Diffusion around oblate ellipsoids—a study on the influence of particle shape on the rate of particle consumption in fluid-particle processes

Abstract

engineering it is often required to consider operations in which there are physi~o-chemical interactions between solid particles and a surrounding fluid. For the discussion which follows relevant examples of these oper- ations are the evaporation or dissolution of solid particles, the combustion of solids and gas phase reactions catalysed by solids. In the quantitative treatment of these operations it is common practice to assume the particles to be spherical and yet this may be far from true (e.g. if the particles come out of a grinding operation). As far as diffusion and reaction rates are concerned it is important to know the error involved in that approximation. Also, if the particles are consumed in the process (e.g. evaporation) it may be important to know how the particle evolves in shape as it is consumed. The treatment of irregular shapes and most regular shapes could only be done by computer and even then for only a few cases. A shape which lends itself to analytical treatment in problems of diffusion is the ellipsoid. Therefore it was decided to take the oblate ellipsoid as a ‘model’ of a non- spherical particle and to study the problems of diffusion around it. The results from this study help assess the error involved in approximating real particles by spheres. Only the limiting processes of pure diffusion control and pure kinetic control are considered. In the treatment of diffusion no allowance is made for any convective terms.