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On the Rallison and Acrivos solution for the deformation and burst of a viscous drop in an extensional flow

Published online by Cambridge University Press:  21 April 2006

Henry Power
Henry Power
Affiliation:
Institute de Mecánica de Fluídos, Universidad Central de Venezuela, Ciudad Universitaria, C.P. 1041-A, Caracas, Venezuela
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Abstract

In this work we prove that the second-kind Fredholm's integral equations proposed by Rallison & Acrivos to solve the deformation and burst of a viscous drop in an extensional flow, with viscosity ratio λ, possess a unique continuous solution u(x) for any continuous datum F(x) when 0 < λ < ∞. In the original work they could only guarantee, analytically, the solvability of the integral equations in a small neighbourhood of λ = 1.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 185 , December 1987 , pp. 547 - 550
Copyright
© 1987 Cambridge University Press

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References

Goursat, E. 1964 A Course in Mathematical Analysis, vol. II, part two. Dover.
Ladyzhenskaya, O. A. 1963 The Mathematical Theory of Viscous Incompresible Flow. Gordon and Breach.
Rallison, J. M. & Acrivos, A. 1978 A numerical study of the deformation and burst of a viscous drop in an extensional flow. J. Fluid Mech. 89, 191–200.Google Scholar
Rallison, J. M. 1984 The deformation of small viscous drops and bubbles in shear flow. Ann. Rev. Fluid Mech. 16, 45–66.Google Scholar