The Stokes resistance of an arbitrary particle—III: Shear fields

doi:10.1016/0009-2509(64)85052-1

Chemical Engineering Science

Volume 19, Issue 9, September 1964, Pages 631-651

https://doi.org/10.1016/0009-2509(64)85052-1 Get rights and content

Abstract

A phenomenological scheme is formulated for relating the Stokes hydrodynamic force and torque experienced by a rigid body in an otherwise uniform shear field to the rate of strain dyadic of the latter. The two intrinsic phenomenological coefficients appearing as proportionality factors between vector force and torque and the product of fluid viscosity times dyadic strain rate are shown to be Gibbsian triadics (third-rank tensors) dependent only on the external shape of the particle. The invariant formulation of these two formulae is such that the results are valid for any orientation of the body relative to the principal axes of strain of the fluid. A systematic investigation is presented of the effects of various types of particle symmetry on the properties of these two fundamental tensors. By way of example, both triadics are computed for a slightly deformed spherical particle, employing integral techniques which do not require corresponding knowledge of the detailed solution of Stokes equations.

Résumé

On formule un schéma phénoménologique permettant d'établir une relation entre la force hydrodynamique de Stokes et le couple exercé sur un corps rigide se trouvant dans un champs d'écoulement à glissement uniforme d'une part et le tenseur des vitesses de déformation de celui-ci d'autre part. On démontre que les deux coefficients intrinsèques phénoménologiques qui apparaissent comme coefficients de proportionnalité entre le vecteur force et le couple d'une part et le produit de la viscosité du fluide par le tenseur de déformation d'autre part sont des triades de Gibbs (tenseurs du 3^e ordre) qui dépendent uniquement de la forme extérieure de la particule. La formulation invariante de ces deux formules est telle que les résultats sont valides quelle que soit l'orientation du corps par rapport aux axes principales de déformation du fluide. On présente une étude systématique des effets de différents types de symmétrie sur les propriétés des deux tenseurs fondamentaux. A titre d'exemple on calcule les triades pour le cas d'une particule sphérique légèrement déformée à l'aide de techniques intégrales qui ne nécessitent pas la connaissance détaillée des solutions des équations de Stokes.

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There are more references available in the full text version of this article.

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¹: On leave 1963–64 at the Chemical Engineering Department, University of Minnesota, Minneapolis 14, Minnesota.

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The Stokes resistance of an arbitrary particle—III: Shear fields

Abstract

Résumé

Chem. Engng. Sci.

Chem. Engng. Sci.

Chem. Engng. Sci.

Chem. Engng. Sci.

Proc. Roy. Soc.

J. Fluid Mech.