Mass transfer and dispersion around active sphere buried in a packed bed

Abstract

AbstractMass transfer around single spheres in granular beds of inerts (packed or fluidized) was analyzed for transport by advection and diffusion/dispersion. Fluid flow in the granular bed around the spheres was assumed to follow Darcy's law; at each point, dispersion of solute was assumed to be determined by the coefficients of transverse and longitudinal dispersion, respectively, in the cross‐stream and streamwise directions. The elliptic equation resulting from a differential mass balance was solved numerically over a wide range of the relevant parameters. Resulting values of the Sherwood number are represented accurately by the product of two terms: the solution for advection plus molecular diffusion, which depends only on the Peclet number relative to the active sphere; the enhancement brought about by convective dispersion, which depends only on the Peclet number relative to the inert particles.