The viscous drag force on a spherical bubble with a time-dependent radius

The expression of the hydrodynamic force experienced by a spherical bubble having a variable radius and moving in a viscous incompressible liquid is derived analytically in two different asymptotic situations. The solution is obtained by rewriting the initial problem in a frame of reference where the bubble has a fixed radius and where the relevant dimensionless parameters are conserved. It is shown that when the assumption of unsteady creeping motion is valid, the bubble radius variation combined with a constant rise velocity produces a nonzero history farce. This contribution can have a significant effect on the bubble motion, especially for a collapsing bubble. (C) 1998 American Institute of Physics.