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Turbulent and transitional velocity measurements in a rectangular microchannel using microscopic particle image velocimetry
Experimental Thermal and Fluid Science 29 (2005) 435–446 www.elsevier.com/locate/etfs
Turbulent and transitional velocity measurements in a rectangular microchannel using microscopic particle image velocimetry Hao Li, Randy Ewoldt, Michael G. Olsen
*
Department of Mechanical Engineering, Iowa State University, 3025 H.M. Black Engineering Building, Ames, IA 50011, USA Received 30 August 2003; received in revised form 15 May 2004; accepted 5 June 2004
Abstract Microscopic particle image velocimetry (microPIV) experiments were performed on a polydimethylsiloxane (PDMS) microchannel with a cross-section measuring 320 lm · 330 lm for Reynolds numbers between 272 and 2853. Care was taken to ensure that the seed particle density was great enough that accurate instantaneous velocity vector fields could be obtained for all the Reynolds numbers investigated. Velocity fluctuations were calculated from ensembles of microPIV velocity fields. The hu 0 i/umax fluctuation showed an increase at Re = 1535 and a further increase as Reynolds numbers were increased, suggesting that transition to turbulence began near Re = 1535, a Reynolds number lower than predicted by classical theory. The hu 0 i/umax data also suggest the flow was fullydeveloped at a Reynolds number between 2630 and 2853, also lower than classical results. This finding was confirmed in plots of the mean velocity profile. For the fully developed flow, the measured h u 0 i/umax fluctuation agreed well with classical results for turbulent duct flow, but the h v 0 i/umax fluctuation was 25–40% lower than turbulent duct flow results. Finally, spatial correlations of velocity fluctuations were calculated to lend some insights into the characteristics of the large-scale turbulent structures observed in the turbulent microchannel flow. 2004 Elsevier Inc. All rights reserved. Keywords: Turbulence; Transition; Microchannel; MicroPIV
1. Introduction Over the past two decades, microelectromechanical systems (MEMS) have become a rapidly developing technology, finding applications in many areas of engineering and science. Microfluidic MEMS devices involve the flow of liquid or gas to accomplish their design purpose. While many microfluidic MEMS devices, including such microscale analysis systems as gas chromatographs and blood and DNA analyzers, are characterized by low Reynolds number flow, there are some application areas where the Reynolds numbers can be much higher, such as the development of microscale *
Corresponding author. Tel.: +1 515 294 0073; fax: +1 515 294 3261. E-mail address: [email protected] (M.G. Olsen). 0894-1777/$ - see front matter 2004 Elsevier Inc. All rights reserved. doi:10.1016/j.expthermflusci.2004.06.001
heat exchangers for heat sinking applications, such as microelectronics cooling [1]. Because of its importance in this crucial area, the characteristics of fluid flow in microchannels, in both the laminar and turbulent regimes, have attracted a great deal of attention from researchers. However, despite the efforts of many researchers in this area, there exist some discrepancies in the results of previous studies. Wu and Little [2,3], performed some of the first experiments in turbulent microchannel flow, measuring the friction factors and heat transfer characteristics of gas flow in etched glass and silicon microchannels with hydraulic diameters between 45.46 and 83.08 lm. Their results showed that the friction factors and Nusselt numbers for both the laminar and turbulent flow regimes were larger than predictions using traditional macroscale correlations. They also found evidence of
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Nomenclature Latin and Greek characters A area of each interrogation window (mm2) C the volumetric concentration of the fluorescent particle solution (1/mm3) D hydraulic diameter (m) M magnification of objective N quantity of particles in each interrogation window W width of the microchannel (lm) R correlation coefficient (–) Re Reynolds number (–) Zcorr the depth of correlation (lm) dp particle diameter (lm) focal number of the lens f# u longitudinal velocity in microchannel (m/s) u0 fluctuation of instantaneous velocity u (m/s)
early transition to turbulence, with transition observed at Reynolds numbers as low as 400. Peng et al. [4–7] studied the laminar–turbulent transition by measuring the friction factors and heat transfer coefficients of water flow in rectangular stainless steel microchannels with hydraulic diameters of 0.133–0.367 mm. They found that laminar flow ceased at a Reynolds number of 200–700, and fully turbulent flow was achieved at Re = 400–1500. Also, the experimental friction factors and Nusselt numbers were different from conventional theory. The measured frictional resistance was greater than the classical prediction while the Nusselt number was smaller. Gui and Scaringe [8] studied single-phase flow and heat transfer in chemical etched microchannels with hydraulic diameters up to 388 lm and found early transition with the critical Re = 1400. However, good agreement was found between the experimental friction factors in both the laminar and transitional regimes with classical solutions, while the experimental Nusselt numbers were higher than analytical solutions in the laminar flow zone. Harms et al. [9] found an early transition in the plot of the experimental friction factor at a critical Reynolds number of 1500, which is lower than the value of 2400 reported for conventional channels. Mala and Li [10] reported a higher friction factor for fully developed turbulent flow in fused silica and steel microtubes than predicted by conventional theory and attributed it to the early occurrence of the laminar–turbulent transition. Their data suggested early transition from Re > 300 to 900 and fully developed turbulent flow at Re > 1000– 1500. Pfund et al. [11] studied pressure drop of water flowing in high aspect ratio channels with depths ranging from 128 to 521 lm for Reynolds numbers between 60 and 3450 and detected transition from both friction
v0 x Dx s k q
fluctuation of instantaneous transverse velocity (m/s) transverse position (lm) displacement in transverse direction (lm) constant = 0.01 surface roughness (m) wavelength of light emitted by the particles (lm) density (kg/m3)
Mathematical symbol hi ensemble averaging value Subscripts center velocity at the center region of the channel max maximum value
factors and flow visualization experiments with a dye stream. They, too, found that the transitional Reynolds number was lower than the critical Reynolds number for macroscopic ducts, and the transitional Reynolds number decreased further with decreasing channel depth. Wu and Cheng [12] measured the friction factor for laminar flow of deionized water in smooth silicon microchannels of trapezoidal cross-section with hydraulic diameters in the range of 25.9–291.0 lm. A slightly early transition was found at Re = 1500–2000 with good agreement between experimental data and the analytical solution for incompressible, fully developed, laminar flow under a no-slip boundary condition. Most of these researchers attributed the early transition to the relatively high surface roughness in microchannels [2,3,10,13,14]. Although early transition has been observed by some researchers, it is very interesting to note that, in the works of other researchers, there is no evidence of early transition occurring at all. For example, Hegab et al. [15] investigated the fluid flow and heat transfer characteristics of single-phase flows of R134a in aluminum microchannels with hydraulic diameters ranging from 112 to 210 lm and aspect ratios from 1.0 to 1.5. The transition from laminar to turbulent flow was found to occur in the range of 2000–4000 in Reynolds number, which is the same as conventional theory. Qu and Mudawar [16] reported no evidence of early transition in their experiments on the fluid flow characteristics of a microchannel heat sink with dimensions of 231 lm · 713 lm. The Reynolds number in their experiments ranged from 39 to 1672, which is within the range of the early transition reported in previous works. Judy et al. [17] measured frictional pressure drop of fluid flow
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in microtubes with hydraulic diameters between 15 and 150 lm for three different fluids (water, methanol, isopropanol), two different tube materials (fused silica, stainless steel), and two different tube cross-section geometries (circular, square). However, there was no ‘‘distinguishable’’ deviation from macroscale viscous flow theory. Chung et al. [18] performed experiments to study single-phase flow characteristics in a 100 lm capillary tube. Good agreement was observed when the measured friction factor was compared with the conventional theory for deionized water flow, although surface roughness was not considered. The measured velocity also matched the theoretical profile for laminar flow in a circular microchannel. For gas flow, the compressibility effect was found to be important to match the experimental data with theory. The previously mentioned experiments used pressure measurements in their investigations of microchannels, but the recent development of microscopic particle image velocimetry [19–22] has added a new tool for the investigation of microscale fluid flows. Since its development, this technique has also been used for noninvasive measurements in many microchannel geometries and complicated microfluidic systems [23–26]. Using this technique, Zeighami [27] studied transitional flow in silicon microchannels with dimensions of 150 lm · 100 lm. In this work, the repeatability of the velocity data was taken as the criteria to distinguish laminar and turbulent flow. Seed particles were also observed to move in and out of the measurement volume, indicating a threedimensional velocity field that would not be characteristic of laminar microchannel flow. With this criteria, early transition was found at Re = 1200–1600. While this study provided valuable information on transition, the particle seed density was not sufficient for Reynolds stresses to be measured or for turbulent structures to be observed. The present work uses microPIV to obtain instantaneous velocity fields of flow through a rectangular channel measuring 320(W) lm · 330(H) lm. The particle seeding was dense enough that Reynolds stresses could be measured. To determine the onset of turbulence, the velocity profile is compared with the laminar analytical solution and fluctuations in the velocity field are measured. The measured Reynolds stresses are then compared with classical results for macroscale ducts. Finally, spatial correlations of velocity fluctuations are calculated and reported.
2. Microchannel fabrication The microchannels used in the presented experiments were fabricated using PDMS replica molding [28–31]. In this technique, the microchannel is made from polydimethylsiloxane (PDMS) that has been cast onto a mold
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Fig. 1. Cross section schematic of microchannel fabrication technique.
master made of patterned photoresist on a silicon wafer. Two pieces of cast PDMS are brought together to assemble the final device. Devices fabricated using this technique are well suited for optical-based studies because the material is transparent between the wavelengths of 230–700 nm, giving nearly unlimited optical access to the interior of the microchannel at these wavelengths. Fig. 1 summarizes the fabrication procedure. 2.1. Mold master The mold was made from patterned negative photoresist (SU-8 2100, MicroChem Corp., Newton, MA) on a silicon wafer (100 mm diameter, Montco Silicon Technologies, Inc, Spring City, PA). A puddle (50 mm wide) of photoresist was dispensed onto the substrate at static conditions. Spin-coating was then performed by rotating the substrate at 500 rpm for 10 s, accelerating at 300 rpm/s, reaching 1800 rpm and holding for 30 s. The viscosity of SU-8 2100 made it extremely difficult to deposit the resist without introducing bubbles. Additionally, after spin-coating, there was a noticeable line in the resist where the edge of the initial puddle once stood. However, these problems were alleviated by a long soft bake at low temperature. A soft bake was performed in a convection oven at 65 C for 4.5 h, then ramped to 95 C and held for 20 min. After soft baking, the resist was exposed to UV light through a high-resolution transparency film acting as a photomask. A post-expose bake was performed to cross-link the resist, and the mold was then developed using
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1-methoxy-2-propanol acetate (PMA) to remove the unexposed resist, leaving a mold in high relief for the channel. The resulting mold was 330 lm high. 2.2. Casting PDMS Polydimethylsiloxane (PDMS) elastomer (Sylgard(R) 184 Silicone Elastomer Kit, Dow Corning, Midland, MI) was used as the bulk material of the channel. The PDMS prepolymer was mixed with the curing agent in a 10:1 ratio and exposed to low pressure in a desiccator to remove bubbles formed during mixing. The prepolymer mixture was poured over the mold and again placed in the desiccator to remove bubbles. The PDMS casting was then cured in a convection oven at 60 C for a minimum of 2 h.
was determined to be approximately 24 nm. This results in a relative roughness es/D 0.000074. The microchannel experienced repeated catastrophic failure at flow rates near 60 ml/min, thus the maximum Reynolds number that could be investigated in the present study was 2853 This failure occurred at the PDMS/ PDMS interface indicating that the failure was due to a limitation in the plasma bonding of the two surfaces. Multiple microchannel prototypes were fabricated using the previously described technique, but all failed at this maximum flowrate. The authors are currently investigating modifications to the fabrication technique in order to produce stronger PDMS/PDMS surface bonding in order to obtain higher maximum flow rates, but thus far all efforts in this area have failed.
2.3. Microchannel assembly
3. Experimental apparatus and methodology
The final product consisted of two PDMS pieces: a top portion that was cast against the photoresist mold containing three walls of the channel and a bottom portion that had been cast against a blank silicon wafer. Assembly of the channel began with the removal of PDMS from the mold. The PDMS was then trimmed, and access holes were punched through the top portion of PDMS. The two halves were placed in an ethanol bath in an ultrasonic cleaner for 5 min to clean the surfaces, and subsequently dehydrated in a convection oven at 60 C for 10 min. The two halves were then exposed to oxygen plasma (20 W, 1 Torr, 1 min) and immediately brought into conformal contact. The channel was kept in a convection oven at 60 C for 30 min to ensure complete adhesion at the PDMS/PDMS interface. Flexible tubing was coated with RTV sealant and inserted into the access holes in the PDMS. Additional sealant was applied to ensure a complete seal. The sealant was allowed to cure for 2 days. This method for bonding the connecting tubing to the PDMS was strong enough to withstand even the highest flowrates studied in the microPIV experiments. Alternative methods of connecting tubing to the channel resulted in failure at the tubing/PDMS interface for flow rates near 45 ml/min.
The experimental apparatus, schematically shown in Fig. 2, consisted of two parts: (i) the flow delivery system; and (ii) the microPIV system. The flow was driven by a microgear pump and pump head (115 VAC console digital dispensing drive and 0.084 ml/rev suction shoe gear pump head, Cole-Parmer Instrument Co., Vernon Hills, IL). This system was chosen over the more commonly used syringe pump for a number of reasons. First, the micro gear pump was found to provide very steady flowrates with an accuracy of around 0.3%. Furthermore, collecting the large ensembles of microPIV images used in the present study required a far longer run time than the syringe pump could provide. Using the microgear pump allowed the system to be run at essentially steady-state, allowing large numbers of microPIV images to be taken during each run. Flow rate and temperature were monitored using a digital flowmeter (0–100 ml/min volumetric water flow meter, ColeParmer Instrument Co., Vernon Hills, IL) with an accuracy of ±2% full scale. The temperature was carefully monitored during each run, as viscous dissipation could potentially increase the temperature and thus vary the fluid viscosity. A fluid reservoir was also added to the system to increase the thermal mass of fluid, and thus allow for longer run times before any viscous heating was discernable. The microchannel was connected to the flow delivery system with flexible tubing. The microPIV system is shown in the lower portion of Fig. 2. The microchannel is placed on the stage of an inverted biological microscope [Nikon model T-300 Inverted Microscope], and fluid containing fluorescent microspheres is allowed to flow through the microchannel. The light beam from a New Wave Research Gemini Nd:YAG PIV laser is expanded before entering the microscope through an aperture in the back. The laser light is then directed towards the microchannel by a dichroic mirror and passes through a microscope objec-
2.4. Resulting device The resulting microchannel was 5 cm long and had a cross-section of 320 lm · 330 lm, yielding a hydraulic diameter of 325 lm. Surface roughness inside the channel was measured with a Dektak IIA surface profile measuring system (Veeco Instruments Inc., Santa Barbara, CA). Linear surface profiles were taken of the cast PDMS. These measurements were limited, as the profilometer stylus could only be used on the top and bottom surfaces of the channel. The arithmetic average roughness was calculated by the Dektak IIA software and
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Reservoir Control valve Control valve Flowmeter Flexible tubing
Gear Pump Microchannel
MicroPIV system
Microscope stage Objective Emission maximum
Excitation maximum
612 nm
542 nm
Mirror
Beamsplitter 545drlp
CCD Camera Mirror
Convex lens
Concave lens
125mm EFL
25mm EFL
Beam expander
532 nm
Nd: YAG Laser
Microscope Fig. 2. Schematic of the experimental setup.
tive, illuminating the seed particles. The laser is capable of producing up to 120 mJ per laser pulse, but only a small fraction of this light is necessary for the microPIV experiments. An optical attenuator is therefore used to reduce the laser energy to approximately 3 mJ/pulse. The 770 nm diameter fluorescent seed particles (Polystyrene microspheres, Interfacial Dynamics Corp., Portland, OR) are excited by the laser light and emit light at a peak excitation wavelength of 612 nm. A beamsplitter removes the illuminating and background light such that only the emitted light from the particles reaches the CCD camera. Two images are captured per realization, and the two images are analyzed using a cross-correlation technique to yield the instantaneous velocity vector field. The PIV system and software include a LaVision Flowmaster 3 camera and DaVis analysis software (Lavision Inc., Ypsilanti, MI). One of the difficulties that had to be overcome in performing these experiments was seeding the flow sufficiently to allow instantaneous velocity vector fields to be obtained. Because obtaining high seed particle density can be difficult in microPIV, a common analysis technique is to ensemble-average many cross-correlation fields for an individual interrogation region, yielding an average velocity field with high spatial resolution. Indeed, using this technique, microPIV results have been reported with spatial resolutions as small as 1 lm [20]. However, such measurements are of limited usefulness
for turbulent flowfields, as they provide no information about instantaneous velocity fields. Therefore, in the present experiments, the authors chose to sacrifice some spatial resolution in order to achieve a high enough seed density to obtain accurate instantaneous velocity fields. The concentration of the fluorescent particle solution was prepared to ensure at least 5–10 seed particles in each interrogation volume, resulting in a minimal amount of bad velocity vectors in each vector field [32]. The necessary minimum seed density was estimated using the equation N ¼ CAð2Z corr Þ
ð1Þ
where, N is the desired minimum number of particles in each interrogation volume; C is the volumetric concentration of the fluorescent particle solution; A is the area of each interrogation window; and 2Zcorr is the depth of correlation [33] which can be estimated by " !#1=2 pffiffi 2 2 #4 ð1 eÞ 5:95ðM þ 1Þ k f 2 pffiffi Z corr ¼ f #2 d p þ e M2 ð2Þ #
where e = 0.01; f is the focal number of the lens; dp is the particle diameter; M is the magnification, and k is the wavelength of light emitted by the particle. Eq. (2) also provides an estimation of the measurement volume depth for the results reported here (note that an
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alternative equation for the depth of correlation derived by Meinhart et al. [34] yields a similar result for the depth of correlation). In the present experiments, a 20X 0.45 NA objective was used, yielding a depth of correlation of 8.3 lm. The interrogation windows in these experiments measure 28 lm square. Adjacent interrogation windows were overlapped by 50%, yielding a spatial resolution of 14 lm. This spatial resolution allowed for 22 vectors to be measured across the width of the microchannel. Achieving this spatial resolution required a volumetric particle concentration of approximately 0.0567%. This volume fraction of seed particles is small enough that any two-phase effects are negligible, and the working fluid can be considered a single-phase fluid. The timing between laser pulses was set such that the particles moved approximately 1/4th of an interrogation window between pulses. The interrogation windows measured 32 camera pixels square, thus the particles moved approximately 8 pixels between laser pulses. Assuming that the measured velocity is accurate to within 1/5th of a pixel [35] results in an experimental uncertainty of less than ±2.5%. In the microPIV experiments, deionized water was used as the working fluid. In order to prevent the buildup of contaminants in the system, air was pumped through the microchannel first to expel stagnant water and other contaminants. The fluorescent-particle-containing deionized water solution was then pumped through the microchannel at a specified volumetric flowrate. Although the flowrate was displayed by the digital gear pump, this reading was also confirmed by the serially connected flow meter in the microPIV system to ensure the accuracy of the reported Reynolds numbers. The experiments were performed at various flow rates corresponding to Reynolds numbers ranging from 272 to 2853. For each set of experiments, sufficient time was allowed to pass after starting the micro gear pump to allow the flow to reach steady-state. For smaller flow rates, it took a longer time to reach a steady-state compared to higher flow rates. For all flow rates, a multipass interrogation scheme with decreasing smaller window sizes was used in the computation of the vector fields to reach the final 32 · 32 interrogation window, and adjacent interrogation windows were overlapped by 50%. The only post-processing performed on the vector fields was the removal of bad vectors. No smoothing of vector fields was performed. The number of velocity fields collected for each Reynolds number ranged from 600 for the lowest, laminar Reynolds numbers to 2000 for the transitional and turbulent Reynolds numbers.
4. Results and discussion Flow field measurements were performed at the various Reynolds numbers from 272 to 2853 at a sufficiently
long distance downstream of the entrance such that the flow was fully developed. This was verified by taking measurements at different downstream locations and comparing the mean velocity profiles. In all cases, velocity fields were measured at the channel midplane. Fig. 3(a) shows one of the instantaneous velocity fields for Re = 272. At Re = 272, the velocity field suggests the parabolic velocity profile one might expect for laminar channel flow. In addition, the velocity vectors at identical transverse locations are observed to be uniform, with no evidence of turbulent fluctuations. As expected due to the steady and laminar nature of the flow at this Reynolds number, all of the realizations for Re = 272 yielded similar results. Notice that the locations of the bad vectors (which have been removed) are located near the channel walls. This was true in all of the measured velocity vector fields: bad vectors were confined to the region close to the microchannel walls. Fig. 3(b) and (c) are examples of instantaneous velocity fields at Re = 1885 and 2853, respectively. More random variation of vectors, including the fluctuating velocity components in the transverse direction, can be observed with the fluctuations more readily apparent at Re = 2853 than 1885. The velocity profiles can also be seen to become less parabolic than in the laminar case, with the velocity profile becoming fuller, suggesting a transitional or turbulent flow. The turbulent nature of the velocity fields is more easily seen if a constant, convective velocity is subtracted from the instantaneous velocity fields. This has been done for instantaneous velocity fields at Re = 2625, 2718, and 2913 which are shown in Fig. 4. Each of these velocity fields shows evidence of large-scale turbulent structures, as labeled in the figures. Indeed, the appearance of these structures is quite similar to what one would observe in large duct or channel. Great variations in the shape, size, and location of turbulent vortices are observed in these figures. Particularly interesting are the two lower labeled turbulent structures in Fig. 4(c), which appear to be undergoing vortex pairing. Varying the convective velocity that is subtracted from these images can make other turbulent structures within the flowfield more apparent. Similar efforts have been applied to the vector fields for Re < 1535 in an effort to detect turbulent structures in these flowfields, but for these Reynolds numbers no apparent turbulent vortices can be observed. The ensemble-averaged longitudinal velocity profiles for various Reynolds numbers are presented in Fig. 5, together with the corresponding fully developed laminar analytical solutions in a rectangular pipe [37]. The transverse positions of data have been normalized by 1/2 of the width of the microchannel, thus 0 corresponds to the microchannel centerline and 1 corresponds the microchannel wall. For Re = 272, which is in the laminar regime, the agreement between the measured veloc-
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Fig. 3. Instantaneous velocity fields at: (a) Re = 272; (b) Re = 1885 and (c) Re = 2853.
ity profiles and the laminar flow solution is quite good, as one would expect. The good agreement between the measured velocity and the laminar solutions continues until a Reynolds number of 1347. At this Reynolds number, some deviation is noticed, as the velocity profile becomes a bit less parabolic, as one would observe in transitional or turbulent flow. This deviation is a bit puzzling since turbulent velocity fluctuations were not observed at this Reynolds number and the measured velocity fluctuations and Reynolds stresses showed no evidence of transition. As Reynolds number is increased beyond 1347, the deviation from the laminar solution becomes greater, with the measured velocity near the channel axis much lower than the laminar flow prediction, and the velocity near the channel walls much higher until at the highest Reynolds numbers measured, the measured velocity profiles begin to resemble fully developed turbulent flow. The changing shape of the mean velocity profiles with increasing Reynolds number can be easily seen in Fig. 6, in which the velocity profiles have been normalized by the centerline velocity. Fig. 6 also suggests that the flow is fully developed at Re = 2853, since at this Reynolds number the measured
velocity profile almost exactly matches that of fully developed turbulent duct flow. In order to analyze the variation of the velocity fields quantitatively, velocity fluctuations and Reynolds shear stress were computed from the microPIV data. Figs. 7–9 show the dimensionless profiles of h u 0 i/umax, h v 0 i/umax, and hu0 v0 i=u2max , respectively. In Fig. 7, for Reynolds numbers below 1535, the measured centerline values of h u 0 i/umax exhibit a nearly uniform value of around 1.5%. The measured fluctuations at these low Reynolds numbers is not evidence of turbulence, but is instead due to measurement uncertainty. Indeed, the measured velocity fluctuations at these Reynolds numbers are comparable to the experimental error described earlier. At Re = 1535, a dramatic increase in h u 0 i/umax is observed, indicating that the flow is beginning to transition at a Reynolds number slightly lower than that predicted by classical theory. The profiles for Re = 2630 and Re = 2853 are nearly identical, indicating that somewhere in this range of Reynolds number, the flow has reached a fully-developed state. These fully-developed values for h u 0 i/umax are slightly higher than classical results for turbulent duct flow [20], but in general, the
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Fig. 4. Instantaneous vector fields with convective velocities subtracted showing turbulent vortices at: (a) Re = 2342; (b) Re = 2630, and (c) Re = 2853.
Fig. 5. Comparison of experimental velocity profiles with analytical laminar solutions.
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Fig. 6. Normalized mean velocity profiles for the experimental data.
Fig. 7. Normalized streamwise velocity fluctuation h u 0 i/umax.
Fig. 8. Normalized transverse velocity fluctuations, h v 0 i/umax.
agreement is good, as all of the results fall within the experimental uncertainty of around 2.5%. A plot of the h v 0 i/umax fluctuation is shown in Fig. 8. For Re < 1885, the curves are clumped together, with h v 0 i/umax around 1%. As with the h u 0 i/umax measurements at the lower Reynolds numbers, these measured fluctuations are due to measurement uncertainty. A
small increase in h v 0 i/umax is observed at Re = 1885, and this is followed by a rapid increase as the Reynolds number is further increased. The data in Fig. 8 also suggest that the flow becomes fully developed between 2630 < Re < 2853. For the highest Reynolds numbers studied, h v 0 i/umax was found to be around 3% at the channel centerline. Comparing Figs. 7 and 8, one finds
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Fig. 9. Normalized Reynolds shearing stress hu0 v0 i=u2max .
that the value of h v 0 i/umax is about 1/2–2/3 that of h u 0 i/ umax. This is due to the predominantly one-dimensional flow in the microchannel, which results in smaller fluctuations in the transverse direction. This ratio is consistent with previous studies of turbulent duct flow [36]. The agreement between the measured h v 0 i/umax fluctuations at the highest Reynolds numbers with classical results for turbulent duct flow is not as good as that as the agreement for h u 0 i/umax. Instead of becoming higher near the channel walls, h v 0 i/umax was found to be nearly constant throughout the microchannel. The measured values were also 25–40% smaller than the previous turbulent duct flow results. Fig. 9 shows the Reynolds shear stress, hu0 v0 i=u2max . For Re < 1885, there is little turbulent shearing stress, and the value of hu0 v0 i=u2max is seen to be very close to zero. At Re = 1885, there is a slight increase in the Reynolds shear stress, and a continual increase in hu0 v0 i=u2max is observed as Re is increased further. The value of hu0 v0 i=u2max is nearly zero in the center of the microchannel, as required by symmetry. The peak values in the plot correspond to the locations where the turbulent friction has its largest value. The fully developed
values of hu0 v0 i=u2max are slightly lower than previous turbulent duct flow results. In summary, the measured velocity fluctuations and Reynolds shear stress suggest a slightly earlier transition for the microchannel flow than is expected by conventional theory. There is some evidence of transition at around 1535 in the h u 0 i/umax data in that the measured velocity fluctuation at this Reynolds number rises above the data for lower Reynolds numbers, but this is not observed in either the h v 0 i/umax or the hu0 v0 i=u2max data. However, the measured values of the v velocity component are very small, and thus small fluctuations may be difficult to detect, resulting in difficulty in identifying transition using these quantities. Since the u velocity component is the one most easily measured, it follows that fluctuations rising above experimental noise would be most readily observable in this component. Thus, the fact that evidence of transition is first observed in the measurements of the h u 0 i/umax fluctuation is not at all surprising. The measured values and behavior of h u 0 i/ umax agree well with classical results for turbulent duct flow, but the results for h v 0 i/umax are lower than the classical results for turbulent duct flow.
1 Re= 1885 Re= 2342 Re= 2555 Re= 2630 Re= 2853
0.8
Ru'u'
0.6
0.4
0.2
0 0
0.2
0.4
0.6
0.8
1
y/(W/2)
Fig. 10. Spatial correlation Ru 0 u 0 with respect to the normalized transverse positions.
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1 Re= 2093 Re= 2342 Re= 2555 Re= 2630 Re= 2853
Rv'v'
0.8
0.6
0.4
0.2
0 0
0.2
0.4
0.6
0.8
1
y/(W/2)
Fig. 11. Spatial correlation Rv 0 v 0 with respect to the normalized transverse positions.
Finally the spatial correlations of the u 0 and v 0 velocity fluctuations, Ru 0 u 0 and Rv 0 v 0 , were calculated and are shown in Figs. 10 and 11, respectively. The Ru 0 u 0 velocity correlation is defined as hu0 ð0Þu0 ðDyÞi Ru0 u0 ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiqffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 hu0 ð0Þ i hu0 ðDyÞ i
ð3Þ
where, u 0 (0) is the longitudinal fluctuating velocity component at a point on the channel axis; and u 0 (Dy) is the longitudinal fluctuation velocity component at a different transverse position. These spatial correlations can provide a statistical description of the large-scale structures in the flowfield. In Fig. 10, Ru 0 u 0 equals 1 at the channel axis because Eq. (3) converts to the velocity autocorrelation when Dy = 0. As the correlation distance vector moves away from the channel centerline, Ru 0 u 0 can be seen to decrease. The same trends can be seen in the Rv 0 v 0 correlation, as shown in Fig. 11. Both the Ru 0 u 0 and the Rv 0 v 0 correlations decay at nearly the same rate, with both correlations dropping to 0.5 at a distance of approximately 0.4 channel half-widths from the microchannel centerline.
5. Conclusions Microscopic particle image velocimetry has been applied to measure instantaneous velocity fields in a 320 lm · 330 lm microchannel at various Reynolds numbers. In the instantaneous velocity vector fields, little evidence of velocity fluctuations or turbulent structures was observed for Re < 1535. However, at the higher Reynolds numbers in the study, great variation is seen in the individual velocity fields due to velocity fluctuations, and large-scale turbulent structures were observed. Results for the measured velocity fluctuations show a slight increase in the h u 0 i/umax at Re = 1535 fluctuation over the measured fluctuation for lower
Reynolds numbers, indicating the beginnings of transition. The flow was reached a fully developed state in the range 2630 < Re < 2853. The velocity fluctuation data thus suggested a slightly earlier transition to turbulence and fully developed state than is typically observed at the macroscale. For the fully developed flow, the measured h u 0 i/umax fluctuation is a bit higher, but generally agreed well with classical results for turbulent duct flow. However, the h v 0 i/umax fluctuation was found to be 25–40% lower than previous turbulent duct flow results. Finally, spatial correlations of velocity fluctuations were calculated. The results displayed the expected trends, with correlation values decreasing as the correlation displacement was increased. The Ru 0 u 0 correlation decreases more rapidly as the Reynolds number is increased, indicating the more turbulent nature of the flowfield as the Reynolds number is increased. A similar trend was not observed in the Rv 0 v 0 correlations, which remained consistent over the range of Reynolds numbers studied.
Acknowledgement The work was funded by the National Science Foundation under grant number CTS-0134469.
References [1] D.B. Tuckerman, R.F. Pease, High-performance heat sinking for VLSI, IEEE Electronic Device Letters 2 (1981) 126– 129. [2] P.Y. Wu, W.A. Little, Measurement of friction factor for flow of gases in very fine channels used for micro-miniature Joule– Thompson refrigerators, Cryogenics 23 (1983) 273–277. [3] P.Y. Wu, W.A. Little, Measurement of the heat transfer characteristics of gas flow in fine channel heat exchanger used for microminiature refrigerators, Cryogenics 24 (1984) 415– 423.
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[4] X.F. Peng, G.P. Peterson, B.X. Wang, Frictional flow characteristics of water flowing through rectangular microchannels, Experimental Heat Transfer 7 (1994) 249–264. [5] X.F. Peng, G.P. Peterson, B.X. Wang, Heat transfer characteristics of water flowing through microchannels, Experimental Heat Transfer 7 (1994) 265–283. [6] X.F. Peng, G.P. Peterson, The effect of thermofluid and geometrical parameters on convection of liquids through rectangular microchannels, International Journal of Heat and Mass Transfer 38 (1995) 755–758. [7] X.F. Peng, G.P. Peterson, Convective heat transfer and fluid flow friction for water flow in microchannel structures, International Journal of Heat and Mass Transfer 39 (1996) 2599–2608. [8] F. Gui, R.P. Scaringe, Enhanced heat transfer in the entrance region of microchannels, in: Proceedings of the 30th Intersociety Energy Conversion Engineering Conference, vol. 2, 1995, pp. 289– 294. [9] T.M. Harms, M.J. Kazmierczak, F.M. Gerner, Developing convective heat transfer in deep rectangular microchannels, International Journal of Heat and Fluid Flow 20 (1999) 149–157. [10] G.M. Mala, D. Li, Flow characteristics of water in microtubes, International Journal of Heat and Fluid Flow 20 (1999) 142–148. [11] D. Pfund, D. Rector, A. Shekarriz, Pressure drop measurements in a microchannel, Fluid Mechanics and Transport Phenomena 46 (8) (2000) 1496–1507. [12] H.Y. Wu, P. Cheng, Friction factors in smooth trapezoidal silicon microchannels with different aspect ratios, International Journal of Heat and Mass Transfer 46 (2003) 2519–2525. [13] Z.Y. Guo, Z.X. Li, Size effect on single-phase channel flow and heat transfer at microscale, International Journal of Heat and Fluid Flow 24 (2003) 284–298. [14] Z.Y. Guo, Z.X. Li, Size effect on microscale single-phase flow and heat transfer, International Journal of Heat and Mass Transfer 46 (2003) 149–159. [15] H.E. Hegab, A. Bari, T. Ameel, Friction and convection studies of R-134a in microchannels within the transition and turbulent flow regimes, Experimental Heat Transfer 15 (2002) 245–259. [16] W. Qu, I. Mudawar, Experimental and numerical study of pressure drop and heat transfer in a single-phase micro-channel heat sink, International Journal of Heat and Mass Transfer 45 (2002) 2549–2565. [17] J. Judy, D. Maynes, B.W. Webb, Characterization of frictional pressure drop for liquid flows through microchannels, International Journal of Heat and Mass Transfer 45 (2002) 3477–3489. [18] P.M.-Y. Chung, M. Kawaji, A. Kawahara, Characteristics of single-phase flow in microchannels, Fluids Engineering Division (Publication) FED 257 (1B) (2002) 1219–1228, American Society of Mechanical Engineers. [19] J.G. Santiago, S.T. Wereley, C.D. Meinhart, D.J. Beebe, R.J. Adrian, A particle image velocimetry system for microfluidics, Experiments in Fluids 25 (1998) 316–319. [20] C.D. Meinhart, S.T. Wereley, J.G. Santiago, PIV measurements of a microchannel flow, Experiments in Fluids 27 (1999) 414–419. [21] M.G. Olsen, R.J. Adrian, Brownian motion and correlation in particle image velocimetry, Optics and Laser Technology 32 (2000) 621–627.
[22] S. Devasenathipathy, J.G. Santiago, S.T. Wereley, C.D. Meinhart, K. Takehara, Particle imaging techniques for microfabricated fluidic systems, Experiments in Fluids 34 (2003) 504–514. [23] H. Klank, G. Goranovic, J.P. Kutter, H. Gjelstrup, J. Michelsen, C.H. Westergaard, PIV measurements in a microfluidic 3Dsheathing structure with three-dimensional flow behaviour, Journal Micromechanics and Microengineering 12 (2002) 862–869. [24] M. Shafiqul Islam, K. Haga, M. Kaminaga, R. Hino, M. Monde, Experimental analysis of turbulent flow structure in a fully developed rib-roughened rectangular channel with PIV, Experiments in Fluids 33 (2002) 296–306. [25] S.W. Stone, C.D. Meinhart, S.T. Wereley, A microfluidic-based nanoscope, Experiments in Fluids 33 (2002) 613–619. [26] J.H. Chan, A.T. Timperman, D. Qin, R. Aebersold, Microfabricated polymer devices for automated sample delivery of peptides for analysis by electrospray ionization tandem mass spectrometry (general description of PDMS replica molding), Anal. Chem. 71 (20) (1999) 4437–4444. [27] R. Zeighami, D. Laser, P. Zhou, M. Asheghi, S. Devasenathipathy, T. Kenny, J. Santiago, K. Goodson, Experimental investigation of flow transition in microchannels using micron-resolution particle image velocimetry, in: Thermomechanical Phenomena in Electronic Systems––Proceedings of the Intersociety Conference, vol. 2, 2000, pp. 148–153. [28] S.Y. Son, K.D. Kihm, J.C. Han, PIV flow measurements for heat transfer characterization in two-pass square channels with smooth and 90 ribbed walls, International Journal of Heat and Mass Transfer 45 (2002) 4809–4822. [29] J.C. McDonald, D.C. Duffy, J.R. Anderson, D.T. Chiu, H. Wu., O.J.A. Schueller, G.M. Whitesides, Fabrication of microfluidic systems in poly(dimethylsiloxane), Electrophoresis. 21 (2000) 27– 40. [30] B.H. Jo, L.M. Van Lerberghe, K.M. Motsegood, D.J. Beebe, Three-dimensional micro-channel fabrication in polydimethylsiloxane (PDMS) elastomer, Journal of Microelectromechanical Systems 9 (1) (2000) 76–81. [31] A. Folch, A. Ayon, O. Hurtado, M.A. Schmidt, M. Toner, Molding of deep polydimethylsiloxane microstructures for microfluidics and biological applications, Journal of Biomechanical Engineering, Transactions of the ASME 121 (1) (1999) 28–34. [32] R.D. Keane, R.J. Adrian, Optimization of particle image velocimeters: I. Double pulsed systems, Measurement Science and Technology 1 (1990) 1202–1215. [33] M.G. Olsen, R.J. Adrian, Out-of-focus effects on particle image visibility and correlation in microscopic particle image velocimetry, Experiments in Fluids 29 (2000) S166–S174. [34] C.D. Meinhart, S.T. Wereley, H.B. Gray, Volume illumination for two-dimensional particle image velocimetry, Measuring Science Technology 11 (2000) 809–814. [35] A.K. Prassad, R.J. Adrian, C.C. Landreth, P.W. Offutt, Effect of resolution on the speed and accuracy of particle image velocimetry interrogation, Experiments in Fluids 13 (1992) 105–116. [36] H. Schlichting, Boundary-Layer Theory, seventh ed., McGrawHill, New York, 1987. [37] F.M. White, Viscous Fluid Flow, second ed., McGraw-Hill, New York, 1991.
Turbulent and transitional velocity measurements in a rectangular microchannel using microscopic particle image velocimetry Hao Li, Randy Ewoldt, Michael G. Olsen
*
Department of Mechanical Engineering, Iowa State University, 3025 H.M. Black Engineering Building, Ames, IA 50011, USA Received 30 August 2003; received in revised form 15 May 2004; accepted 5 June 2004
Abstract Microscopic particle image velocimetry (microPIV) experiments were performed on a polydimethylsiloxane (PDMS) microchannel with a cross-section measuring 320 lm · 330 lm for Reynolds numbers between 272 and 2853. Care was taken to ensure that the seed particle density was great enough that accurate instantaneous velocity vector fields could be obtained for all the Reynolds numbers investigated. Velocity fluctuations were calculated from ensembles of microPIV velocity fields. The hu 0 i/umax fluctuation showed an increase at Re = 1535 and a further increase as Reynolds numbers were increased, suggesting that transition to turbulence began near Re = 1535, a Reynolds number lower than predicted by classical theory. The hu 0 i/umax data also suggest the flow was fullydeveloped at a Reynolds number between 2630 and 2853, also lower than classical results. This finding was confirmed in plots of the mean velocity profile. For the fully developed flow, the measured h u 0 i/umax fluctuation agreed well with classical results for turbulent duct flow, but the h v 0 i/umax fluctuation was 25–40% lower than turbulent duct flow results. Finally, spatial correlations of velocity fluctuations were calculated to lend some insights into the characteristics of the large-scale turbulent structures observed in the turbulent microchannel flow. 2004 Elsevier Inc. All rights reserved. Keywords: Turbulence; Transition; Microchannel; MicroPIV
1. Introduction Over the past two decades, microelectromechanical systems (MEMS) have become a rapidly developing technology, finding applications in many areas of engineering and science. Microfluidic MEMS devices involve the flow of liquid or gas to accomplish their design purpose. While many microfluidic MEMS devices, including such microscale analysis systems as gas chromatographs and blood and DNA analyzers, are characterized by low Reynolds number flow, there are some application areas where the Reynolds numbers can be much higher, such as the development of microscale *
Corresponding author. Tel.: +1 515 294 0073; fax: +1 515 294 3261. E-mail address: [email protected] (M.G. Olsen). 0894-1777/$ - see front matter 2004 Elsevier Inc. All rights reserved. doi:10.1016/j.expthermflusci.2004.06.001
heat exchangers for heat sinking applications, such as microelectronics cooling [1]. Because of its importance in this crucial area, the characteristics of fluid flow in microchannels, in both the laminar and turbulent regimes, have attracted a great deal of attention from researchers. However, despite the efforts of many researchers in this area, there exist some discrepancies in the results of previous studies. Wu and Little [2,3], performed some of the first experiments in turbulent microchannel flow, measuring the friction factors and heat transfer characteristics of gas flow in etched glass and silicon microchannels with hydraulic diameters between 45.46 and 83.08 lm. Their results showed that the friction factors and Nusselt numbers for both the laminar and turbulent flow regimes were larger than predictions using traditional macroscale correlations. They also found evidence of
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Nomenclature Latin and Greek characters A area of each interrogation window (mm2) C the volumetric concentration of the fluorescent particle solution (1/mm3) D hydraulic diameter (m) M magnification of objective N quantity of particles in each interrogation window W width of the microchannel (lm) R correlation coefficient (–) Re Reynolds number (–) Zcorr the depth of correlation (lm) dp particle diameter (lm) focal number of the lens f# u longitudinal velocity in microchannel (m/s) u0 fluctuation of instantaneous velocity u (m/s)
early transition to turbulence, with transition observed at Reynolds numbers as low as 400. Peng et al. [4–7] studied the laminar–turbulent transition by measuring the friction factors and heat transfer coefficients of water flow in rectangular stainless steel microchannels with hydraulic diameters of 0.133–0.367 mm. They found that laminar flow ceased at a Reynolds number of 200–700, and fully turbulent flow was achieved at Re = 400–1500. Also, the experimental friction factors and Nusselt numbers were different from conventional theory. The measured frictional resistance was greater than the classical prediction while the Nusselt number was smaller. Gui and Scaringe [8] studied single-phase flow and heat transfer in chemical etched microchannels with hydraulic diameters up to 388 lm and found early transition with the critical Re = 1400. However, good agreement was found between the experimental friction factors in both the laminar and transitional regimes with classical solutions, while the experimental Nusselt numbers were higher than analytical solutions in the laminar flow zone. Harms et al. [9] found an early transition in the plot of the experimental friction factor at a critical Reynolds number of 1500, which is lower than the value of 2400 reported for conventional channels. Mala and Li [10] reported a higher friction factor for fully developed turbulent flow in fused silica and steel microtubes than predicted by conventional theory and attributed it to the early occurrence of the laminar–turbulent transition. Their data suggested early transition from Re > 300 to 900 and fully developed turbulent flow at Re > 1000– 1500. Pfund et al. [11] studied pressure drop of water flowing in high aspect ratio channels with depths ranging from 128 to 521 lm for Reynolds numbers between 60 and 3450 and detected transition from both friction
v0 x Dx s k q
fluctuation of instantaneous transverse velocity (m/s) transverse position (lm) displacement in transverse direction (lm) constant = 0.01 surface roughness (m) wavelength of light emitted by the particles (lm) density (kg/m3)
Mathematical symbol hi ensemble averaging value Subscripts center velocity at the center region of the channel max maximum value
factors and flow visualization experiments with a dye stream. They, too, found that the transitional Reynolds number was lower than the critical Reynolds number for macroscopic ducts, and the transitional Reynolds number decreased further with decreasing channel depth. Wu and Cheng [12] measured the friction factor for laminar flow of deionized water in smooth silicon microchannels of trapezoidal cross-section with hydraulic diameters in the range of 25.9–291.0 lm. A slightly early transition was found at Re = 1500–2000 with good agreement between experimental data and the analytical solution for incompressible, fully developed, laminar flow under a no-slip boundary condition. Most of these researchers attributed the early transition to the relatively high surface roughness in microchannels [2,3,10,13,14]. Although early transition has been observed by some researchers, it is very interesting to note that, in the works of other researchers, there is no evidence of early transition occurring at all. For example, Hegab et al. [15] investigated the fluid flow and heat transfer characteristics of single-phase flows of R134a in aluminum microchannels with hydraulic diameters ranging from 112 to 210 lm and aspect ratios from 1.0 to 1.5. The transition from laminar to turbulent flow was found to occur in the range of 2000–4000 in Reynolds number, which is the same as conventional theory. Qu and Mudawar [16] reported no evidence of early transition in their experiments on the fluid flow characteristics of a microchannel heat sink with dimensions of 231 lm · 713 lm. The Reynolds number in their experiments ranged from 39 to 1672, which is within the range of the early transition reported in previous works. Judy et al. [17] measured frictional pressure drop of fluid flow
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in microtubes with hydraulic diameters between 15 and 150 lm for three different fluids (water, methanol, isopropanol), two different tube materials (fused silica, stainless steel), and two different tube cross-section geometries (circular, square). However, there was no ‘‘distinguishable’’ deviation from macroscale viscous flow theory. Chung et al. [18] performed experiments to study single-phase flow characteristics in a 100 lm capillary tube. Good agreement was observed when the measured friction factor was compared with the conventional theory for deionized water flow, although surface roughness was not considered. The measured velocity also matched the theoretical profile for laminar flow in a circular microchannel. For gas flow, the compressibility effect was found to be important to match the experimental data with theory. The previously mentioned experiments used pressure measurements in their investigations of microchannels, but the recent development of microscopic particle image velocimetry [19–22] has added a new tool for the investigation of microscale fluid flows. Since its development, this technique has also been used for noninvasive measurements in many microchannel geometries and complicated microfluidic systems [23–26]. Using this technique, Zeighami [27] studied transitional flow in silicon microchannels with dimensions of 150 lm · 100 lm. In this work, the repeatability of the velocity data was taken as the criteria to distinguish laminar and turbulent flow. Seed particles were also observed to move in and out of the measurement volume, indicating a threedimensional velocity field that would not be characteristic of laminar microchannel flow. With this criteria, early transition was found at Re = 1200–1600. While this study provided valuable information on transition, the particle seed density was not sufficient for Reynolds stresses to be measured or for turbulent structures to be observed. The present work uses microPIV to obtain instantaneous velocity fields of flow through a rectangular channel measuring 320(W) lm · 330(H) lm. The particle seeding was dense enough that Reynolds stresses could be measured. To determine the onset of turbulence, the velocity profile is compared with the laminar analytical solution and fluctuations in the velocity field are measured. The measured Reynolds stresses are then compared with classical results for macroscale ducts. Finally, spatial correlations of velocity fluctuations are calculated and reported.
2. Microchannel fabrication The microchannels used in the presented experiments were fabricated using PDMS replica molding [28–31]. In this technique, the microchannel is made from polydimethylsiloxane (PDMS) that has been cast onto a mold
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Fig. 1. Cross section schematic of microchannel fabrication technique.
master made of patterned photoresist on a silicon wafer. Two pieces of cast PDMS are brought together to assemble the final device. Devices fabricated using this technique are well suited for optical-based studies because the material is transparent between the wavelengths of 230–700 nm, giving nearly unlimited optical access to the interior of the microchannel at these wavelengths. Fig. 1 summarizes the fabrication procedure. 2.1. Mold master The mold was made from patterned negative photoresist (SU-8 2100, MicroChem Corp., Newton, MA) on a silicon wafer (100 mm diameter, Montco Silicon Technologies, Inc, Spring City, PA). A puddle (50 mm wide) of photoresist was dispensed onto the substrate at static conditions. Spin-coating was then performed by rotating the substrate at 500 rpm for 10 s, accelerating at 300 rpm/s, reaching 1800 rpm and holding for 30 s. The viscosity of SU-8 2100 made it extremely difficult to deposit the resist without introducing bubbles. Additionally, after spin-coating, there was a noticeable line in the resist where the edge of the initial puddle once stood. However, these problems were alleviated by a long soft bake at low temperature. A soft bake was performed in a convection oven at 65 C for 4.5 h, then ramped to 95 C and held for 20 min. After soft baking, the resist was exposed to UV light through a high-resolution transparency film acting as a photomask. A post-expose bake was performed to cross-link the resist, and the mold was then developed using
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1-methoxy-2-propanol acetate (PMA) to remove the unexposed resist, leaving a mold in high relief for the channel. The resulting mold was 330 lm high. 2.2. Casting PDMS Polydimethylsiloxane (PDMS) elastomer (Sylgard(R) 184 Silicone Elastomer Kit, Dow Corning, Midland, MI) was used as the bulk material of the channel. The PDMS prepolymer was mixed with the curing agent in a 10:1 ratio and exposed to low pressure in a desiccator to remove bubbles formed during mixing. The prepolymer mixture was poured over the mold and again placed in the desiccator to remove bubbles. The PDMS casting was then cured in a convection oven at 60 C for a minimum of 2 h.
was determined to be approximately 24 nm. This results in a relative roughness es/D 0.000074. The microchannel experienced repeated catastrophic failure at flow rates near 60 ml/min, thus the maximum Reynolds number that could be investigated in the present study was 2853 This failure occurred at the PDMS/ PDMS interface indicating that the failure was due to a limitation in the plasma bonding of the two surfaces. Multiple microchannel prototypes were fabricated using the previously described technique, but all failed at this maximum flowrate. The authors are currently investigating modifications to the fabrication technique in order to produce stronger PDMS/PDMS surface bonding in order to obtain higher maximum flow rates, but thus far all efforts in this area have failed.
2.3. Microchannel assembly
3. Experimental apparatus and methodology
The final product consisted of two PDMS pieces: a top portion that was cast against the photoresist mold containing three walls of the channel and a bottom portion that had been cast against a blank silicon wafer. Assembly of the channel began with the removal of PDMS from the mold. The PDMS was then trimmed, and access holes were punched through the top portion of PDMS. The two halves were placed in an ethanol bath in an ultrasonic cleaner for 5 min to clean the surfaces, and subsequently dehydrated in a convection oven at 60 C for 10 min. The two halves were then exposed to oxygen plasma (20 W, 1 Torr, 1 min) and immediately brought into conformal contact. The channel was kept in a convection oven at 60 C for 30 min to ensure complete adhesion at the PDMS/PDMS interface. Flexible tubing was coated with RTV sealant and inserted into the access holes in the PDMS. Additional sealant was applied to ensure a complete seal. The sealant was allowed to cure for 2 days. This method for bonding the connecting tubing to the PDMS was strong enough to withstand even the highest flowrates studied in the microPIV experiments. Alternative methods of connecting tubing to the channel resulted in failure at the tubing/PDMS interface for flow rates near 45 ml/min.
The experimental apparatus, schematically shown in Fig. 2, consisted of two parts: (i) the flow delivery system; and (ii) the microPIV system. The flow was driven by a microgear pump and pump head (115 VAC console digital dispensing drive and 0.084 ml/rev suction shoe gear pump head, Cole-Parmer Instrument Co., Vernon Hills, IL). This system was chosen over the more commonly used syringe pump for a number of reasons. First, the micro gear pump was found to provide very steady flowrates with an accuracy of around 0.3%. Furthermore, collecting the large ensembles of microPIV images used in the present study required a far longer run time than the syringe pump could provide. Using the microgear pump allowed the system to be run at essentially steady-state, allowing large numbers of microPIV images to be taken during each run. Flow rate and temperature were monitored using a digital flowmeter (0–100 ml/min volumetric water flow meter, ColeParmer Instrument Co., Vernon Hills, IL) with an accuracy of ±2% full scale. The temperature was carefully monitored during each run, as viscous dissipation could potentially increase the temperature and thus vary the fluid viscosity. A fluid reservoir was also added to the system to increase the thermal mass of fluid, and thus allow for longer run times before any viscous heating was discernable. The microchannel was connected to the flow delivery system with flexible tubing. The microPIV system is shown in the lower portion of Fig. 2. The microchannel is placed on the stage of an inverted biological microscope [Nikon model T-300 Inverted Microscope], and fluid containing fluorescent microspheres is allowed to flow through the microchannel. The light beam from a New Wave Research Gemini Nd:YAG PIV laser is expanded before entering the microscope through an aperture in the back. The laser light is then directed towards the microchannel by a dichroic mirror and passes through a microscope objec-
2.4. Resulting device The resulting microchannel was 5 cm long and had a cross-section of 320 lm · 330 lm, yielding a hydraulic diameter of 325 lm. Surface roughness inside the channel was measured with a Dektak IIA surface profile measuring system (Veeco Instruments Inc., Santa Barbara, CA). Linear surface profiles were taken of the cast PDMS. These measurements were limited, as the profilometer stylus could only be used on the top and bottom surfaces of the channel. The arithmetic average roughness was calculated by the Dektak IIA software and
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Reservoir Control valve Control valve Flowmeter Flexible tubing
Gear Pump Microchannel
MicroPIV system
Microscope stage Objective Emission maximum
Excitation maximum
612 nm
542 nm
Mirror
Beamsplitter 545drlp
CCD Camera Mirror
Convex lens
Concave lens
125mm EFL
25mm EFL
Beam expander
532 nm
Nd: YAG Laser
Microscope Fig. 2. Schematic of the experimental setup.
tive, illuminating the seed particles. The laser is capable of producing up to 120 mJ per laser pulse, but only a small fraction of this light is necessary for the microPIV experiments. An optical attenuator is therefore used to reduce the laser energy to approximately 3 mJ/pulse. The 770 nm diameter fluorescent seed particles (Polystyrene microspheres, Interfacial Dynamics Corp., Portland, OR) are excited by the laser light and emit light at a peak excitation wavelength of 612 nm. A beamsplitter removes the illuminating and background light such that only the emitted light from the particles reaches the CCD camera. Two images are captured per realization, and the two images are analyzed using a cross-correlation technique to yield the instantaneous velocity vector field. The PIV system and software include a LaVision Flowmaster 3 camera and DaVis analysis software (Lavision Inc., Ypsilanti, MI). One of the difficulties that had to be overcome in performing these experiments was seeding the flow sufficiently to allow instantaneous velocity vector fields to be obtained. Because obtaining high seed particle density can be difficult in microPIV, a common analysis technique is to ensemble-average many cross-correlation fields for an individual interrogation region, yielding an average velocity field with high spatial resolution. Indeed, using this technique, microPIV results have been reported with spatial resolutions as small as 1 lm [20]. However, such measurements are of limited usefulness
for turbulent flowfields, as they provide no information about instantaneous velocity fields. Therefore, in the present experiments, the authors chose to sacrifice some spatial resolution in order to achieve a high enough seed density to obtain accurate instantaneous velocity fields. The concentration of the fluorescent particle solution was prepared to ensure at least 5–10 seed particles in each interrogation volume, resulting in a minimal amount of bad velocity vectors in each vector field [32]. The necessary minimum seed density was estimated using the equation N ¼ CAð2Z corr Þ
ð1Þ
where, N is the desired minimum number of particles in each interrogation volume; C is the volumetric concentration of the fluorescent particle solution; A is the area of each interrogation window; and 2Zcorr is the depth of correlation [33] which can be estimated by " !#1=2 pffiffi 2 2 #4 ð1 eÞ 5:95ðM þ 1Þ k f 2 pffiffi Z corr ¼ f #2 d p þ e M2 ð2Þ #
where e = 0.01; f is the focal number of the lens; dp is the particle diameter; M is the magnification, and k is the wavelength of light emitted by the particle. Eq. (2) also provides an estimation of the measurement volume depth for the results reported here (note that an
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alternative equation for the depth of correlation derived by Meinhart et al. [34] yields a similar result for the depth of correlation). In the present experiments, a 20X 0.45 NA objective was used, yielding a depth of correlation of 8.3 lm. The interrogation windows in these experiments measure 28 lm square. Adjacent interrogation windows were overlapped by 50%, yielding a spatial resolution of 14 lm. This spatial resolution allowed for 22 vectors to be measured across the width of the microchannel. Achieving this spatial resolution required a volumetric particle concentration of approximately 0.0567%. This volume fraction of seed particles is small enough that any two-phase effects are negligible, and the working fluid can be considered a single-phase fluid. The timing between laser pulses was set such that the particles moved approximately 1/4th of an interrogation window between pulses. The interrogation windows measured 32 camera pixels square, thus the particles moved approximately 8 pixels between laser pulses. Assuming that the measured velocity is accurate to within 1/5th of a pixel [35] results in an experimental uncertainty of less than ±2.5%. In the microPIV experiments, deionized water was used as the working fluid. In order to prevent the buildup of contaminants in the system, air was pumped through the microchannel first to expel stagnant water and other contaminants. The fluorescent-particle-containing deionized water solution was then pumped through the microchannel at a specified volumetric flowrate. Although the flowrate was displayed by the digital gear pump, this reading was also confirmed by the serially connected flow meter in the microPIV system to ensure the accuracy of the reported Reynolds numbers. The experiments were performed at various flow rates corresponding to Reynolds numbers ranging from 272 to 2853. For each set of experiments, sufficient time was allowed to pass after starting the micro gear pump to allow the flow to reach steady-state. For smaller flow rates, it took a longer time to reach a steady-state compared to higher flow rates. For all flow rates, a multipass interrogation scheme with decreasing smaller window sizes was used in the computation of the vector fields to reach the final 32 · 32 interrogation window, and adjacent interrogation windows were overlapped by 50%. The only post-processing performed on the vector fields was the removal of bad vectors. No smoothing of vector fields was performed. The number of velocity fields collected for each Reynolds number ranged from 600 for the lowest, laminar Reynolds numbers to 2000 for the transitional and turbulent Reynolds numbers.
4. Results and discussion Flow field measurements were performed at the various Reynolds numbers from 272 to 2853 at a sufficiently
long distance downstream of the entrance such that the flow was fully developed. This was verified by taking measurements at different downstream locations and comparing the mean velocity profiles. In all cases, velocity fields were measured at the channel midplane. Fig. 3(a) shows one of the instantaneous velocity fields for Re = 272. At Re = 272, the velocity field suggests the parabolic velocity profile one might expect for laminar channel flow. In addition, the velocity vectors at identical transverse locations are observed to be uniform, with no evidence of turbulent fluctuations. As expected due to the steady and laminar nature of the flow at this Reynolds number, all of the realizations for Re = 272 yielded similar results. Notice that the locations of the bad vectors (which have been removed) are located near the channel walls. This was true in all of the measured velocity vector fields: bad vectors were confined to the region close to the microchannel walls. Fig. 3(b) and (c) are examples of instantaneous velocity fields at Re = 1885 and 2853, respectively. More random variation of vectors, including the fluctuating velocity components in the transverse direction, can be observed with the fluctuations more readily apparent at Re = 2853 than 1885. The velocity profiles can also be seen to become less parabolic than in the laminar case, with the velocity profile becoming fuller, suggesting a transitional or turbulent flow. The turbulent nature of the velocity fields is more easily seen if a constant, convective velocity is subtracted from the instantaneous velocity fields. This has been done for instantaneous velocity fields at Re = 2625, 2718, and 2913 which are shown in Fig. 4. Each of these velocity fields shows evidence of large-scale turbulent structures, as labeled in the figures. Indeed, the appearance of these structures is quite similar to what one would observe in large duct or channel. Great variations in the shape, size, and location of turbulent vortices are observed in these figures. Particularly interesting are the two lower labeled turbulent structures in Fig. 4(c), which appear to be undergoing vortex pairing. Varying the convective velocity that is subtracted from these images can make other turbulent structures within the flowfield more apparent. Similar efforts have been applied to the vector fields for Re < 1535 in an effort to detect turbulent structures in these flowfields, but for these Reynolds numbers no apparent turbulent vortices can be observed. The ensemble-averaged longitudinal velocity profiles for various Reynolds numbers are presented in Fig. 5, together with the corresponding fully developed laminar analytical solutions in a rectangular pipe [37]. The transverse positions of data have been normalized by 1/2 of the width of the microchannel, thus 0 corresponds to the microchannel centerline and 1 corresponds the microchannel wall. For Re = 272, which is in the laminar regime, the agreement between the measured veloc-
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Fig. 3. Instantaneous velocity fields at: (a) Re = 272; (b) Re = 1885 and (c) Re = 2853.
ity profiles and the laminar flow solution is quite good, as one would expect. The good agreement between the measured velocity and the laminar solutions continues until a Reynolds number of 1347. At this Reynolds number, some deviation is noticed, as the velocity profile becomes a bit less parabolic, as one would observe in transitional or turbulent flow. This deviation is a bit puzzling since turbulent velocity fluctuations were not observed at this Reynolds number and the measured velocity fluctuations and Reynolds stresses showed no evidence of transition. As Reynolds number is increased beyond 1347, the deviation from the laminar solution becomes greater, with the measured velocity near the channel axis much lower than the laminar flow prediction, and the velocity near the channel walls much higher until at the highest Reynolds numbers measured, the measured velocity profiles begin to resemble fully developed turbulent flow. The changing shape of the mean velocity profiles with increasing Reynolds number can be easily seen in Fig. 6, in which the velocity profiles have been normalized by the centerline velocity. Fig. 6 also suggests that the flow is fully developed at Re = 2853, since at this Reynolds number the measured
velocity profile almost exactly matches that of fully developed turbulent duct flow. In order to analyze the variation of the velocity fields quantitatively, velocity fluctuations and Reynolds shear stress were computed from the microPIV data. Figs. 7–9 show the dimensionless profiles of h u 0 i/umax, h v 0 i/umax, and hu0 v0 i=u2max , respectively. In Fig. 7, for Reynolds numbers below 1535, the measured centerline values of h u 0 i/umax exhibit a nearly uniform value of around 1.5%. The measured fluctuations at these low Reynolds numbers is not evidence of turbulence, but is instead due to measurement uncertainty. Indeed, the measured velocity fluctuations at these Reynolds numbers are comparable to the experimental error described earlier. At Re = 1535, a dramatic increase in h u 0 i/umax is observed, indicating that the flow is beginning to transition at a Reynolds number slightly lower than that predicted by classical theory. The profiles for Re = 2630 and Re = 2853 are nearly identical, indicating that somewhere in this range of Reynolds number, the flow has reached a fully-developed state. These fully-developed values for h u 0 i/umax are slightly higher than classical results for turbulent duct flow [20], but in general, the
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Fig. 4. Instantaneous vector fields with convective velocities subtracted showing turbulent vortices at: (a) Re = 2342; (b) Re = 2630, and (c) Re = 2853.
Fig. 5. Comparison of experimental velocity profiles with analytical laminar solutions.
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Fig. 6. Normalized mean velocity profiles for the experimental data.
Fig. 7. Normalized streamwise velocity fluctuation h u 0 i/umax.
Fig. 8. Normalized transverse velocity fluctuations, h v 0 i/umax.
agreement is good, as all of the results fall within the experimental uncertainty of around 2.5%. A plot of the h v 0 i/umax fluctuation is shown in Fig. 8. For Re < 1885, the curves are clumped together, with h v 0 i/umax around 1%. As with the h u 0 i/umax measurements at the lower Reynolds numbers, these measured fluctuations are due to measurement uncertainty. A
small increase in h v 0 i/umax is observed at Re = 1885, and this is followed by a rapid increase as the Reynolds number is further increased. The data in Fig. 8 also suggest that the flow becomes fully developed between 2630 < Re < 2853. For the highest Reynolds numbers studied, h v 0 i/umax was found to be around 3% at the channel centerline. Comparing Figs. 7 and 8, one finds
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Fig. 9. Normalized Reynolds shearing stress hu0 v0 i=u2max .
that the value of h v 0 i/umax is about 1/2–2/3 that of h u 0 i/ umax. This is due to the predominantly one-dimensional flow in the microchannel, which results in smaller fluctuations in the transverse direction. This ratio is consistent with previous studies of turbulent duct flow [36]. The agreement between the measured h v 0 i/umax fluctuations at the highest Reynolds numbers with classical results for turbulent duct flow is not as good as that as the agreement for h u 0 i/umax. Instead of becoming higher near the channel walls, h v 0 i/umax was found to be nearly constant throughout the microchannel. The measured values were also 25–40% smaller than the previous turbulent duct flow results. Fig. 9 shows the Reynolds shear stress, hu0 v0 i=u2max . For Re < 1885, there is little turbulent shearing stress, and the value of hu0 v0 i=u2max is seen to be very close to zero. At Re = 1885, there is a slight increase in the Reynolds shear stress, and a continual increase in hu0 v0 i=u2max is observed as Re is increased further. The value of hu0 v0 i=u2max is nearly zero in the center of the microchannel, as required by symmetry. The peak values in the plot correspond to the locations where the turbulent friction has its largest value. The fully developed
values of hu0 v0 i=u2max are slightly lower than previous turbulent duct flow results. In summary, the measured velocity fluctuations and Reynolds shear stress suggest a slightly earlier transition for the microchannel flow than is expected by conventional theory. There is some evidence of transition at around 1535 in the h u 0 i/umax data in that the measured velocity fluctuation at this Reynolds number rises above the data for lower Reynolds numbers, but this is not observed in either the h v 0 i/umax or the hu0 v0 i=u2max data. However, the measured values of the v velocity component are very small, and thus small fluctuations may be difficult to detect, resulting in difficulty in identifying transition using these quantities. Since the u velocity component is the one most easily measured, it follows that fluctuations rising above experimental noise would be most readily observable in this component. Thus, the fact that evidence of transition is first observed in the measurements of the h u 0 i/umax fluctuation is not at all surprising. The measured values and behavior of h u 0 i/ umax agree well with classical results for turbulent duct flow, but the results for h v 0 i/umax are lower than the classical results for turbulent duct flow.
1 Re= 1885 Re= 2342 Re= 2555 Re= 2630 Re= 2853
0.8
Ru'u'
0.6
0.4
0.2
0 0
0.2
0.4
0.6
0.8
1
y/(W/2)
Fig. 10. Spatial correlation Ru 0 u 0 with respect to the normalized transverse positions.
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1 Re= 2093 Re= 2342 Re= 2555 Re= 2630 Re= 2853
Rv'v'
0.8
0.6
0.4
0.2
0 0
0.2
0.4
0.6
0.8
1
y/(W/2)
Fig. 11. Spatial correlation Rv 0 v 0 with respect to the normalized transverse positions.
Finally the spatial correlations of the u 0 and v 0 velocity fluctuations, Ru 0 u 0 and Rv 0 v 0 , were calculated and are shown in Figs. 10 and 11, respectively. The Ru 0 u 0 velocity correlation is defined as hu0 ð0Þu0 ðDyÞi Ru0 u0 ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiqffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 hu0 ð0Þ i hu0 ðDyÞ i
ð3Þ
where, u 0 (0) is the longitudinal fluctuating velocity component at a point on the channel axis; and u 0 (Dy) is the longitudinal fluctuation velocity component at a different transverse position. These spatial correlations can provide a statistical description of the large-scale structures in the flowfield. In Fig. 10, Ru 0 u 0 equals 1 at the channel axis because Eq. (3) converts to the velocity autocorrelation when Dy = 0. As the correlation distance vector moves away from the channel centerline, Ru 0 u 0 can be seen to decrease. The same trends can be seen in the Rv 0 v 0 correlation, as shown in Fig. 11. Both the Ru 0 u 0 and the Rv 0 v 0 correlations decay at nearly the same rate, with both correlations dropping to 0.5 at a distance of approximately 0.4 channel half-widths from the microchannel centerline.
5. Conclusions Microscopic particle image velocimetry has been applied to measure instantaneous velocity fields in a 320 lm · 330 lm microchannel at various Reynolds numbers. In the instantaneous velocity vector fields, little evidence of velocity fluctuations or turbulent structures was observed for Re < 1535. However, at the higher Reynolds numbers in the study, great variation is seen in the individual velocity fields due to velocity fluctuations, and large-scale turbulent structures were observed. Results for the measured velocity fluctuations show a slight increase in the h u 0 i/umax at Re = 1535 fluctuation over the measured fluctuation for lower
Reynolds numbers, indicating the beginnings of transition. The flow was reached a fully developed state in the range 2630 < Re < 2853. The velocity fluctuation data thus suggested a slightly earlier transition to turbulence and fully developed state than is typically observed at the macroscale. For the fully developed flow, the measured h u 0 i/umax fluctuation is a bit higher, but generally agreed well with classical results for turbulent duct flow. However, the h v 0 i/umax fluctuation was found to be 25–40% lower than previous turbulent duct flow results. Finally, spatial correlations of velocity fluctuations were calculated. The results displayed the expected trends, with correlation values decreasing as the correlation displacement was increased. The Ru 0 u 0 correlation decreases more rapidly as the Reynolds number is increased, indicating the more turbulent nature of the flowfield as the Reynolds number is increased. A similar trend was not observed in the Rv 0 v 0 correlations, which remained consistent over the range of Reynolds numbers studied.
Acknowledgement The work was funded by the National Science Foundation under grant number CTS-0134469.
References [1] D.B. Tuckerman, R.F. Pease, High-performance heat sinking for VLSI, IEEE Electronic Device Letters 2 (1981) 126– 129. [2] P.Y. Wu, W.A. Little, Measurement of friction factor for flow of gases in very fine channels used for micro-miniature Joule– Thompson refrigerators, Cryogenics 23 (1983) 273–277. [3] P.Y. Wu, W.A. Little, Measurement of the heat transfer characteristics of gas flow in fine channel heat exchanger used for microminiature refrigerators, Cryogenics 24 (1984) 415– 423.
446
H. Li et al. / Experimental Thermal and Fluid Science 29 (2005) 435–446
[4] X.F. Peng, G.P. Peterson, B.X. Wang, Frictional flow characteristics of water flowing through rectangular microchannels, Experimental Heat Transfer 7 (1994) 249–264. [5] X.F. Peng, G.P. Peterson, B.X. Wang, Heat transfer characteristics of water flowing through microchannels, Experimental Heat Transfer 7 (1994) 265–283. [6] X.F. Peng, G.P. Peterson, The effect of thermofluid and geometrical parameters on convection of liquids through rectangular microchannels, International Journal of Heat and Mass Transfer 38 (1995) 755–758. [7] X.F. Peng, G.P. Peterson, Convective heat transfer and fluid flow friction for water flow in microchannel structures, International Journal of Heat and Mass Transfer 39 (1996) 2599–2608. [8] F. Gui, R.P. Scaringe, Enhanced heat transfer in the entrance region of microchannels, in: Proceedings of the 30th Intersociety Energy Conversion Engineering Conference, vol. 2, 1995, pp. 289– 294. [9] T.M. Harms, M.J. Kazmierczak, F.M. Gerner, Developing convective heat transfer in deep rectangular microchannels, International Journal of Heat and Fluid Flow 20 (1999) 149–157. [10] G.M. Mala, D. Li, Flow characteristics of water in microtubes, International Journal of Heat and Fluid Flow 20 (1999) 142–148. [11] D. Pfund, D. Rector, A. Shekarriz, Pressure drop measurements in a microchannel, Fluid Mechanics and Transport Phenomena 46 (8) (2000) 1496–1507. [12] H.Y. Wu, P. Cheng, Friction factors in smooth trapezoidal silicon microchannels with different aspect ratios, International Journal of Heat and Mass Transfer 46 (2003) 2519–2525. [13] Z.Y. Guo, Z.X. Li, Size effect on single-phase channel flow and heat transfer at microscale, International Journal of Heat and Fluid Flow 24 (2003) 284–298. [14] Z.Y. Guo, Z.X. Li, Size effect on microscale single-phase flow and heat transfer, International Journal of Heat and Mass Transfer 46 (2003) 149–159. [15] H.E. Hegab, A. Bari, T. Ameel, Friction and convection studies of R-134a in microchannels within the transition and turbulent flow regimes, Experimental Heat Transfer 15 (2002) 245–259. [16] W. Qu, I. Mudawar, Experimental and numerical study of pressure drop and heat transfer in a single-phase micro-channel heat sink, International Journal of Heat and Mass Transfer 45 (2002) 2549–2565. [17] J. Judy, D. Maynes, B.W. Webb, Characterization of frictional pressure drop for liquid flows through microchannels, International Journal of Heat and Mass Transfer 45 (2002) 3477–3489. [18] P.M.-Y. Chung, M. Kawaji, A. Kawahara, Characteristics of single-phase flow in microchannels, Fluids Engineering Division (Publication) FED 257 (1B) (2002) 1219–1228, American Society of Mechanical Engineers. [19] J.G. Santiago, S.T. Wereley, C.D. Meinhart, D.J. Beebe, R.J. Adrian, A particle image velocimetry system for microfluidics, Experiments in Fluids 25 (1998) 316–319. [20] C.D. Meinhart, S.T. Wereley, J.G. Santiago, PIV measurements of a microchannel flow, Experiments in Fluids 27 (1999) 414–419. [21] M.G. Olsen, R.J. Adrian, Brownian motion and correlation in particle image velocimetry, Optics and Laser Technology 32 (2000) 621–627.
[22] S. Devasenathipathy, J.G. Santiago, S.T. Wereley, C.D. Meinhart, K. Takehara, Particle imaging techniques for microfabricated fluidic systems, Experiments in Fluids 34 (2003) 504–514. [23] H. Klank, G. Goranovic, J.P. Kutter, H. Gjelstrup, J. Michelsen, C.H. Westergaard, PIV measurements in a microfluidic 3Dsheathing structure with three-dimensional flow behaviour, Journal Micromechanics and Microengineering 12 (2002) 862–869. [24] M. Shafiqul Islam, K. Haga, M. Kaminaga, R. Hino, M. Monde, Experimental analysis of turbulent flow structure in a fully developed rib-roughened rectangular channel with PIV, Experiments in Fluids 33 (2002) 296–306. [25] S.W. Stone, C.D. Meinhart, S.T. Wereley, A microfluidic-based nanoscope, Experiments in Fluids 33 (2002) 613–619. [26] J.H. Chan, A.T. Timperman, D. Qin, R. Aebersold, Microfabricated polymer devices for automated sample delivery of peptides for analysis by electrospray ionization tandem mass spectrometry (general description of PDMS replica molding), Anal. Chem. 71 (20) (1999) 4437–4444. [27] R. Zeighami, D. Laser, P. Zhou, M. Asheghi, S. Devasenathipathy, T. Kenny, J. Santiago, K. Goodson, Experimental investigation of flow transition in microchannels using micron-resolution particle image velocimetry, in: Thermomechanical Phenomena in Electronic Systems––Proceedings of the Intersociety Conference, vol. 2, 2000, pp. 148–153. [28] S.Y. Son, K.D. Kihm, J.C. Han, PIV flow measurements for heat transfer characterization in two-pass square channels with smooth and 90 ribbed walls, International Journal of Heat and Mass Transfer 45 (2002) 4809–4822. [29] J.C. McDonald, D.C. Duffy, J.R. Anderson, D.T. Chiu, H. Wu., O.J.A. Schueller, G.M. Whitesides, Fabrication of microfluidic systems in poly(dimethylsiloxane), Electrophoresis. 21 (2000) 27– 40. [30] B.H. Jo, L.M. Van Lerberghe, K.M. Motsegood, D.J. Beebe, Three-dimensional micro-channel fabrication in polydimethylsiloxane (PDMS) elastomer, Journal of Microelectromechanical Systems 9 (1) (2000) 76–81. [31] A. Folch, A. Ayon, O. Hurtado, M.A. Schmidt, M. Toner, Molding of deep polydimethylsiloxane microstructures for microfluidics and biological applications, Journal of Biomechanical Engineering, Transactions of the ASME 121 (1) (1999) 28–34. [32] R.D. Keane, R.J. Adrian, Optimization of particle image velocimeters: I. Double pulsed systems, Measurement Science and Technology 1 (1990) 1202–1215. [33] M.G. Olsen, R.J. Adrian, Out-of-focus effects on particle image visibility and correlation in microscopic particle image velocimetry, Experiments in Fluids 29 (2000) S166–S174. [34] C.D. Meinhart, S.T. Wereley, H.B. Gray, Volume illumination for two-dimensional particle image velocimetry, Measuring Science Technology 11 (2000) 809–814. [35] A.K. Prassad, R.J. Adrian, C.C. Landreth, P.W. Offutt, Effect of resolution on the speed and accuracy of particle image velocimetry interrogation, Experiments in Fluids 13 (1992) 105–116. [36] H. Schlichting, Boundary-Layer Theory, seventh ed., McGrawHill, New York, 1987. [37] F.M. White, Viscous Fluid Flow, second ed., McGraw-Hill, New York, 1991.