Analytical Solution of Oseen's Equation for Creeping Flow around a Spherical Gas-bubble in Liquid

抄録

The first-order solution to Oseen's equation is determined for liquid flow around a spherical gas-bubble at low Reynolds numbers under the assumption that the velocities and the stress are continuous at the interface between gas and liquid. This solution leads to new drag-coefficients of a spherical gas-bubble rising in quiescent liquid as Cd = 16 (1+ Re/8)/Re, where Re is Reynolds number related to the diameter of a spherical gas-bubble. The measurements of hydro-dynamic drags experienced by small gas-bubbles in quiescent liquid at the Reynolds number between 0.03 and 1.0 show good agreement with the new drag formula introduced in the present paper. The visualized streamlines around a spherical gas-bubble at the Reynolds numbers below 0.3 agree well with the streamlines predicted by the first-order solution to Oseen's equation.