Unsteady state mass transfer through the interface of spherical particles—I: Physical and mathematical description of the mass-transfer problem

Abstract

Unsteady state mass transfer through the interface of spherical particles has been thoroughly investigated using numerical methods. The particles may be bubbles, drops and solids. Mass transfer may occur in a motionless system and in a system with either the surrounding fluid only or both fluids being in motion. Creeping flow conditions are assumed for the surrounding fluid, so that the equations presented by Hadamard and Rybczinski for the velocity field can be used for calculations of the concentration field. The first part of the paper is devoted to a comprehensive discussion of the various mass-transfer conditions. This discussion is the basis for an understanding of the differential equations governing the concentration field inside and outside the sphere and the pertaining initial, boundary and interfacial conditions. These conditions are given for the general case of mass-transfer resistance in both phases as well as for the two limiting cases, for which mass-transfer resistance occurs in one of the two phases only.