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Slip over rough and coated surfaces

Published online by Cambridge University Press:  26 April 2006

Michael J. Miksis  and
Stephen H. Davis
Michael J. Miksis
Affiliation:
Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, IL 60208, USA
Stephen H. Davis
Affiliation:
Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, IL 60208, USA
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Abstract

We study the effect of surface roughness and coatings on fluid flow over a solid surface. In the limit of small-amplitude roughness and thin lubricating films we are able to derive asymptotically an effective slip boundary condition to replace the no-slip condition over the surface. When the film is absent, the result is a Navier slip condition in which the slip coefficient equals the average amplitude of the roughness. When a layer of a second fluid covers the surface and acts as a lubricating film, the slip coefficient contains a term which is proportional to the viscosity ratio of the two fluids and which depends on the dynamic interaction between the film and the fluid. Limiting cases are identified in which the film dynamics can be decoupled from the outer flow.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 273 , 25 August 1994 , pp. 125 - 139
Copyright
© 1994 Cambridge University Press

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References

Dussan, V., E. B. 1976 The moving contact line: the slip boundary condition. J. Fluid Mech. 77, 665–684.Google Scholar
Dussan, V., E. B. 1979 On the spreading of liquids on solid surfaces: Static and dynamic contact lines. Ann. Rev. Fluid Mech. 11, 371–400.Google Scholar
Dussan, V. E. B. & Davis, S. H. 1974 On the motion of a fluid-fluid interface along a solid surface. J. Fluid Mech. 65, 71–95.Google Scholar
Haley, P. J. & Miksis, M. J. 1991 The effect of the contact line on droplet spreading. J. Fluid Mech. 223, 57–81.Google Scholar
Hocking, L. M. 1976 A moving fluid on a rough surface. J. Fluid Mech. 76, 801–817.Google Scholar
Huh, C. & Mason, S. G. 1977 Effects of surface roughness on wetting (theoretical). J. Colloid Interface Sci. 60, 11–38.Google Scholar
Jansons, K. M. 1986 Moving contact lines at non-zero capillary number. J. Fluid Mech. 167, 393–407.Google Scholar
Jansons, K. M. 1988 Determination of the macroscopic (partial) slip boundary conditions for a viscous flow over a randomly rough surface with a perfect slip microscopic boundary condition. Phys. Fluids 31, 15–17.Google Scholar
Richardson, S. 1971 A model for the boundary condition of a porous material. Part 2. J. Fluid Mech. 49, 327–336.Google Scholar
Richardson, S. 1973 On the no-slip boundary condition. J. Fluid Mech. 59, 707–719.Google Scholar