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- W2023145557 abstract "At small particle Reynolds numbers it is demonstrated that the intrinsic hydrodynamic resistance of an arbitrary particle to translational motion through an incompressible, unbounded, viscous fluid can be represented by a symmetric second-rank tensor (dyadic), uniquely determined by the exterior geometry of the particle. Similar remarks apply to the intrinsic resistance of the body to rotation about an axis. Unlike the previous tensor, however, the rotation tensor is shown to vary with position, an explicit formula for its variation being derived. The existence of a unique geometrical point, through which the hydrodynamic force always acts, is established. It is pointed out that this point serves to differentiate translational and rotational particle motions. The ultimate, stable orientation attained by a particle settling under the influence of gravity is shown to devolve upon the relative positions of its centres of mass, buoyancy and “hydrodynamic stress”, the latter being the point referred to in the previous paragraph. General dynamical equations are derived for the steady and unsteady motion of a settling particle and their solutions given for a few simple cases. Extension of the fundamental formulae to the case of a fluid in net flow is discussed. L'auteur montre que pour des particules de faible nombre de Reynolds, la résistance hydrodynamique intrinsèque d'une particule à un mouvement de translation à travers un fluide incompressible peut être représenté par un tenseur symétrique du second ordre, entièrement déterminé par la géométrie de la particule. Des remarques similaires sont faites pour la résistance hydrodynamique intrinsèque à un mouvement de rotation autour d'un axe, mais cette fois le tenseur de rotation dépend aussi de la position de la particule. Une formule explicite cette dépendance. Il existe un point géométrique unique sur lequel les forces hydrodynamiques agissent toujours. L'orientation stable d'une particule soumise à l'influence de la pesanteur dépend des positions relatives du centre de gravité, de la poussée d'Archimède et du point géométrique précédent. On en déduit des équations générales de la dynamique pour une particule qui sédimente et leur solution en est donnée dans quelques cas simples. L'extension de la formule fondamentale au cas d'un fluide s'écoulant est discutée." @default.
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- W2023145557 date "1963-01-01" @default.
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- W2023145557 title "The Stokes resistance of an arbitrary particle" @default.
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