Hostname: page-component-5cf477f64f-zrtmk Total loading time: 0 Render date: 2025-04-03T02:54:44.685Z Has data issue: false hasContentIssue false
  • English
  • Français

On the no-slip boundary condition

Published online by Cambridge University Press:  29 March 2006

S. Richardson
S. Richardson
Affiliation:
Applied Mathematics, University of Edinburgh
Get access Rights & Permissions [Opens in a new window]

Abstract

It has been argued that the no-slip boundary condition, applicable when a viscous fluid flows over a solid surface, may be an inevitable consequence of the fact that all such surfaces are, in practice, rough on a microscopic scale: the energy lost through viscous dissipation as a fluid passes over and around these irregularities is sufficient to ensure that it is effectively brought to rest. The present paper analyses the flow over a particularly simple model of such a rough wall to support these physical ideas.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 59 , Issue 4 , 7 August 1973 , pp. 707 - 719
Copyright
© 1973 Cambridge University Press

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

Benbow, J. J. & Lamb, P. 1963 New aspects of melt fracture S.P.E. Trans. 3, 1.Google Scholar
Fletcher, A. 1940 A table of complete elliptic integrals. Phil. Mag. 30 (7), 516.Google Scholar
Goldstein, S. 1938 Modern Developments in Fluid Dynamics. Oxford University Press.
Lighthill, M. J. 1963 In Laminar Boundary Layers (ed. L. Rosenhead), chap. I. Oxford University Press.
Nye, J. F. 1969 A calculation on the sliding of ice over a wavy surface using a Newtonian viscous approximation. Proc. Roy. Soc. A 311, 445.Google Scholar
Nye, J. F. 1970 Glacier sliding without cavitation in a linear viscous approximation. Proc. Roy. Soc. A 315, 381.Google Scholar
Pearson, J. R. A. & Petrie, C. J. S. 1965 On the melt-flow instability of extruded polymers. Proc. 4th Int. Cong. Rheol., Part 3 (ed. E. H. Lee), p. 265. Interscience.
Pearson, J. R. A. & Petrie, C. J. S. 1968 On melt flow instability of extruded polymers. Polymer Systems: Deformation and Flow, Proc. 1966 Ann. Conf. Brit. Soc. Rheol. (ed. R. E. Wetton & R. W. Whorlow), p. 163. Macmillan.
Richardson, S. 1968 Two-dimensional bubbles in slow viscous flows J. Fluid Mech. 33, 475.Google Scholar