Low Peclet mass transport in assemblages of spherical particles for two different adsorption mechanisms

The problem of flow and mass transport within an assemblage of spherical solid absorbers is investigated. We present and compare results from the numerical solution of the convection-diffusion equation in the sphere-in-cell geometry and in stochastically constructed 3-D spherical particle assemblages. In the first case, we make use of an analytical solution of the creeping flow field in the sphere-in-cell model while in the second we employ a full numerical solution of the flow field in the realistic geometry of sphere assemblages. Low to moderate Peclet numbers (Pe<10(2)) are considered where the validity of the sphere-in-cell model is uncertain. On the other hand, the selected porosities range from values close to unity, where the sphere-in-cell approximation is expected to hold, to intermediate values, where its applicability becomes again uncertain. In all cases, instantaneous and Langmuir adsorption is studied. It is found that the simplified sphere-in-cell approach performs adequately provided that proper account of the actual porous media properties (porosity and internal surface area) is taken. A simple match of porosity is not sufficient for a reliable estimation of adsorption efficiencies.