Creeping flow mass transfer to a single active sphere in a random spherical inactive particle cloud at high schmidt numbers

Using the solution by Tam of Navier-Stokes equations for creeping flow around an active sphere surrounded by a random cloud of inactive spheres, an asymptotic solution of the convective diffusion equation is obtained for high Schmidt numbers. The Sherwood number for the overall mass transfer coefficient to the active sphere has been analytically related to the Peclet number as {A figure is presented}. It agrees very well with the experimental mass transfer data on single active spheres for σ = 0476, Re < 10 and large Sc. This analytical result becomes invalid as σ decreases to 0.33. Pfeffer's model for the same problem has excellent agreement with the mass transfer data on single active spheres for σ = 026, Re < 10 and Sc = 1600. Pfeffer's model seems to be quite satisfactory for the usual range of void volume fractions in packed beds. The present model seems to be more accurate at higher values of void volume fractions in packed and distended beds.