Topology of pair-sphere trajectories in finite inertia suspension shear flow and its effects on microstructure and rheology

Abstract

The relative motion of pairs of spheres in finite inertia shear flow is examined. The pair relative trajectory is studied, using lattice-Boltzmann simulation, both for pairs which are isolated and for pairs in suspension of solid volume fraction of ϕ ≤ 0.3. For the suspension, the average trajectory and aspects of its dispersion are considered. For neutrally buoyant particles in simple-shear flow, particle-scale inertia is represented by a Reynolds number Re=ργ̇a2μ, where γ̇ is the shear rate, a is the particle radius, and ρ and μ are the density and viscosity of the Newtonian suspending fluid. The pair trajectories in a dilute inertial suspension have the same basic features as the streamlines around an isolated particle at similar Re: reversing, in-plane and off-plane spiraling, and open but fore-aft asymmetric trajectories are observed. The origin of the off-plane spirals is examined in detail in this work. The average pair trajectory space in a suspension of finite volume fraction is found to be qualitatively similar to the dilute suspension pair trajectories, as the spiraling and reversing zones are retained; the influence of ϕ and Re on the extension of different zones is described. The role of the average pair trajectory in setting the microstructure of the suspension is analyzed through a convection equation description of the pair distribution function, showing extreme accumulation at contact consistent with sampling from simulation. The influence of the microstructure on the bulk rheology is considered, with a focus on the combined effects of ϕ and Re on the near contact structural effects on rheology.