Summary
A calculation is given of the viscous force, exerted by a flowing fluid on a dense swarm of particles. The model underlying these calculations is that of a spherical particle embedded in a porous mass. The flow through this porous mass is decribed by a modification of Darcy's equation. Such a modification was necessary in order to obtain consistent boundary conditions. A relation between permeability and particle size and density is obtained. Our results are compared with an experimental relation due to Carman.
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References
J. M. Burgers, Proc. roy. Acad. Amsterdam44, 1045, 1177, 1941;45, 9, 126, 1942.
H. Darcy, Les fontaines publiques de la ville de Dijon (1856). Cf. M. Muskat, The flow of homogeneous fluids through porous media (New York 1937).
A. Einstein, Ann. Physik.19, 289, 1906;34, 591, 1911.
W. Carman, Trans. Inst. Chem. Engrs.15, 150, 1937.
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Brinkman, H.C. A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles. Appl. Sci. Res. 1, 27–34 (1949). https://doi.org/10.1007/BF02120313
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DOI: https://doi.org/10.1007/BF02120313