The Effect of Permeability on the Drag of a Porous Sphere in a Uniform Stream

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Abstract
The present investigation is concerned with the problem of studying the effect of permeability on drag coefficient for the flow past a porous sphere placed in an otherwise uniform incident stream at low Reynolds number. The problem is formulated using the full Navier‐Stokes equations describing the flow outside the sphere while Darcy's law governs the flow inside the sphere. The solution is, then, sought by the method of matched asymptotic expansions involving three simultaneous expansions up to an order Re. It is found that the effect of porosity on the drag is that it reduces the effective radius a of the sphere by a factor (1 + k'/2a2)−1, where k' is the permeability.

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