Motion of a gas bubble inside a spherical liquid container with a vertical temperature gradient

The steady-state motion of a gas bubble inside a non-isothermal, spherical, liquid-filled container is described by taking into account the effects of gravity, the thermally induced gradient of the gas-liquid interfacial tension, and the finite size of the liquid container. The flow fields inside and outside the bubble located at the center of the container are calculated using a low-Reynolds-number approximation of the fluid equations. The temperature fields are determined by using a low-Prandtl-number approximation of the heat equations. A general expression is obtained for the steady-state migration velocity of the bubble which, under certain conditions, reduces to expressions previously derived by a number of investigators. Finally, an expression for the vertical temperature gradient that will maintain a stationary gas bubble at the center of the container is formulated.