Particle and bubble dynamics in a creeping flow

Abstract

Dynamics of a solid particle and non-deformable gaseous bubble in viscous fluid are studied analytically and numerically within the framework of creeping flow regime (flow at vanishingly small Reynolds numbers). Equations of motion for the particle and bubble include the consideration of the buoyancy force, Stokes drag force and memory-integral drag force. Exact analytical solutions are obtained and categorised in terms of inclusion (particle or bubble) density with respect to the density of a surrounding fluid. Through the analytical and numerical solutions, the dynamics of solid particle and air bubble in water have been found to behave differently especially at the early stages of motion, whereas some qualitative similarities exist in the long-term asymptotic.