Diffusion and convective dispersion through arrays of spheres with surface adsorption, diffusion, and unequal solute partitioning

Abstract

The effective diffusivity (as well as convective dispersivity) of cubical arrays of neutrally buoyant spheres on whose surfaces solute adsorbs and subsequently diffuses is derived via macrotransport (i.e., generalized Taylor dispersion) theory. The role of unequal solute partitioning in the continuous and dispersed phases is also elucidated. Solute adsorption is shown to diminish the overall diffusivity of the suspension (emulsion), while—for a fixed surface adsorption—the consequence of increasing surface diffusivity is to enhance the emulsion's effective diffusivity. As expected, the role of unequal partitioning is to monotonically vary (as the dispersed-phase partition coefficient, K, ranges from 0 to 1) the magnitude of the effective diffusivity between the zero (nonconducting) and equal (conducting) partitioning cases. On the other hand, solute adsorption onto the surfaces of solid spheres whose centers are locked into the lattice points of a cubic array—through whose interstices a Newtonian fluid flows with mean (macroscopically homogeneous) interstitial velocity v ∗—measurably influences only the purely diffusive contribution to the convective dispersivity of the fixed bed, at least for highly porous beds and small to moderate Peclet and Reynolds numbers.