Abstract
Direct measurement of slip length is based on the measured fluid velocity near solid boundary. However, previous micro particle image velocimetry/particle tracking velocimetry (microPIV/PTV) measurements have reported surprisingly large measured near-wall velocities of pressuredriven flow in apparent contradiction with the no-slip hypothesis and experimental results from other techniques. To better interpret the measured results of the microPIV/PTV, we performed velocity profile measurements near a hydrophilic wall (z = 0.25–1.5 μm) with two sizes of tracer particles (ϕ 50 nm and ϕ200 nm). The experimental results indicate that, at less than 1 μm from the wall, the deviations between the measured velocities and no-slip theoretical values obviously decrease from 93% of ϕ200 nm particles to 48% of ϕ50 nm particles. The Boltzmann-like exponential measured particle concentrations near wall were found. Based on the non linear Boltzmann distribution of particle concentration and the effective focus plane thickness, we illustrated the reason of the apparent velocity increase near wall and proposed a method to correct the measured velocity profile. By this method, the deviations between the corrected measured velocities and the no-slip theoretical velocity decrease from 45.8% to 10%, and the measured slip length on hydrophilic glass is revised from 75 nm to 16 nm. These results indicated that the particle size and the biased particle concentration distribution can significantly affect near wall velocity measurement via microPIV/PTV, and result in larger measured velocity and slip length close to wall.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Navier, C.L.M.H.: Mémoire sur les lois du mouvement des fluids Mem. Acad. Sci. Inst. Fr. 6, 389 (1823)
Santiago, J.G., Wereley, S.T., Meinhart, C.D., et al.: A particle image velocimetry system for microfluidics. Exp Fluids 25, 316–319 (1998)
Meinhart, C.D., Wereley, S.T., Santiago, J.G.: PIV measurements of a microchannel flow. Exp. Fluids 25, 414–419 (1999)
Tretheway, D.C, Meinhart, C.D.: Apparent fluid slip at hydrophobic microchannel wall. Phys. Fluids 14, L9–L11 (2002)
Joseph, P., Tabeling, P.: Direct measurement of the apparent slip length. Phys. Rev. E 71, 035303 (2005)
Zheng, X., Silber-Li, Z.H.: Measurement of velocity profiles in a rectangular microchannel with aspect ratio α = 0.35. Exp. Fluids 44, 951–959 (2008)
Lauga, E., Brenner, M.P., Stone, H.A.: Microfluidics: The noslip boundary condition. In: Handbook of Experimental Fluid Dynamics, Springer, New York (2005)
Neto, C., Evans, D.R., Bonaccurso, E., et al.: Boundary slip in Newtonian liquids: A review of experimental studies. Rep. Prog. Phys. 68, 2859–2897 (2005)
Craig, V.S.J., Neto, C., Williams, D.R.M.: Shear-dependent boundary slip in an aqueous Newtonian liquid. Physical Review Letters 87, 054504 (2001)
Cottin-Bizonne, C., Cross, B., Steinberger, A., et al.: Boundary slip on smooth hydrophobic surfaces: Intrinsic effects and possible artifacts. Physical Review Letter 94, 056102 (2005)
Huang, P., Guasto, J.F., Breuer, K.: Direct measurement of slip velocities using three-dimensional total internal reflection velocimetry. J. Fluid Mech. 566, 447–464 (2006)
Olsen, M.G., Adrian, R.J.: Out-of-focus effects on particle image visibility and correlation in microscopic particle image velocimetry. Exp. Fluids 29, S166–S174 (2000)
Lauga, E.: Apparent slip due to the motion of suspended particles in flows of electrolyte solutions. Langmuir 20, 8924–8930 (2004)
Hartman, Kok P.J.A., Kazarian, S.G., Briscoe, B.J., et al.: Effects of particle size on near-wall depletion in mono-dispersed colloidal suspensions. J. Colloid and Interface Science 280, 511–517 (2004)
Goldman, A.J., Cox, R.G., Brenner, H.: Slow viscous motion of a sphere parallel to a plane wall-II: Couette flow. Chem. Engng. Sci. 22, 653–660 (1967)
Zheng, X., Silber-Li, Z.H.: The influence of Saffman lift force on nanoparticle concentration distribution near a wall. Applied Physics Letters 95, 124105 (2009)
Inoue, H.S.: Video Microscopy. (2nd edn.). Plenum Press, Oxford (1997)
Meinhart, C.D., Zhang, H.: The flow structure inside a microfabricated inkjet prinhead. J. Mems. 9, 67–75 (2000)
White, F.: Viscous Fluid Flow. McGraw-Hill, Inc. New York, 123, (1974)
Schlichting, H.: Boundary Layer Theory. (7th edn.). Springer, New York, 613–614 (1979)
Bouzigues, C.I., Tabeling, P., Bocquet, L.: Nanofluidics in the debye layer at hydrophilic and hydrophobic surfaces. Phys. Rev. Letter 101, 114503 (2008)
Author information
Authors and Affiliations
Corresponding author
Additional information
The project was supported by the National Natural Science Foundation of China (10872203), the National Basic Research Program (2007AC744701) and the CAS Research and Development Program of China (KSCX2-YW-H18).
Rights and permissions
About this article
Cite this article
Zheng, X., Kong, GP. & Silber-Li, ZH. The influence of nano-particle tracers on the slip length measurements by microPTV. Acta Mech Sin 29, 411–419 (2013). https://doi.org/10.1007/s10409-013-0027-0
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10409-013-0027-0