Mass or heat transfer from spheroidal gas bubbles rising through a stationary liquid

Abstract

Mass transfer was studied for the case of a spheroidal bubble rising through a stationary liquid. A numerical code that solves the Navier–Stokes equations and the diffusion–advection equation for the concentration was used to characterize the transfer from the bubble to the surrounding liquid phase. Simulations were carried over systematically for Reynolds number ranging from 1 to 1000, Schmidt numbers from 1 to 500 and bubble aspect ratio from 1 to 3. It appears that the use of the equivalent diameter as the characteristic length is the more appropriate to describe the transfer. The effect of bubble aspect ratio on the Sherwood number has been analyzed. At first order the extension of Boussinesq expression using the equivalent diameter can be used for practical purposes. The evolution of the correction factor that compares the Sherwood number to the one of a sphere with same equivalent Peclet number is presented and described using simple correlations. The implementation of these results into Euler–Euler simulations of mass transfer is discussed. It appears that the modification of the interfacial area combined to the modification of the Sherwood number gives a significant contribution to the interfacial source term in the equation of the concentration. Note that the results can also be considered for heat transfer and used for inviscid drops.