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An experimental study of slip considering the effects of non-uniform colloidal tracer distributions

Published online by Cambridge University Press:  17 September 2010

HAIFENG LI  and
MINAMI YODA
HAIFENG LI
Affiliation:
G. W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0405, USA
MINAMI YODA*
Affiliation:
G. W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0405, USA
*
†Email address for correspondence: minami@gatech.edu
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Abstract

Various studies have suggested that the no-slip condition may not hold for Newtonian liquids flowing over (for the most part) non-wetting surfaces. This paper describes an experimental study of steady Poiseuille flow at various Reynolds numbers up to 0.12 of four different aqueous monovalent electrolyte solutions through naturally hydrophilic and hydrophobically coated fused-silica channels with a depth of 33 μm. The slip lengths for these flows were estimated using a local method based on a new particle velocimetry technique that determines velocities at three different wall-normal distances within the first 400 nm next to the wall. These results are corrected using direct measurements of the near-wall particle distribution, which is highly non-uniform as expected due to repulsive electric double-layer interactions between the 100 nm tracer particles and the wall. In all cases, the slip lengths were not more than 23 nm and for all but one case, zero within their uncertainties. As illustrated here, the standard assumption of uniformly distributed tracers can significantly increase slip length estimates obtained using local methods and near-wall velocity data.

JFM classification

Micro-/Nano-fluid dynamics: Micro-/Nano-fluid dynamics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 662 , 10 November 2010 , pp. 269 - 287
Copyright
Copyright © Cambridge University Press 2010

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References

REFERENCES

Baek, S. J. & Lee, S. J. 1996 A new two-frame particle tracking algorithm using match probability. Exp. Fluids 22 (1), 23–32.CrossRefGoogle Scholar
Batchelor, G. K. 1967 An Introduction to Fluid Mechanics. Cambridge University Press.Google Scholar
Bocquet, L. & Barrat, J. L. 2007 Flow boundary conditions from nano- to micro-scales. Soft Matter 3 (6), 685–693.CrossRefGoogle ScholarPubMed
Bonaccurso, E., Butt, H. J. & Craig, V. S. J. 2003 Surface roughness and hydrodynamic boundary slip of a Newtonian fluid in a completely wetting system. Phys. Rev. Lett. 90 (14), 144501.CrossRefGoogle Scholar
Bonaccurso, E., Kappl, M. & Butt, H. J. 2002 Hydrodynamic force measurements: boundary slip of water on hydrophilic surfaces and electrokinetic effects. Phys. Rev. Lett. 88 (7), 076103.CrossRefGoogle ScholarPubMed
Breedveld, V., Van den Ende, D., Tripathi, A. & Acrivos, A. 1998 The measurement of the shear-induced particle and fluid tracer diffusivities in concentrated suspensions by a novel method. J. Fluid Mech. 375, 297–318.CrossRefGoogle Scholar
Cheng, J. T. & Giordano, N. 2002 Fluid flow through nanometer-scale channels. Phys. Rev. E 65, 031206.CrossRefGoogle ScholarPubMed
Cherukat, P. & McLaughlin, J. B. 1994 The inertial lift on a rigid sphere in a linear shear flow field near a flat wall. J. Fluid Mech. 263, 1–18.CrossRefGoogle Scholar
Cho, J. H. J., Law, B. M. & Rieutord, F. 2004 Dipole-dependent slip of Newtonian liquids at smooth solid hydrophobic surfaces. Phys. Rev. Lett. 92 (16), 166102.CrossRefGoogle ScholarPubMed
Choi, C. H., Westin, K. J. A. & Breuer, K. S. 2003 Apparent slip flows in hydrophilic and hydrophobic microchannels. Phys. Fluids 15 (10), 2897–2902.CrossRefGoogle Scholar
Cottin-Bizonne, C., Steinberger, A., Cross, B., Raccurt, O. & Charlaix, E. 2008 Nanohydrodynamics: the intrinsic flow boundary condition on smooth surfaces. Langmuir 24 (4), 1165–1172.CrossRefGoogle ScholarPubMed
Crocker, J. C. & Grier, D. G. 1996 Methods of digital video microscopy for colloidal studies. J. Colloid Interface Sci. 179 (1), 298–310.CrossRefGoogle Scholar
Goldman, A. J., Cox, R. G. & Brenner, H. 1967 Slow viscous motion of a sphere parallel to a plane wall. Part II. Couette flow. Chem. Engng Sci. 22, 653–660.CrossRefGoogle Scholar
Guasto, J. S., Huang, P. & Breuer, K. S. 2006 Statistical particle tracking velocimetry using molecular and quantum dot tracer particles. Exp. Fluids 41, 869–880.CrossRefGoogle Scholar
Henry, C. L., Neto, C., Evans, D. R., Biggs, S. & Craig, V. S. J. 2004 The effect of surfactant adsorption on liquid boundary slippage. Physica A 339 (1–2), 60–65.CrossRefGoogle Scholar
Honig, C. D. F. & Ducker, W. A. 2007 No-slip hydrodynamic boundary condition for hydrophilic particles. Phys. Rev. Lett. 98 (2), 028305.CrossRefGoogle ScholarPubMed
Huang, P. & Breuer, K. S. 2007 Direct measurement of slip length in electrolyte solutions. Phys. Fluids 19 (2), 028104.CrossRefGoogle Scholar
Huang, P., Guasto, J. S. & Breuer, K. S. 2006 Direct measurement of slip velocities using three-dimensional total internal reflection velocimetry. J. Fluid Mech. 566, 447–464.CrossRefGoogle Scholar
Israelachvili, J. N. 1992 Intermolecular and Surface Forces. Academic Press.Google Scholar
Joly, L., Ybert, C. & Bocquet, L. 2006 Probing the nanohydrodynamics at liquid–solid interfaces using thermal motion. Phys. Rev. Lett. 96 (4), 046101.CrossRefGoogle ScholarPubMed
Joseph, P. & Tabeling, P. 2005 Direct measurement of the apparent slip length. Phys. Rev. E 71, 035303(R).CrossRefGoogle ScholarPubMed
Kanda, K., Ogata, S., Jingu, K. & Yang, M. 2007 Measurement of particle distribution in microchannel flow using a 3D-TIRFM technique. J. Vis. Japan 10 (2), 207–215.CrossRefGoogle Scholar
Krystek, M. & Anton, M. 2007 A weighted total least-squares algorithm for fitting a straight line. Meas. Sci. Technol. 18, 3348–3442.CrossRefGoogle Scholar
Lasne, D., Maali, A., Amarouchene, Y., Cognet, L., Lounis, B. & Kellay, H. 2008 Velocity profiles of water flowing past solid glass surfaces using fluorescent nanoparticles and molecules as velocity probes. Phys. Rev. Lett. 100 (21), 214502.CrossRefGoogle ScholarPubMed
Lauga, E., Brenner, M. P. & Stone, H. A. 2005 Microfluidics: the no-slip boundary condition. In Handbook of Experimental Fluid Dynamics (ed. Tropea, C., Foss, J. & Yarin, A.), pp. 1219–1240. Springer.Google Scholar
Li, H. F. 2008 An evanescent-wave-based particle image velocimetry technique. PhD thesis, Georgia Institute of Technology, Atlanta, GA.Google Scholar
Li, H. F., Sadr, R. & Yoda, M. 2006 Multilayer nano-particle image velocimetry. Exp. Fluids 41 (2), 185–194.CrossRefGoogle Scholar
Li, H. F. & Yoda, M. 2008 Multilayer nano-particle image velocimetry (MnPIV) in microscale Poiseuille flows. Meas. Sci. Technol. 19 (7), 075402.CrossRefGoogle Scholar
Lumma, D., Best, A., Gansen, A., Feuillebois, F., Radler, J. O. & Vinogradova, O. I. 2003 Flow profile near a wall measured by double-focus fluorescence cross-correlation. Phys. Rev. E 67, 056313.CrossRefGoogle Scholar
Maccarini, M. 2007 Water at solid surfaces: a review of selected theoretical aspects and experiments on the subject. Biointerphases 2 (3), MR1–MR15.CrossRefGoogle Scholar
Navier, C. L. M. H. 1823 On the laws of movement of fluids. Mem. de l'Acad. roy. des Sciences de l'inst. de France 6, 389–440.Google Scholar
Neto, C., Craig, V. S. J. & Williams, D. R. M. 2003 Evidence of shear-dependent boundary slip in Newtonian liquids. Eur. Phys. J. E 12, S71–S74.CrossRefGoogle ScholarPubMed
Neto, C., Evans, D. R., Bonaccurso, E., Butt, H. J. & Craig, V. S. J. 2005 Boundary slip in Newtonian liquids: a review of experimental studies. Rep. Prog. Phys. 68 (12), 2859–2897.CrossRefGoogle Scholar
Pit, R., Hervet, H. & Leger, L. 2000 Direct experimental evidence of slip in hexadecane: solid interfaces. Phys. Rev. Lett. 85 (5), 980–983.CrossRefGoogle ScholarPubMed
Priezjev, N. V. & Troian, S. M. 2006 Influence of periodic wall roughness on the slip behaviour at liquid/solid interfaces: molecular-scale simulations versus continuum predictions. J. Fluid Mech. 554, 25–46.CrossRefGoogle Scholar
Sadr, R., Hohenegger, C., Li, H. F., Mucha, P. J. & Yoda, M. 2007 Diffusion-induced bias in near-wall velocimetry. J. Fluid Mech. 577, 443–456.CrossRefGoogle Scholar
Sbragaglia, M., Benzi, R., Biferale, L., Succi, S. & Toschi, F. 2006 Surface roughness-hydrophobicity coupling in microchannel and nanochannel flows. Phys. Rev. Lett. 97 (20), 204503.CrossRefGoogle ScholarPubMed
Schmatko, T., Hervet, H. & Leger, L. 2005 Friction and slip at simple fluid–solid interfaces: the roles of the molecular shape and the solid–liquid interaction. Phys. Rev. Lett. 94 (24), 244501.CrossRefGoogle Scholar
Schmatko, T., Hervet, H. & Leger, L. 2006 Effect of nanometric-scale roughness on slip at the wall of simple fluids. Langmuir 22 (16), 6843–6850.CrossRefGoogle ScholarPubMed
Thompson, P. A. & Troian, S. M. 1997 A general boundary condition for liquid flow at solid surfaces. Nature 389 (6649), 360–362.CrossRefGoogle Scholar
Tretheway, D. C. & Meinhart, C. D. 2002 Apparent fluid slip at hydrophobic microchannel walls. Phys. Fluids 14 (3), L9–L12.CrossRefGoogle Scholar
Tretheway, D. C. & Meinhart, C. D. 2004 A generating mechanism for apparent fluid slip in hydrophobic microchannels. Phys. Fluids 16 (5), 1509–1515.CrossRefGoogle Scholar
Vinogradova, O. I., Koynov, K., Best, A. & Feuillebois, F. 2009 Direct measurements of hydrophobic slippage using double-focus fluorescence cross-correlation. Phys. Rev. Lett. 102, 118302.CrossRefGoogle ScholarPubMed
Yi, Y. W., Robinson, H. G., Knappe, S., Maclennan, J. E., Jones, C. D., Zhu, C., Clark, N. A. & Kitching, J. 2008 Method for characterizing self-assembled monolayers as antirelaxation wall coatings for alkali vapor cells. J. Appl. Phys. 104, 023534.CrossRefGoogle Scholar
Zhu, Y. & Granick, S. 2001 Rate-dependent slip of Newtonian liquid at smooth surfaces. Phys. Rev. Lett. 87 (9), 096105.CrossRefGoogle ScholarPubMed
Zhu, Y. & Granick, S. 2002 Limits of the hydrodynamic no-slip boundary condition. Phys. Rev. Lett. 88 (10), 106102.CrossRefGoogle ScholarPubMed