(100f) Pair Hydrodynamics And Structure In Finite-Inertia Suspensions

Hydrodynamic interactions of neutrally-buoyant spheres suspended in finite-inertia simple-shear flow are studied using the lattice-Boltzmann method. Isolated pair interactions of equal and unequal spheres and the pair microstructure at moderate concentrations of monodisperse suspensions are described here. The simulation employs a wall-bounded geometry with periodicity in the flow and vorticity directions. The inertia of the flow at the particle scale is characterized by the shear flow Reynolds number Re_p = ρ γ a²/μ, where μ and ρ are the viscosity and density of the fluid respectively, γ is the shear rate and a is the larger sphere radius. The simulated pair trajectories over a sampling of initial conditions sufficient to map out the pair trajectory space for 0< Re_p ≤ 1 have been determined. These trajectories are qualitatively different from those predicted for Re_p = 0. Inertia, apparently at any level, causes the closed Stokes trajectories to vanish and give rise to spiralling trajectories, which draw particles together in a spiralling motion along the vorticity axis before they depart to infinite separation. Reversing, or swapping, trajectories are also introduced by inertia: in these, a pair never passes in the mean flow direction, but instead approaches as expected based on the shear flow at their positions before exchanging relative positions with respect to the gradient direction and departing in the same direction as they came. For O(100) spheres in the simulation cell, the microstructure and rheology of dilute (small solid fraction, φ ) suspensions at finite inertia has been determined. The pair distribution function and rheology are presented; rheology is determined from the force on the walls, and compared with detailed mechanics (evaluation of stresslets and Reynolds stresses). Results are presented for Re_p = 0.1, 0.2 and 0.5 and φ = 0.05, 0.1 and 0.2.