Prediction of transport processes within porous media: Creeping flow relative to a fixed swarm of spherical particles

Abstract

Abstract A geometric model for an homogeneous swarm of spherical particles was introduced by us in an earlier paper and successfully employed in a theoretical investigation of diffusive transport processes occurring therein. The same geometric model is used here in a theoretical study of the hydrodynamic transport process occurring within a fixed swarm of spherical particles. The product of the application of this model to the problem of incompressible, creeping fluid flow within an homogeneous swarm of impermeable spherical particles may be regarded as a logical extension of the well‐known Brinkman model; it permits physical representation and rigorous mathematical solution, yielding predictions which are in good agreement with experimental data throughout the entire porosity range. For porosities in excess of 0.7, the predictions agree closely with those obtained by means of Happel's free surface model.