel for compressibility effects.

Fig. 15. Pressure deviation inside the microchannel for compressibility effects at the fully developed region.

Fig. 15 shows that the pressure data inside the channel varies for different pressure ratios starting from 10% downstream from channel inlet, which is within the fully developed region. Experimental data from Ho et al. [3], with nitrogen gas and pressure ratio of 2.38 and Knudsen number of 0.04, is included in Fig. 15 for comparison. The data were taken at a similar pressure ratio but higher Knudsen number condition. Another experimental data set from Jang et al. [9] is also included with similar pressure and Knudsen number conditions. The values of P1 and P2 are critical for the normalization process. Thus, the first and last pressure data points are approximated by a least square fit with a second-order polynomial on the first ten and last ten data points. The theoretical pressure data are plotted with experimental data from PSP for comparison. The theoretical pressure distribution is calculated from the following equation [10]: P˜ (˜ x) = −a +

(a)2 + (1 + 2a)˜ x + (Π2 + 2aΠ)(1 − x ˜) (5)


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TABLE II TEST CONDITION OF KNUDSEN NUMBER EFFECT MEASUREMENTS

Fig. 16. Pressure deviation with the standard deviation inside the microchannel for compressibility effects at the fully developed region.

where a =6 Π=

2 − σm Kn σm

Pi . Po

(6) (7)

It is important to note that the theoretical analysis is calculated from the TMAC value of PSP, with the assumption that all the walls are coated with PSP. For the experimental measurements, however, only one side of the channel wall is coated with paint, whereas the other three surfaces are aluminum surfaces that have higher roughness values. Fig. 16 shows the pressure distribution inside the microchannel with standard deviation. The compressibility effects in the channel flow show the curvature in the pressure distribution. It can be seen that the curvature increases as the pressure ratio increases, as the compressibility effects begin to dominate the flow. VI. R AREFACTION E FFECT To evaluate the rarefaction effects in the microchannel flow, another PSP, namely, PdTFPP/TMSP, was used for recording measurements in the low-pressure range. The pressure inside the microchannel varies from 0.03 to 2.11 psia. The pressure data inside the microchannel at low-pressure conditions are measured at different Knudsen numbers, varying from 0.09 to 0.4 at the channel exit, whereas the pressure ratio is controlled at about 16. The Reynolds numbers in the lowpressure condition are below 1, varying from 0.36 to 0.01. The conditions for each case are listed in Table II. The deviation data are plotted with x∗ in Fig. 17 to compare the data at the fully developed flow region for the rarefaction effect. When the Knudsen number increases, the boundary condition at the sidewall changes from the no-slip condition to the slip-flow condition. This helps the flow to accelerate and increases the mass flow rate. The rarefaction effect makes the pressure distribution flatter, and the maximum deviation point is shifted from 0.68 at a Knudsen number of 0.09, to 0.6 at a Knudsen

Fig. 17. Pressure deviation with the standard deviation inside the microchannel for rarefaction effects at the fully developed region.

number of 0.4 after using a second-order polynomial fit to the data. VII. E NTRANCE E FFECT For a channel flow connected with a reservoir, the entrance flow path is important for the starting flow due to the entrance effect. Past measurements in microchannels have shown steep pressure gradients in the channel entrance region. However, it is difficult to build pressure sensors that can be located at the channel entrance because of the small channel size. Despite this limitation, it is important to understand the starting flow at the beginning of the microchannel. The pressure map near the channel entrance has been acquired and can be seen in Fig. 18 with spatial resolution up to 5 µm. Fig. 19 shows the pressure distribution along the center of the microchannel. In Fig. 19, the pressure ratio changes from 1.36 to 4.44, whereas the Knudsen number is controlled at 0.004. The pressure drop at the channel entrance can be seen for all cases. In Fig. 20, the Knudsen numbers varies from 0.003 to 0.078, with a pressure ratio controlled at around 3.60. The pressure drop at the channel entrance reduces while the Knudsen number increases. There are some local pressure increases that occur downstream of the channel entrance, which may be caused by the flow separation inside the microchannel. Fig. 20 shows the pressure distribution with the standard deviation for different pressure ratio and Knudsen number conditions, respectively.

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Fig. 18. Pressure map at the microchannel entrance for the pressure ratio of 3.49.

Fig. 19. Pressure distribution with the standard deviation at the microchannel inlet for the entrance effect with different pressure ratios.

Fig. 21. Experimental and theoretical comparison for the entrance length in the microchannel at different Reynolds numbers.

It can be seen that the pressure drop only appears at high pressure and low Knudsen number conditions, and it diminishes as the Knudsen number increases. It can be seen that at a Knudsen number of approximately 0.004, the pressure data show a steep drop at the channel entrance, even for a pressure ratio as low as 1.36. As the Knudsen number increases, the pressure drop at the entrance becomes more gradual. This is because the slip-flow condition at higher Knudsen numbers helps the flow go into the channel, thus reducing the entrance effect. The magnitude of the pressure drop diminishes as the Knudsen number approaches 0.078. The theoretical entrance distance for the low Reynolds number flow is about 60% of the hydraulic diameter of the microchannel, which is about 0.2% of the channel length. The theoretical entrance distance can be calculated using the following equations and is plotted in Fig. 21 for the comparison of experimental data and theoretical analysis [11]: Le ≈ 0.06 · ReDh Dh

(8)

Le 0.6 ≈ + 0.056 · ReDh . Dh 1 + 0.035 ReDh

(9)

The experimental data differ from the simple analytical result which does not include effects of Knudsen number. There are some deviations in the experimental data for Reynolds numbers between 1 and 100. It is noted that the shear stress at the wall and the flow separation near the channel entrance will change the entrance distance for different experimental conditions. VIII. C ONCLUSION

Fig. 20. Pressure distribution with the standard deviation at the microchannel inlet for the entrance effect with different Knudsen number conditions.

The PSP measurements in microchannels provide a detailed pressure distribution inside the microchannel, showing the nonlinear pressure distribution along the channel due to the


compressibility effect. Increasing the Knudsen number decreases the curvature in the pressure distribution due to the rarefaction effect. Detailed information around the microchannel inlet has also been obtained with PSP sensors, with spatial resolution up to 5 µm in the pressure maps. The pressure drop at the microchannel inlet due to the entrance effect decreases as the Knudsen number increases. The entrance length of the microchannel approaches 60% of the hydraulic diameter when the Reynolds number is equal to 0.007, agreeing with theoretical analysis at low Reynolds number conditions. R EFERENCES [1] T. Liu and J. P. Sullivan, Pressure and Temperature Sensitive Paints. Berlin, Germany: Springer-Verlag, 2005. [2] J. P. Sullivan, “Advanced measurement techniques,” in Proc. von Karman Insitute for Fluid Mechanics Lecture Series 2000–2001, 2001. [3] K.-C. Pong, C.-M. Ho, J. Liu, and Y.-C. Tai, “Non-linear pressure distribution in uniform microchannels,” Appl. Microfabrication Fluid Mech., vol. 197, pp. 51–56, 1994. [4] S. Roy, R. Raju, H. F. Chuang, B. A. Cruden, and M. Meyyappan, “Modeling gas flow through microchannels and nanopores,” J. Appl. Phys., vol. 93, no. 8, pp. 4870–4879, Apr. 2003. [5] A. Beskok, G. E. Karniadakis, and W. Trimmer, “Rarefaction and compressibility effects in gas microflows,” J. Fluids Eng., vol. 118, no. 3, pp. 448–456, 1996. [6] D. Jie, X. Diao, K. B. Cheong, and L. K. Yong, “Navier-Stokes simulations of gas flow in micro devices,” J. Micromech. Microeng., vol. 10, no. 3, pp. 372–379, 2000. [7] A. Beskok, “Validation of a new velocity-slip model for separated gas microflows,” Numer. Heat Transf., Fundam., vol. 40, no. 6, pp. 451–471, Dec. 2001. [8] J. Jang, Y. Zhao, and S. T. Wereley, “Leak microchannels and MEMS-based flow sensors,” Progress Report of 21st Century Project, Indiana, 2002. [9] J. Jang and S. T. Wereley, “Pressure distribution of gaseous slip flow in straight and uniform rectangular microchannels,” Microfluid. Nanofluid., 2004. [10] B. C. Arkilic, “Measurement of the mass flow and tangential momentum accommodation coefficient in silicon micromachined channels,” Ph.D. dissertation, Massachusetts Inst. Technol., Cambridge, MA, 1996. [11] N.-T. Nguyen and S. T. Wereley, Fundamentals and Application of Microfluidics. Norwood, MA: Artech House, 2002.

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Chihyung Huang received the B.S. degree in aerospace engineering from Tamkang University, Taipei, Taiwan, R.O.C., in 1995, the M.S. degree in aerospace engineering from National Cheng Kung University, Tainan, Taiwan, in 1997, and the Ph.D. degree from Purdue University, West Lafayette, IN. His current research interest is the application of PSP measurements in microdevices such as micronozzles, microjets, microchannels, and microturbines. He is currently a Postdoctoral Fellow in the School of Industrial Engineering, Purdue University.

James W. Gregory received the Bachelor’s degree in aerospace engineering from Georgia Institute of Technology, Atlanta, in 1999, and the M.S. and Ph.D. degrees in aeronautics and astronautics from Purdue University, West Lafayette, IN, in 2002 and 2005, respectively. He is a National Research Council Postdoctoral Research Fellow at the U.S. Air Force Academy, Colorado Springs, CO. His work involves the development of pressure-sensitive paint for unsteady aerodynamic applications, as well as the development of plasma actuators and fluidic oscillators as flow control actuators. Dr. Gregory received the American Institute of Aeronautics and Astronautics (AIAA) Wright Brothers Graduate Award in 2005, the Boeing Engineering Student of the Year Award in 2006, and the First Place in the AIAA National Student Paper Competition in 2004.

John P. Sullivan received the B.S. degree in mechanical and aerospace sciences (with honors) from the University of Rochester, Rochester, NY, in 1967, and the M.S. and Sc.D. degrees in aeronautical engineering from the Massachusetts Institute of Technology, Cambridge, in 1969 and 1973, respectively. He has been a Faculty Member in the School of Aeronautics and Astronautics, Purdue University, West Lafayette, IN, since 1975. He served as the Director of the Aerospace Sciences Laboratory, Purdue University, from 1983 to 1995, was the Head of the Department of Aeronautics and Astronautics from 1993 to 1998, and has been the Director of the Center for Advanced Manufacturing since 2004. His research interests include experimental aerodynamics, as well as advanced measurement techniques in fluid dynamics.