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Pair-sphere trajectories in finite-Reynolds-number shear flow

2008; Cambridge University Press; Volume: 596; Linguagem: Inglês

10.1017/s0022112007009627

1469-7645

Pandurang M. Kulkarni, Jeffrey F. Morris,

Fluid Dynamics and Turbulent Flows

The pair trajectories of neutrally buoyant rigid spheres immersed in finite-inertia simple-shear flow are described. The trajectories are obtained using the lattice-Boltzmann method to solve the fluid motion, with Newtonian dynamics describing the sphere motions. The inertia is characterized by the shear-flow Reynolds number ${\it Re} \,{=}\,\rho\dot{\gamma}a^2/\mu$ , where μ and ρ are the viscosity and density of the fluid respectively, $\dot{\gamma}$ is the shear rate and a is the radius of the larger of the pair of spheres in the case of unequal sizes; the majority of results presented are for pairs of equal radii. Reynolds numbers of 0 ≤ Re ≤ 1 are considered with a focus on inertia at Re = O (0.1). At finite inertia, the topology of the pair trajectories is altered from that predicted at Re = 0, as closed trajectories found in Stokes flow vanish and two new forms of trajectories are observed. These include spiralling and reversing trajectories in addition to largely undisturbed open trajectories. For Re = O (0.1), the limits of the various regions in pair space yielding open, reversing and spiralling trajectories are roughly defined.