Journal of Fluid Mechanics

Slow flow through stationary random beds and suspensions of spheres

T. S.  Lundgren 

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Stokes flow through a random, moderately dense bed of spheres is treated by a generalization of Brinkman's (1947) method, which is applicable to both stationary beds and suspensions. For stationary beds, Darcy's law with a permeability result similar to Brinkman's is derived. For suspensions an effective viscosity μ/(1–2·60ψ) is found, where ψ is the volume fraction of spheres. Also, an expression for the settling velocity is derived.

(Published Online March 29 2006)
(Received May 10 1971)