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Effect of Altitude Concentration Gradient of Soluble Gaseous Pollutants on Their Scavenging by Falling Rain Droplets

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  • 1 Department of Mechanical Engineering, The Pearlstone Center for Aeronautical Engineering Studies, Ben-Gurion University of the Negev, Beer-Sheva, Israel
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Abstract

This paper analyzes absorption of soluble atmospheric trace gases by falling rain droplets with internal circulation, which is caused by interfacial shear stresses. It is assumed that the concentration of soluble trace gases in the atmosphere varies in a vertical direction. In the analysis the accumulation of the absorbate in the bulk of the falling rain droplet was accounted for. The problem is solved in the approximation of a thin concentration boundary layer in the droplet and in the surrounding air. It was assumed that the bulk of a droplet, beyond the diffusion boundary layer, is completely mixed and that concentration of the absorbate is 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 for absorbate transport in liquid and gaseous phases with time-dependent boundary conditions is reduced to a linear-convolution Volterra integral equation of the second kind, which is solved numerically. It is shown that the nonuniform vertical distribution of absorbate in a gaseous phase strongly affects mass transfer during gas absorption by a falling droplet.

Corresponding author address: Tov Elperin, Department of Mechanical Engineering, Ben-Gurion University of the Negev, P.O. Box 653, Beer-Sheva 84105, Israel. Email: elperin@bgu.ac.il

Abstract

This paper analyzes absorption of soluble atmospheric trace gases by falling rain droplets with internal circulation, which is caused by interfacial shear stresses. It is assumed that the concentration of soluble trace gases in the atmosphere varies in a vertical direction. In the analysis the accumulation of the absorbate in the bulk of the falling rain droplet was accounted for. The problem is solved in the approximation of a thin concentration boundary layer in the droplet and in the surrounding air. It was assumed that the bulk of a droplet, beyond the diffusion boundary layer, is completely mixed and that concentration of the absorbate is 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 for absorbate transport in liquid and gaseous phases with time-dependent boundary conditions is reduced to a linear-convolution Volterra integral equation of the second kind, which is solved numerically. It is shown that the nonuniform vertical distribution of absorbate in a gaseous phase strongly affects mass transfer during gas absorption by a falling droplet.

Corresponding author address: Tov Elperin, Department of Mechanical Engineering, Ben-Gurion University of the Negev, P.O. Box 653, Beer-Sheva 84105, Israel. Email: elperin@bgu.ac.il

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