Abstract
In this work, we measured 14 horizontal velocity profiles along the vertical direction of a rectangular microchannel with aspect ratio α = h/w = 0.35 (h is the height of the channel and w is the width of the channel) using microPIV at Re = 1.8 and 3.6. The experimental velocity profiles are compared with the full 3D theoretical solution, and also with a Poiseuille parabolic profile. It is shown that the experimental velocity profiles in the horizontal and vertical planes are in agreement with the theoretical profiles, except for the planes close to the wall. The discrepancies between the experimental data and 3D theoretical results in the center vertical plane are less than 3.6%. But the deviations between experimental data and Poiseuille’s results approaches 5%. It indicates that 2D Poiseuille profile is no longer a perfect theoretical approximation since α = 0.35. The experiments also reveal that, very near the hydrophilic wall (z = 0.5–1 μm), the measured velocities are significantly larger than the theoretical velocity based on the no-slip assumption. A proper discussion on some physical effects influencing the near wall velocity measurement is given.
Similar content being viewed by others
References
Boussinesq J (1868) Memoire sur l’influence des frottements dans les mouvements reguliers des fluids. J Math Pures Appl Deuxieme Ser 13:377–424
Cottin-Bizonne C, Cross B, Steinberger A, Charlaix E (2005) Boundary slip on smooth hydrophobic surfaces: intrinsic effects and possible artifacts. Phys Rev Lett 94:056102
Degré G, Joseph P, Tabeling P, Lerouge S, Cloitre M, Ajdan A (2006) Rheology of complex fluids by particle image velocimetry in microchannels. Appl Phys Lett 89:024104
Devasenathipathy S, Santiago JG, Wereley ST, Meinhart CD, Takehara K (2003) Particle imaging techniques for microfabricated fluidic systems. Exp Fluids 34:504–514
Goldman AJ, Cox RG, Brenner H (1967) Slow viscous motion of a sphere parallel to a plane wall—ii: Couette flow. Chem Eng Sci 22:653–660
Gui L, Wereley ST, Lee SY (2002) Digital filters for reducing background noise in microPIV measurements. In: Proceedings of the 11th international symposium on the application of laser techniques to fluid mechanics, Lisbon
Hartman Kok PJA, Kazarian SG, Briscoe BJ, Lawrence CJ (2004) Effects of particle size on near-wall depletion in mono-dispersed colloidal suspensions. J Colloid Interface Sci 280:511–517
Honig CDF, Ducker WA (2007) No-slip hydrodynamic boundary condition for hydrophilic particles. Phys Rev Lett 98:028305
Huang P, Guasto JF, Breuer K (2006) Direct measurement of slip velocities using three-dimensional total internal reflection velocimetry. J Fluid Mech 566:447–464
Joseph P, Tabeling P (2005) Direct measurement of the apparent slip length. Phys Rev E 71:035303
Lauga E (2004) Apparent slip due to the motion of suspended particles in flows of electrolyte solutions. Langmuir 20:8924–8930
Lauga E, Brenner MP, Stone HA (2007) Microfluidics: the no-slip boundary condition. In: Handbook of experimental fluid dynamics. Springer, Berlin
Lauga E, Squires TM (2005) Brownian motion near a partial-slip boundary: a local probe of the no-slip condition. Phys Fluids 17:103102
Li H, Olsen MG (2006) MicroPIV measurements of turbulent flow in square microchannels with hydraulic diameters from 200 μm to 640 μm. Int J Heat Fluid Flow 27(1):123–134
Lumma D, Best A, Gansen A, Feuilebois F, Radler JO, Vinogradova OI (2003) Flow profile near a wall measured by double focus fluorescence cross-section. Phys Rev E 67:056313
Meinhart CD, Wereley ST, Santiago JG (1999) PIV measurements of a microchannel flow. Exp Fluids 25:414–419
Navier CLMH (1823) Mémoire sur les lois du mouvement des fluids Mem. Acad Sci Inst Fr 6:389–416
Neto C, Evans DR, Bonaccurso E, Butt H-J, Craig V (2005) Boundary slip in Newtonian liquids: a review of experimental studies. Rep Prog Phys 68:2859–2897
Olsen MG, Adrian RJ (2000) Out-of-focus effects on particle image visibility and correlation in microscopic particle image velocimetry. Exp Fluids 29(7):S166–S174
Ou J, Rothstein JP (2005) Direct velocity measurements of the flow past drag-reducting ultrahydrophobic surfaces. Phys Fluids 17:103606
Patel VC, Head MR (1969) Some observations on skin friction and velocity profiles in fully developed pipe and channel flows. J Fluid Mech 38:181–201
Santiago JG, Wereley ST, Meinhart CD, Beebe DJ, Adrian RJ (1998) A partical image velocimetry system for microfluidics. Exp Fluids 25:316–319
Schlichting H (1979) Boundary layer theory, 7th edn. McGraw-Hill Book Company, New York, pp 612–615
Silber-Li ZH, Tan YP, Weng PF (2004) A microtube viscometer with a thermostat. Exp Fluids 36(4):586–592
Stone HA, Strook AD, Ajdari A (2004) Engineering flows in small devices: microfluidics toward a Lab-on-Chip. Annu Rev Fluid Mech 36:381–411
Tretheway DC, Meinhart CD (2002) Apparent fluid slip at hydrophobic microchannel wall. Phys Fluids 14(3):L9–L11
White FM (1974) Viscous fluid flow. McGraw-Hill Book Company, New York, pp 123
Acknowledgments
The authors gratefully acknowledge the support of this work by the Major Innovation Project of Chinese Academy of Sciences (KJCX2-SW-L2) and National Natural Science Foundation of China (10672172).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Zheng, X., Silber-Li, Zh. Measurement of velocity profiles in a rectangular microchannel with aspect ratio α = 0.35. Exp Fluids 44, 951–959 (2008). https://doi.org/10.1007/s00348-007-0454-4
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00348-007-0454-4