Mass Transfer and Dispersion around a Soluble Solid Particle Immersed in a Packed Bed of Inert Particles

Abstract

The present work describes the mass transfer process between a moving fluid and a soluble solid mass (sphere, cylinder or a plane surface aligned with the flow) buried in a packed bed of small inert particles with uniform voidage. Numerical solutions of the partial differential equations describing solute mass conservation were undertaken (for solute transport by both advection and diffusion) to obtain the concentration field in the vicinity of the soluble surface and the mass transfer flux was integrated to give the Sherwood number as a function of the relevant parameters (e.g. Peclet number, Schmidt number, aspect ratio of the soluble mass). Mathematical expressions are proposed that describe accurately the dependencies found. The solutions of these problems are useful in the analysis of a variety of physical situations, as in establishing a simple method for the measurement of the diffusion coefficient of slightly soluble solutes, at temperatures that may differ significantly from ambient value, and in the analytical models of continuous injection of solute at a point source, in a uniform stream, to estimate the distance from the "contaminant source" beyond which the levels of contaminant are expected to fall below some safe limit. The correlations obtained were also assessed through the measurement of diffusivity for different solutes released by slightly soluble solids, and the experimental values obtained were in good agreement with the values reported in literature.