Mass transfer and concentration contours around surfaces buried in granular beds and exposed to fluid flow

Abstract

This work describes the process of mass transfer which takes place when a fluid flowspast a soluble surface buried in a packed bed of small inert spherical particles of uniform voidage.The fluid is assumed to have uniform velocity far from the buried surface and different surfacegeometries are considered; namely, cylinder in cross flow and in flow aligned with the axis, flatsurface aligned with the flow and sphere.The differential equations describing fluid flow and mass transfer by advection and diffusion inthe interstices of the bed are presented and the method for obtaining their numerical solution isindicated. From the near surface concentration fields, given by the numerical solution, rates of masstransfer from the surface are computed and expressed in the form of a Sherwood number (Sh). Thedependence between Sh and the Peclet number for flow past the surface is then established for eachof the flow geometries.Finally, equations are derived for the concentration contour surfaces at a large distance from thesoluble solids, by substituting the information obtained on mass transfer rates in the equationdescribing solute spreading in uniform flow past a point (or line) source.