Shear-driven flow of athermal, frictionless, spherocylinder suspensions in two dimensions: Particle rotations and orientational ordering

We use numerical simulations to study the flow of a bidisperse mixture of athermal, frictionless, soft-core two-dimensional spherocylinders driven by a uniform steady-state simple shear applied at a fixed volume and a fixed finite strain rate (gamma) over dot Energy dissipation is via a viscous drag with respect to a uniformly sheared host fluid, giving a simple model for flow in a non-Brownian suspension with Newtonian rheology. Considering a range of packing fractions phi and particle asphericities alpha at small (gamma) over dot, we study the angular rotation (theta) over dot(i) and the nematic orientational ordering S-2 of the particles induced by the shear flow, finding a nonmonotonic behavior as the packing phi is varied. We interpret this nonmonotonic behavior as a crossover from dilute systems at small phi, where single-particle-like behavior occurs, to dense systems at large phi, where the geometry of the dense packing dominates and a random Poisson-like process for particle rotations results. We also argue that the finite nematic ordering S-2 is a consequence of the shearing serving as an ordering field, rather than a result of long-range cooperative behavior among the particles. We arrive at these conclusions by consideration of (i) the distribution of waiting times for a particle to rotate by pi, (ii) the behavior of the system under pure, as compared to simple, shearing, (iii) the relaxation of the nematic order parameter S-2 when perturbed away from the steady state, and (iv) by construction, a numerical mean-field model for the rotational motion of a particle. Our results also help to explain the singular behavior observed when taking the alpha -> 0 limit approaching circular disks.