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

  • HAIFENG LI (a1) and MINAMI YODA (a1)


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.


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Baek, S. J. & Lee, S. J. 1996 A new two-frame particle tracking algorithm using match probability. Exp. Fluids 22 (1), 2332.
Batchelor, G. K. 1967 An Introduction to Fluid Mechanics. Cambridge University Press.
Bocquet, L. & Barrat, J. L. 2007 Flow boundary conditions from nano- to micro-scales. Soft Matter 3 (6), 685693.
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.
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.
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, 297318.
Cheng, J. T. & Giordano, N. 2002 Fluid flow through nanometer-scale channels. Phys. Rev. E 65, 031206.
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, 118.
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.
Choi, C. H., Westin, K. J. A. & Breuer, K. S. 2003 Apparent slip flows in hydrophilic and hydrophobic microchannels. Phys. Fluids 15 (10), 28972902.
Cottin-Bizonne, C., Steinberger, A., Cross, B., Raccurt, O. & Charlaix, E. 2008 Nanohydrodynamics: the intrinsic flow boundary condition on smooth surfaces. Langmuir 24 (4), 11651172.
Crocker, J. C. & Grier, D. G. 1996 Methods of digital video microscopy for colloidal studies. J. Colloid Interface Sci. 179 (1), 298310.
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, 653660.
Guasto, J. S., Huang, P. & Breuer, K. S. 2006 Statistical particle tracking velocimetry using molecular and quantum dot tracer particles. Exp. Fluids 41, 869880.
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), 6065.
Honig, C. D. F. & Ducker, W. A. 2007 No-slip hydrodynamic boundary condition for hydrophilic particles. Phys. Rev. Lett. 98 (2), 028305.
Huang, P. & Breuer, K. S. 2007 Direct measurement of slip length in electrolyte solutions. Phys. Fluids 19 (2), 028104.
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, 447464.
Israelachvili, J. N. 1992 Intermolecular and Surface Forces. Academic Press.
Joly, L., Ybert, C. & Bocquet, L. 2006 Probing the nanohydrodynamics at liquid–solid interfaces using thermal motion. Phys. Rev. Lett. 96 (4), 046101.
Joseph, P. & Tabeling, P. 2005 Direct measurement of the apparent slip length. Phys. Rev. E 71, 035303(R).
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), 207215.
Krystek, M. & Anton, M. 2007 A weighted total least-squares algorithm for fitting a straight line. Meas. Sci. Technol. 18, 33483442.
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.
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. 12191240. Springer.
Li, H. F. 2008 An evanescent-wave-based particle image velocimetry technique. PhD thesis, Georgia Institute of Technology, Atlanta, GA.
Li, H. F., Sadr, R. & Yoda, M. 2006 Multilayer nano-particle image velocimetry. Exp. Fluids 41 (2), 185194.
Li, H. F. & Yoda, M. 2008 Multilayer nano-particle image velocimetry (MnPIV) in microscale Poiseuille flows. Meas. Sci. Technol. 19 (7), 075402.
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.
Maccarini, M. 2007 Water at solid surfaces: a review of selected theoretical aspects and experiments on the subject. Biointerphases 2 (3), MR1MR15.
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, 389440.
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, S71S74.
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), 28592897.
Pit, R., Hervet, H. & Leger, L. 2000 Direct experimental evidence of slip in hexadecane: solid interfaces. Phys. Rev. Lett. 85 (5), 980983.
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, 2546.
Sadr, R., Hohenegger, C., Li, H. F., Mucha, P. J. & Yoda, M. 2007 Diffusion-induced bias in near-wall velocimetry. J. Fluid Mech. 577, 443456.
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.
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.
Schmatko, T., Hervet, H. & Leger, L. 2006 Effect of nanometric-scale roughness on slip at the wall of simple fluids. Langmuir 22 (16), 68436850.
Thompson, P. A. & Troian, S. M. 1997 A general boundary condition for liquid flow at solid surfaces. Nature 389 (6649), 360362.
Tretheway, D. C. & Meinhart, C. D. 2002 Apparent fluid slip at hydrophobic microchannel walls. Phys. Fluids 14 (3), L9L12.
Tretheway, D. C. & Meinhart, C. D. 2004 A generating mechanism for apparent fluid slip in hydrophobic microchannels. Phys. Fluids 16 (5), 15091515.
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.
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.
Zhu, Y. & Granick, S. 2001 Rate-dependent slip of Newtonian liquid at smooth surfaces. Phys. Rev. Lett. 87 (9), 096105.
Zhu, Y. & Granick, S. 2002 Limits of the hydrodynamic no-slip boundary condition. Phys. Rev. Lett. 88 (10), 106102.
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An experimental study of slip considering the effects of non-uniform colloidal tracer distributions

  • HAIFENG LI (a1) and MINAMI YODA (a1)


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