Asymptotic solutions of the problem of heat and mass transfer of particles in a fluid

Abstract

Some questions related to asymptotic analysis (as P → ∞, where P is the Peclet number) of problems involving heat and mass transfer of particles in a fluid are considered. The first part of the paper investigates the stationary convective diffusion of a solute to a particle near its front critical point (incidence point). An explicit expression is obtained for the concentration in the region of the front critical point of a solid or liquid particle around which a Stokes flow occurs. In the second part of the paper, a unified formula is obtained for the concentration distribution behind the particle. Appropriate limits in this formula determine the concentration in the mixing region and the inner and convective boundary-layer regions of the diffusion wake. In the final part of the paper, a study is made of the diffusion to a chain of absorbing solid spheres of equal radius a at distances1, 1 ≪1/a ≪ P1/3, from each other on the axis of an oncoming Stokes flow; an integral equation is obtained for the local diffusion flux when a chemical reaction with arbitrary kinetics takes place on the surfaces of the spheres. A certain heterogeneity of the material in the paper is due to the investigation in it of various questions that arise in the solution of more general problems (see, for example, [1–14]) which have not been considered hitherto.