Mass Transfer Around a Single Soluble Solid with Different Shapes Buried in a Packed Bed and Exposed to Fluid Flow

The present work describes the mass transfer process between a moving fluid and a soluble solid mass (a sphere, a cylinder or a plane surface aligned with the flow, a cylinder in cross-flow, a prolate spheroid and a oblate spheroid) 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 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.

Keywords: Concentration profiles, numerical simulation, diffusion, dispersion, peclet number, Schmidt number, fluid flow, flat slab, cylinder, sphere, cylinder in cross flow, prolate spheroid, oblate spheroid.