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A critique of slip and stick hydrodynamics for ellipsoidal bodies

1993; Taylor & Francis; Volume: 80; Issue: 6 Linguagem: Inglês

10.1080/00268979300103131

1362-3028

Shuang Tang, Glenn T. Evans,

Sports Dynamics and Biomechanics

Translational friction coefficients of hard prolate ellipsoids (having aspect ratios of 1–10) have been calculated by solving the linearized Navier-Stokes equations of hydrodynamics, using the method of Faxén's theorem. When the stick boundary condition was used, the present results reproduce the famous work of Lamb. The new information derived from this study arises from the analysis of the friction under the influence of the slip hydrodynamic boundary condition. It was found that the slip friction perpendicular to the long axis of the prolate ellipsoid increases monotonically with aspect ratio, whereas the parallel component of the friction decreases monotonically to an apparent limiting value. The ratio f ⊥/f ‖ of friction coefficients perpendicular and parallel to the long axis of the particle, calculated using slip hydrodynamics, scales roughly as the aspect ratio of the ellipsoid, in accord with the findings from an Enskog (uncorrelated binary collision) kinetic theory of hard ellipsoids and from the estimate derived from molecular dynamics. In contrast, f ⊥/f ‖ derived by means of stick hydrodynamics shows a weak dependence on the aspect ratio and disagrees with kinetic theory and molecular dynamics findings.