title: 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.
authors.affiliation: Department of Physics, Gothenburg University, SE-41296 Gothenburg, Sweden.
authors.forename: J
authors.initials: J
authors.lastname: Einarsson
authors.affiliation: University of Aix-Marseille, CNRS, IUSTI UMR 7343, 13 013 Marseille, Cedex 13, France.
authors.forename: F
authors.initials: F
authors.lastname: Candelier
authors.affiliation: KTH Royal Institute of Technology, SE-100 44 Stockholm, Sweden.
authors.forename: F
authors.initials: F
authors.lastname: Lundell
authors.affiliation: Department of Mathematics and Mechanics, LUSAC-ESIX 50130 Cherbourg, University of Caen, France.
authors.forename: J R
authors.initials: JR
authors.lastname: Angilella
authors.affiliation: Department of Physics, Gothenburg University, SE-41296 Gothenburg, Sweden.
authors.forename: B
authors.initials: B
authors.lastname: Mehlig