Viscous Irrotational Theories and the Force on an Expanding Bubble: A Cell-Model Analysis

Abstract

The dynamics of a bounded viscous incompressible fluid surrounding a spherical bubble in rectilinear motion simultaneously experiencing volume changes is examined by means of two viscous irrotational theories, namely, viscous potential flow and the dissipation method. The forces that the liquid produces on the bubble and on the outer spherical boundary of the liquid are determined from these two approaches at the instant when the bubble is concentric with the outer surface. Viscous potential flow involves surface integration of the irrotational normal stress; the dissipation method stems from the mechanical energy balance, including the dissipation integral, evaluated in potential flow. In the inner boundary, zero tangential stress is enforced. Two choices for the tangential stress condition on the outer boundary are considered: zero tangential stress or irrotational tangential stress. In a sense, this is an extension to include viscous effects of the inviscid analysis by Sherwood [Int. J. Multiphase Flow...