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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 |

### Keywords:

buoyancy-driven convection; linear quasistatic Stokes equation; stick boundary conditions; sedimentation of a homgeneous suspension; plane geometries; shape-dependent contributions; sedimentation velocity; infinitely distant container walls; laboratory reference frame; local frame of reference; average volume velocity
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\textit{C. W. J. Beenakker} and \textit{P. Mazur}, Phys. Fluids 28, 3203--3206 (1985; Zbl 0588.76163)

### References:

[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) |

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