Within the framework of the Stokes approximation, a method is proposed for calculating the drag and the torque acted on a rigid particle by an incompressible viscous fluid, when the fluid–particle boundary conditions are slip conditions. By using the Fourier Transform and a reciprocity formula, the drag and torque are deduced from these obtained for two simple vibration motions of the particle in a fluid at rest. The results are explicitly given in the case of a spherical particle. They are in agreement with the formulae known in various special cases.
Dans le cadre de l'approximation de Stokes, une méthode est proposée pour calculer les efforts exercés sur une particule solide par un fluide visqueux incompressible, les conditions aux limites fluide–particule étant celles du glissement. En utilisant la Transformée de Fourier et une formule de réciprocité, les efforts sont déduits de ceux obtenus pour deux mouvements simples de vibration de la particule dans un fluide au repos. Les résultats sont explicités pour une particule sphérique. Ils sont en accord avec les expressions connues de la littérature.
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Mot clés : Mécanique des fluides, Equations de Stokes, Traînée, Couple, Terme d'histoire de Boussinesq–Basset
Renée Gatignol 1
@article{CRMECA_2007__335_9-10_606_0,
author = {Ren\'ee Gatignol},
title = {On the history term of {Boussinesq{\textendash}Basset} when the viscous fluid slips on the particle},
journal = {Comptes Rendus. M\'ecanique},
pages = {606--616},
publisher = {Elsevier},
volume = {335},
number = {9-10},
year = {2007},
doi = {10.1016/j.crme.2007.08.013},
language = {en},
}
Renée Gatignol. On the history term of Boussinesq–Basset when the viscous fluid slips on the particle. Comptes Rendus. Mécanique, Volume 335 (2007) no. 9-10, pp. 606-616. doi : 10.1016/j.crme.2007.08.013. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2007.08.013/
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