Abstract
The several possible solutions to the problem of creeping flow relative to an isolated permeable sphere are discussed and compared quantitatively. The most satisfactory solutions is that based upon Brinkman's extension of Darcy's Law. This solution is generalized, using Happel's free-surface model, to cover the practically important problem of flow relative to a swarm of permeable spheres. A physically realistic and mathematically consistent expression for the hydrodynamic resistance experienced by a typical sphere within such a system is derived. This expression is then used to predict the settling rate and the overall permeability of the swarm.
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