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Is sedimentation container-shape dependent? (English) Zbl 0588.76163

The question is addressed as to the dependence of sedimentation of a homgeneous suspension on the shape of the container. It is demonstrated, by comparing calculations for spherical and plane geometries, that shape- dependent contributions to the sedimentation velocity remain in the limit of infinitely distant container walls. Upon transformation from the laboratory reference frame to a local frame of reference that moves with the average volume velocity, this shape dependence is found to disappear.

MSC:

76R99 Diffusion and convection
82C70 Transport processes in time-dependent statistical mechanics
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[9] Equation (2) results from Eq. (5.1) of Ref. 6, with the addition of the term denoted by 3Ai0(1,3)(3,3)-1A0j(3,1) in that paper. The order of the terms not explicitly written down in Eq. (2) follows from the general expression for the mobility given in Ref. 6 [Eq. (4.2)], making essential use of the fact that Ri=0.
[10] As in Paper I we ignore the influence of Brownian motion on sedimentation, cf. note 13 in I.
[11] This limit expresses the well-known fact that the fluid velocity field caused by the motion of one spherical particle in an unbounded fluid does not contain terms of order R-n with n. (HereRis the distance to the particle).
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