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The Quarterly Journal of Mechanics and Applied Mathematics 1982 35(4):531-548; doi:10.1093/qjmam/35.4.531
© 1982 by Oxford University Press
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HELE SHAW FLOWS WITH TIME-DEPENDENT FREE BOUNDARIES IN INFINITE AND SEMI-INFINITE STRIPS

S. RICHARDSON

( Department of Mathematics, University of Edinburgh Edinburgh, Scotland )

Suppose that a Newtonian fluid is injected at a given point into the narrow gap between two plane parallel surfaces, and consider the growth of the plan-view of the resultant blob of fluid when it is restricted by barriers placed within the gap. An analytic description of this growth is obtained when it is confined, firstly, to an infinite strip bounded by two infinite parallel lines and, secondly, to a semi-infinite strip bounded by two semi-infinite parallel lines and a finite line segment perpendicular to them. The solution for expansion within the infinite strip is generally applicable; that for expansion within the semi-infinite strip is applicable when the injection point is so placed that the portion of the semi-infinite strip not occupied by the blob remains connected throughout the motion—that is when, in physical terms, no air is trapped in the corners.


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