We analyze non-isothermal absorption of soluble atmospheric trace gases by the falling rain droplets with internal circulation which is caused by interfacial shear stresses. It is assumed that the concentration of soluble trace gases and temperature in the atmosphere varies in a vertical direction. In the analysis we accounted for the accumulation of the absorbate in the bulk of the falling rain droplet. The problem is solved in the approximation of a thin concentration and temperature boundary layers in the droplet and in the surrounding air. We assumed that the bulk of a droplet, beyond the diffusion boundary layer, is completely mixed and concentration of the absorbate and temperature are homogeneous and time-dependent in the bulk. By combining the generalized similarity transformation method with Duhamel’s theorem, the system of transient conjugate equations of convective diffusion and energy conservation for absorbate transport in liquid and gaseous phases with time-dependent boundary conditions is reduced to a system of linear convolution Volterra integral equations of the second kind which is solved numerically. It is shown that the non-uniform vertical distribution of absorbate and temperature in a gaseous phase strongly affects mass transfer during gas absorption by a falling droplet.

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