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Steady and quasi-steady thin viscous flows near the edge of a solid surface

Published online by Cambridge University Press:  07 May 2010

G. I. BARENBLATT ,
M. BERTSCH  and
L. GIACOMELLI
G. I. BARENBLATT
Affiliation:
Department of Mathematics and E.O. Lawrence Berkeley National Laboratory, University of California, Berkeley, CA 94720-3840, USA
M. BERTSCH
Affiliation:
Dipartimento di Matematica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica, 00133 Roma, Italy, and Istituto per le Applicazioni del Calcolo “M. Picone”, C.N.R., Via dei Taurini 19, 00185 Roma, Italy
L. GIACOMELLI
Affiliation:
Dipartimento Me.Mo.Mat., Università di Roma “La Sapienza”, Via Scarpa 16, 00161 Roma, Italy email: [email protected]
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Abstract

A new approach is proposed for the description of thin viscous flows near the edges of a solid surface. For a steady flow, the lubrication approximation and the no-slip condition are assumed to be valid on most of the surface, except for relatively small neighbourhoods of the edges, where a universality principle is postulated: the behaviour of the liquid in these regions is universally determined by flux, external conditions and material properties. The resulting mathematical model is formulated as an ordinary differential equation involving the height of the liquid film and the flux as unknowns, and analytical results are outlined. The form of the universal functions which describe the behaviour in the edge regions is also discussed, obtaining conditions of compatibility with lubrication theory for small fluxes. Finally, an ordinary differential equation is introduced for the description of intermediate asymptotic profiles of a liquid film which flows off a bounded solid surface.

Type
Papers
Information
European Journal of Applied Mathematics , Volume 21 , Issue 3 , June 2010 , pp. 253 - 270
Copyright
Copyright © Cambridge University Press 2010

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