Evaluation of pressure and viscous drags of a rising bubble at small Reynolds numbers

Pressure and viscous drags acting on a bubble rising in a viscous fluid are numerically estimated to obtain the corresponding drag coefficients that are rarely reported in the existing papers. The numerical method has been successfully validated by solving the existing benchmark problems of a bubble rising in a quiescent liquid at various flow regimes. For spherical cap bubbles, the formula of total drag coefficient is proposed in a similar form to that by viscous potential flow theory expressed by the Reynolds number, and the corresponding formulas for pressure and viscous drag coefficients are derived. Furthermore, the effect of the density ratio of a bubble and the surrounding liquid on terminal velocity is also investigated for fixed Morton and Eotvos numbers: the lighter bubble has a higher terminal velocity having an asymptotic value as the density ratio increases although the Reynolds numbers based on the terminal velocity are nearly constant.