Effect of weak fluid inertia upon Jeffery orbits - Archive ouverte HAL
Journal Articles Physical Review E : Statistical, Nonlinear, and Soft Matter Physics Year : 2015

Effect of weak fluid inertia upon Jeffery orbits

Abstract

We consider the rotation of small neutrally buoyant axisymmetric particles in a viscous steady shear flow. When inertial effects are negligible the problem exhibits infinitely many periodic solutions, the ``Jeffery orbits.'' We compute how inertial effects lift their degeneracy by perturbatively solving the coupled particle-flow equations. We obtain an equation of motion valid at small shear Reynolds numbers, for spheroidal particles with arbitrary aspect ratios. We analyze how the linear stability of the ``log-rolling'' orbit depends on particle shape and find it to be unstable for prolate spheroids. This resolves a puzzle in the interpretation of direct numerical simulations of the problem. In general, both unsteady and nonlinear terms in the Navier-Stokes equations are important.
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Dates and versions

hal-01459164 , version 1 (05-03-2019)

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J. Einarsson, F. Candelier, F. Lundell, J. R. Angilella, B. Mehlig. Effect of weak fluid inertia upon Jeffery orbits. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2015, 91 (4), ⟨10.1103/PhysRevE.91.041002⟩. ⟨hal-01459164⟩
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