Mass transfer from cylinders and plane surfaces buried in packed beds in alignment with the flow direction

Abstract

The present work describes the mass transfer process between a moving fluid and a slightly soluble cylinder buried in a packed bed, in alignment with the direction of flow. The bed of inert particles is taken to have uniform voidage. Numerical solution of the partial differential equation (PDE) describing mass conservation of the solute gave the concentration field near the soluble surface and the mass transfer flux was integrated to give values of the Sherwood number as a function of the relevant parameters. A mathematical expression is proposed (given as Eq. (32) in the paper) that describes accurately the dependence found numerically between the value of the Sherwood number and the values of Peclet number and aspect ratio, L/d(1), of the cylinder. For large enough diameter of the cylinder, the problem degenerates into mass transfer from a plane surface and the same equation applies, with L/d(1) = 0. The equation was tested through the measurement of diffusivity for different solutes released by slightly soluble solids, and the experimental values obtained were in excellent agreement with the values found in literature. An important feature of the paper is the detailed discussion of the finite difference method adopted, with emphasis on the high-resolution schemes used in the discretisation of the convection term of the PDE.