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

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.