Hostname: page-component-5c6d5d7d68-lvtdw Total loading time: 0 Render date: 2024-08-16T05:20:20.952Z Has data issue: false hasContentIssue false

Slip velocity over a perforated or patchy surface

Published online by Cambridge University Press:  15 January 2010

C. POZRIKIDIS*
Affiliation:
Department of Chemical Engineering, University of Massachusetts, 686 North Pleasant Street, Amherst, MA 01003, USA
*
Email address for correspondence: cpozrikidis@ecs.umass.edu

Abstract

Shear flow over a solid surface containing perforations or patches of zero shear stress is discussed with a view to evaluating the slip velocity. In both cases, the functional dependence of the slip velocity on the solid fraction of the surface strongly depends on the surface geometry, and a universal law cannot be established. Numerical results for flow over a plate with circular or square perforations or patches of zero shear stress, and flow over a plate consisting of separated square or circular tiles corroborate the assertion.

Type
Papers
Copyright
Copyright © Cambridge University Press 2010

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

Davis, A. M. J. 1991 Shear flow disturbance due to a hole in the plane. Phys. Fluids A 3, 478480.CrossRefGoogle Scholar
Hasimoto, H. 1959 On the periodic fundamental solutions of the Stokes equations and their application to viscous flow past a cubic array of spheres. J. Fluid Mech. 5, 317328.CrossRefGoogle Scholar
Karniadakis, G. & Beskok., A. 2001 Microflows: Fundamentals and Simulation. Springer.Google Scholar
Ng, C. O. & Wang, C. W. 2009 Stokes shear flow over a grating: implications for superhydrophobic slip. Phys. Fluids 21, 013602.CrossRefGoogle Scholar
Philip, J. R. 1972 a Flows satisfying mixed no-slip and no-shear conditions. Z. Angew. Math. Phys. 23, 353370.CrossRefGoogle Scholar
Philip, J. R. 1972 b Integral properties of flows satisfying mixed no-slip and no-shear conditions. Z. Angew. Math. Phys. 23, 960968.CrossRefGoogle Scholar
Pozrikidis, C. 1996 Computation of periodic Green's functions of Stokes flow. J. Engng Math. 30, 7996.CrossRefGoogle Scholar
Pozrikidis, C. 2001 Shear flow over a particulate or fibrous plate. J. Engng Math. 39, 324.CrossRefGoogle Scholar
Pozrikidis, C. 2004 Boundary conditions for shear flow past a permeable interface modelled as an array of cylinders. Comput. Fluids 33, 117.CrossRefGoogle Scholar
Pozrikidis, C. 2005 Effect of membrane thickness on the slip and drift velocity in parallel shear flow. J. Fluids Struct. 20, 177187.CrossRefGoogle Scholar
Sampson, R. A. 1891 On Stokes current function. Phil. Trans. R. Soc. Lond. A 182, 449518.Google Scholar
Sbragaglia, M. & Prosperetti, A. 2007 Effective velocity boundary condition at a mixed slip surface. J. Fluid Mech. 578, 435451.CrossRefGoogle Scholar
Smith, S. H. 1987 Stokes flow past slits and holes. Intl J. Multiph. Flow 13, 219231.CrossRefGoogle Scholar
Sparrow, E. M. & Loeffler, A. L. 1959 Longitudinal laminar flow between cylinders arranged in a regular array. AIChE J. 5, 325330.CrossRefGoogle Scholar
Tio, K.-K. & Sadhal, S. 1994 Boundary conditions for Stokes flows near a porous membrane. Appl. Sci. Res. 52, 120.CrossRefGoogle Scholar
Wang, C. Y. 1994 Stokes flow through a thin screen with patterned holes. AIChE J. 40, 419423.CrossRefGoogle Scholar
Wang, C. Y. 2001 Stokes flow due to the sliding of a smooth plate over a slotted plate. Eur. J. Mech. B Fluids 20, 651656.CrossRefGoogle Scholar
Zheng, Q.-S., Yu, Y. & Zhao, Z.-H. 2005 Effects of hydraulic pressure on the stability and transition of wetting modes of superhydrophobic surfaces. Langmuir 21, 1220712212.CrossRefGoogle ScholarPubMed