Hostname: page-component-8448b6f56d-c47g7 Total loading time: 0 Render date: 2024-04-19T17:13:02.460Z Has data issue: false hasContentIssue false
  • English
  • Français

Tensorial hydrodynamic slip

Published online by Cambridge University Press:  01 October 2008

MARTIN Z. BAZANT  and
OLGA I. VINOGRADOVA
MARTIN Z. BAZANT
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA CNRS UMR Gulliver 7083 and PMMH 7636, École Supérieure de Physique et de Chimie Industrielles, 10 rue Vauquelin, F-75005 Paris, France
OLGA I. VINOGRADOVA
Affiliation:
A. N. Frumkin Institute of Physical Chemistry and Electrochemistry, Russian Academy of Sciences, 31 Leninsky Prospect, 119991 Moscow, Russia CNRS UMR Gulliver 7083 and PMMH 7636, École Supérieure de Physique et de Chimie Industrielles, 10 rue Vauquelin, F-75005 Paris, France
Get access Rights & Permissions [Opens in a new window]

Abstract

We describe a tensorial generalization of the Navier slip boundary condition and illustrate its use in solving for flows around anisotropic textured surfaces. Tensorial slip can be derived from molecular or microstructural theories or simply postulated as a constitutive relation, subject to certain general constraints on the interfacial mobility. The power of the tensor formalism is to capture complicated effects of surface anisotropy, while preserving a simple fluid domain. This is demonstrated by exact solutions for laminar shear flow and pressure-driven flow between parallel plates of arbitrary and different textures. From such solutions, the effects of rotating a texture follow from simple matrix algebra. Our results may be useful for extracting local slip tensors from global measurements, such as the permeability of a textured channel or the force required to move a patterned surface, in experiments or simulations.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 613 , 25 October 2008 , pp. 125 - 134
Copyright
Copyright © Cambridge University Press 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Ajdari, A. 2002 Transverse electrokinetic and microfluidic effects in micropatterned channels: Lubrication analysis for slab geometries. Phys. Rev. E 65, 016301.Google ScholarPubMed
Bocquet, L. & Barrat, J. L. 1994 Hydrodynamic boundary conditions, correlation functions, and kubo relations for confined fluids. Phys. Rev. E 49, 3079–3092.Google ScholarPubMed
Bocquet, L. & Barrat, J. L. 2007 Flow boundary conditions from nano- to micro-scales. Soft Matter 3, 685–693.CrossRefGoogle ScholarPubMed
Choi, C. H., Ulmanella, U., Kim, J., Ho, C. M. & Kim, C. J. 2006 Effective slip and friction reduction in nanograted superhydrophobic microchannels. Phys. Fluids 18, 087105.CrossRefGoogle Scholar
Cottin-Bizonne, C., Barrat, J. L., Bocquet, L. & Charlaix, E. 2003 Low-friction flows of liquid at nanopatterned interfaces. Nat. Mater. 2, 237–240.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle ScholarPubMed
Einzel, D., Panzer, P. & Liu, M. 1990 Boundary-condition for fluid-flow – curved or rough surfaces. Phys. Rev. Lett. 64, 2269–2272.CrossRefGoogle ScholarPubMed
Heidenreich, S., Ilg, P. & Hess, S. 2007 Boundary conditions for fluids with internal orientational degrees of freedom: Apparent velocity slip associated with the molecular alignment. Phys. Rev. E 75, 066302.Google ScholarPubMed
Hess, S. & Loose, W. 1989 Slip flow and slip boundary coefficient of a dense fluid via nonequilibrium molecular dynamics. Physica A 162, 138–144.CrossRefGoogle Scholar
Joly, L., Ybert, C. & Bocquet, L. 2006 Probing the nanohydrodynamics at liquid-solid interfaces using thermal motion. Phys. Rev. Lett. 96, 046101.CrossRefGoogle ScholarPubMed
Joseph, P., Cottin-Bizonne, C, Benoi, J. M., Ybert, C., Journet, C., Tabeling, P. & Bocquet, L. 2006 Slippage of water past superhydrophobic carbon nanotube forests in microchannels. Phys. Rev. Lett. 97, 156104.CrossRefGoogle ScholarPubMed
Lauga, E., Brenner, M. P. & Stone, H. A. 2007 Handbook of Experimental Fluid Dynamics, chap. 19, pp. 1219–1240. Springer.Google Scholar
Lauga, E., Stroock, A. D. & Stone, H. A. 2004 Three-dimensional flows in slowly varying planar geometries. Phys. Fluids 16, 3051–3062.CrossRefGoogle Scholar
Lecoq, N., Anthore, R., Cichocki, B., Szymczak, P. & Feuillebois, F. 2004 Drag force on a sphere moving towards a corrugated wall. J. Fluid Mech. 513, 247–264.CrossRefGoogle Scholar
Navier, C. L. M. H. 1823 Mémoire sur les lois du mouvement des fluides. Mém. l'Acad. R. Sci. línst. France 6, 389–440.Google Scholar
Ou, J. & Rothstein, J. P. 2005 Direct velocity measurements of the flow past drag-reducing ultrahydrophobic surfaces. Phys. Fluids 17, 103606.CrossRefGoogle Scholar
Quéré, D. 2005 Non-sticking drops. Rep. Prog. Phys. 68, 2495–2532.CrossRefGoogle Scholar
Sbragaglia, M. & Prosperetti, A. 2007 A note on the effective slip properties for microchannel flows with ultrahydrophobic surfaces. Phys. Fluids 19, 043603.CrossRefGoogle Scholar
Squires, T. M. & Quake, S. R. 2005 Microfluidics: Fluid physics at the nanoliter scale. Rev. Mod. Phys. 77, 977.CrossRefGoogle Scholar
Stone, H. A., Stroock, A. D. & Ajdari, A. 2004 Engineering flows in small devices. Annu. Rev. Fluid Mech. 36, 381–411.CrossRefGoogle Scholar
Stroock, A. D., Dertinger, S. K. W., Ajdari, A., Mezić, I., Stone, H. A. & Whitesides, G. M. 2002 a Chaotic mixer for microchannels. Science 295, 647–651.CrossRefGoogle ScholarPubMed
Stroock, A. D., Dertinger, S. K., Whitesides, G. M. & Ajdari, A. 2002 b Patterning flows using grooved surfaces. Anal. Chem. 74, 5306–5312.CrossRefGoogle ScholarPubMed
Vinogradova, O. I. 1995 Drainage of a thin liquid film confined between hydrophobic surfaces. Langmuir 11, 2213–2220.CrossRefGoogle Scholar
Vinogradova, O. I. 1999 Slippage of water over hydrophobic surfaces. Intl J. Miner. Proc. 56, 31–60.CrossRefGoogle Scholar
Vinogradova, O. I., Bunkin, N. F., Churaev, N. V., Kiseleva, O. A., Lobeyev, A. V. & Ninham, B. W. 1995 Submicrocavity structure of water between hydrophobic and hydrophilic walls as revealed by optical cavitation. J. Colloid Interface Sci. 173, 443–447.CrossRefGoogle Scholar
Vinogradova, O. I. & Yakubov, G. E. 2003 Dynamic effects on force measurements. 2. lubrication and the atomic force microscope. Langmuir 19, 1227–1234.CrossRefGoogle Scholar
Wang, C. Y. 2003 Flow over a surface with parallel grooves. Phys. Fluids 15, 1114–1121.CrossRefGoogle Scholar