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A Direct Boundary Element Formulation For The Evolution Of The Radial Finger At The Interface Between Two Viscous Liquids


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H. Power


A direct boundary element formulation for the evolution of the radial finger at the interface between two viscous liquids H. Power* Wessex Institute of Technology, University of Portsmouth, Ashurst Lodge, Ashurst, Southampton, S040 7AA, UK Summary The problem of determining the evolution of a radial finger in a Hele-Shaw cell filled with two different viscous liquids is formulated as a classical potential problem in terms of the corresponding Green's integral representation formulae. The normal derivative of the representation formulae together with the match- ing conditions at the interface between the two liquids yield a uniquely solvable Fredholm integral equation of the second kind with non-singular kernel, whose non-homogeneous term is given in terms of a hypersingular integral. Introduction The phenomenon of viscous fingering in a Hele-Shaw cell refers to the onset and evolution of instabilities that occur in the displacement of the interface between two immis