Axisymmetric flow due to a porous sphere sedimenting towards a solid sphere or a solid wall: Application to scavenging of small particles

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Abstract
A classic difficulty in applying a boundary condition is handled by a new mathematical approximation, correct to second order, which is used to reduce to a double set of difference equations the creeping flow problem posed by the sedimentation of a solid sphere and a porous sphere within which the Brinkman equation is assumed to be valid. It is shown that the permeability allows heavier small solid particles to be captured and markedly reduces the force experienced by a porous sphere approaching a solid plane.