Effect of viscocity and surface tension on the taylor instability of the surface of a cavitation bubble

Abstract

This thesis is devoted to a consideration of the following problem: A spherical mass of fluid of density ??, viscosity ?? and external radius R is surrounded by a fluid of density ?? and viscosity ??. The fluids are immiscible and incompressible. The interface is accelerated radially by ‘e?’ to study the effect of viscosity and surface tension on the stability of the interface. By analyzing the problem in spherical harmonics, the mathematical problem is reduced to one of characteristic determinant equation. The particular case of a cavity bubble where the density and viscosity of the fluid inside the bubble are negligible in comparison with the density and viscosity ?? respectively, of the fluid outside is considered in some detail. It is shown that viscosity has a stabilizing role on the interface; and when combined with surface tension, the stabilizing role of both viscosity and surface tension is more pronounced than would result when either of them is taken individually.