A NOTE ON THE HISTORY FORCE ON A SPHERICAL BUBBLE AT FINITE REYNOLDS-NUMBER

An approximate expression for the history force on a spherical bubble is proposed for finite Reynolds number, Re. At small time, the history-force kernel is a constant, which decreases with increasing Re, and the kernel decays as t-2 for large time. For an impulsively started flow over a bubble, accurate finite difference results show that the history force on the bubble decays as t-2 at large time. Satisfactory agreement is observed between the presently proposed history force and the numerical solution.