Mass transfer and concentration contours between an oblate spheroid buried in granular beds and a flowing fluid

Abstract

The present work describes the mass transfer process between a moving fluid and a soluble oblate spheroid buried in a packed bed of small inert particles with uniform voidage. A general solution of this problem is not available analytically and in the present work we only consider the limiting cases of mass transfer with a thin concentration boundary layer, to which corresponds high values of Peclet number. The solution of this problem is useful in the analysis of a variety of physical situations, such as 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 obtained analytical solution, Eq. (20), describes the mass transfer between a large soluble oblate spheroid and the fluid flowing around it in the interstices of a packed bed, for high values of Peclet number. This expression was also used to obtain the concentration contour surfaces using the well-known analytical solution of continuous injection of solute at a point source.