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.


76R99 Diffusion and convection
82C70 Transport processes in time-dependent statistical mechanics
Full Text: DOI Link


[1] Burgers, Proc. K. Ned. Akad. Wet. 44 pp 1045, 1177– (1941)
[2] Burgers 45 pp 9, 126– (1942)
[3] Hill, Int. J. Multiph. Flow 3 pp 561– (1977)
[4] M. Smoluchowski,Proceedings of the 5th International Congress of Mathematicians, edited by E. W. Hobson and A. E. H. Love (Cambridge U.P., Cambridge, 1913), Vol. 2, p. 192. · JFM 44.0907.02
[5] Beenakker, Phys. Fluids 28 pp 767– (1985)
[6] Beenakker, Physica 127A pp 451– (1984)
[7] Beenakker, Physica 131A pp 311– (1985)
[8] Batehelor, J. Fluid Mech. 52 pp 245– (1972)
[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).
[12] Kinosita, J. Colloid Sci. 4 pp 525– (1949)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.