Skip to main content Accessibility help

Tensorial hydrodynamic slip

  • MARTIN Z. BAZANT (a1) (a2) and OLGA I. VINOGRADOVA (a3) (a2)


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.



Hide All
Ajdari, A. 2002 Transverse electrokinetic and microfluidic effects in micropatterned channels: Lubrication analysis for slab geometries. Phys. Rev. E 65, 016301.
Bocquet, L. & Barrat, J. L. 1994 Hydrodynamic boundary conditions, correlation functions, and kubo relations for confined fluids. Phys. Rev. E 49, 30793092.
Bocquet, L. & Barrat, J. L. 2007 Flow boundary conditions from nano- to micro-scales. Soft Matter 3, 685693.
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.
Cottin-Bizonne, C., Barrat, J. L., Bocquet, L. & Charlaix, E. 2003 Low-friction flows of liquid at nanopatterned interfaces. Nat. Mater. 2, 237240.
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.
Einzel, D., Panzer, P. & Liu, M. 1990 Boundary-condition for fluid-flow – curved or rough surfaces. Phys. Rev. Lett. 64, 22692272.
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.
Hess, S. & Loose, W. 1989 Slip flow and slip boundary coefficient of a dense fluid via nonequilibrium molecular dynamics. Physica A 162, 138144.
Joly, L., Ybert, C. & Bocquet, L. 2006 Probing the nanohydrodynamics at liquid-solid interfaces using thermal motion. Phys. Rev. Lett. 96, 046101.
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.
Lauga, E., Brenner, M. P. & Stone, H. A. 2007 Handbook of Experimental Fluid Dynamics, chap. 19, pp. 12191240. Springer.
Lauga, E., Stroock, A. D. & Stone, H. A. 2004 Three-dimensional flows in slowly varying planar geometries. Phys. Fluids 16, 30513062.
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, 247264.
Navier, C. L. M. H. 1823 Mémoire sur les lois du mouvement des fluides. Mém. l'Acad. R. Sci. línst. France 6, 389440.
Ou, J. & Rothstein, J. P. 2005 Direct velocity measurements of the flow past drag-reducing ultrahydrophobic surfaces. Phys. Fluids 17, 103606.
Quéré, D. 2005 Non-sticking drops. Rep. Prog. Phys. 68, 24952532.
Sbragaglia, M. & Prosperetti, A. 2007 A note on the effective slip properties for microchannel flows with ultrahydrophobic surfaces. Phys. Fluids 19, 043603.
Squires, T. M. & Quake, S. R. 2005 Microfluidics: Fluid physics at the nanoliter scale. Rev. Mod. Phys. 77, 977.
Stone, H. A., Stroock, A. D. & Ajdari, A. 2004 Engineering flows in small devices. Annu. Rev. Fluid Mech. 36, 381411.
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, 647651.
Stroock, A. D., Dertinger, S. K., Whitesides, G. M. & Ajdari, A. 2002 b Patterning flows using grooved surfaces. Anal. Chem. 74, 53065312.
Vinogradova, O. I. 1995 Drainage of a thin liquid film confined between hydrophobic surfaces. Langmuir 11, 22132220.
Vinogradova, O. I. 1999 Slippage of water over hydrophobic surfaces. Intl J. Miner. Proc. 56, 3160.
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, 443447.
Vinogradova, O. I. & Yakubov, G. E. 2003 Dynamic effects on force measurements. 2. lubrication and the atomic force microscope. Langmuir 19, 12271234.
Wang, C. Y. 2003 Flow over a surface with parallel grooves. Phys. Fluids 15, 11141121.
MathJax is a JavaScript display engine for mathematics. For more information see

Tensorial hydrodynamic slip

  • MARTIN Z. BAZANT (a1) (a2) and OLGA I. VINOGRADOVA (a3) (a2)


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed