Influence of inert admixtures on diffusion-controlled collapse of a rising bubble

In this study we considered mass transfer in a system comprising a rising gas bubble composed of a solvable and inert gases and liquid. In the analysis the resistance to mass transfer in both phases is taken into account. It is assumed that the bulk of a bubble, beyond the diffusion boundary layer, is completely mixed, and concentration of absorbate is homogeneous and time-dependent in the bulk. The thermodynamic parameters of a system are considered constant, and the bubble shape is assumed to be spherical. The moving boundary problem is solved in the approximations of thin concentration boundary layers in the gaseous and liquid phases and infinite dilution of an absorbate in the absorbent. The partial parabolic differential equations of mass conservation for gaseous and liquid phases with time-dependent velocity components and time-dependent boundary conditions are solved by combining generalized similarity transformation method with Duhamel's theorem, and the solution is obtained in the form of integral equation. The asymptotic behavior of the obtained solutions is discussed.