The bursting of two-dimensional drops in slow viscous flow

Abstract

We consider the deformation of two-dimensional drops when immersed in a slow viscous corner flow. The problem is formulated as one of analytic function theory and simplified by assuming that both the drop and the exterior fluid have the same viscosity. An approximate analysis is carried out, in which the conditions at the interface are satisfied in an average sense, and this reveals the following features of the solution. A drop of given physical properties (volume, surface tension and viscosity), when immersed in a corner flow, has no steady equilibrium shape if the rate of strain of the applied flow is too large. On the other hand, if the rate of strain is small enough for a steady solution to exist, then in general there are two possible solutions. These features are confirmed by formulating the exact problem in terms of a nonlinear integro-differential equation, which is solved numerically.