@MISC{Gilmore03thecalculation, author = {Jeffrey R. P. Gilmore}, title = {The calculation of interface motion of a . . . }, year = {2003} }

Share

OpenURL

Abstract

Simulating time-evolving bubbles in a slow viscous flow presents a challenging free boundary value problem. The fluid motion is described with the Stokes equations and the interface of the bubble is advanced using the kinematic condition. Limiting our model to two-dimensional flow, complex variable theory of the biharmonic equation is exploited to formulate the problem in terms of analytic functions. By finding these harmonic functions subject to certain conditions on the boundary of the domain, analytical solutions can be found for a class of polynomial initial bubble shapes. For bubbles with a more general initial shape, numerical calculation is necessary. Numerical and analytical solutions have been found for bubbles with a constant surface tension. The case where the surface tension varies according to the concentration of a surface active agent (surfactant) coating on the bubble adds additional analytical and numerical complications. While some significant work has been done on this problem, there is still a need to develop ecient, robust and highly accurate numerical methods in order to handle