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.