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

Abstract

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 rateγ. 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 φ and particle asphericities α at smallγ, we study the angular rotationθi and the nematic orientational ordering S2 of the particles induced by the shear flow, finding a non-monotonic behavior as the packing φ is varied. We interpret this non-monotonic behavior as a crossover from dilute systems at small φ, where single-particle-like behavior occurs, to dense systems at large φ, 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 S2 is a consequence of the shearing serving as an ordering field, rather than a result of long-ranged 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 π, (ii) the behavior of the system under pure, as compared to simple, shearing, (iii) the relaxation of the nematic order parameter S2 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 α → 0 limit approaching circular disks.

Shear-driven flow of athermal, frictionless, spherocylinder suspensions in two dimensions: Spatial structure and correlations

“…In this work we continue our studies of this 2D spherocylinder model, but now concentrating on the spatial structure of the sheared system, and the spatial correlations of various quantities, including the particle density, nematic order parameter, and angular velocity. We confirm the assertion in [8], that there is no long-range cooperative behavior causing the finite nematic ordering, by showing that correlations of the nematic order parameter are short-ranged. By comparing the behavior of a sizebidisperse system of particles with a size-monodisperse system, and finding that the monodisperse system has a greater local spatial ordering, we find further evidence for our claim in [8] that at large φ it is the specific geometry of the dense packing that determines particle rotations and nematic ordering.…”

“…2 we show a plot of the magnitude of the nematic order parameter S 2 vs φ for these two cases. As noted in our previous work [8,11], S 2 is non-monotonic in φ, with a peak at φ S2 max that lies somewhat below the jamming φ J . For α = 4 we have φ S2 max ≈ 0.67 and φ J ≈ 0.906; for α = 0.01, we have φ S2 max ≈ 0.83 and φ J ≈ 0.845.…”

“…As this work is a continuation of our prior work on this system, the description of the model presented here is abbreviated. We refer the reader to our earlier works [7,8] for a discussion of the broader context of, and motivation for, our model, a more complete list of references, and more details of the derivation of our equations of motion.…”

“…We assume a uniform constant mass density for both our small and big particles. One of the distinguishing features of aspherical particles in simple shear flow is that they tumble as they flow, and that they show a finite nematic orientational ordering S 2 [8,[11][12][13][14][15][16][17][18], with the spines of the spherocylinders tending to align about a given direction. The extent of the alignment is given by the magnitude of the nematic order parameter S 2 , while the direction of alignment is given by the angle θ 2 with respect to the flow direction x.…”

“…For the α = 4 configuration, which has a relatively large global S 2 ≈ 0.78, we see that the S 2 (r) clearly look ordered, with for the most part nearly equal magnitudes S 2 (r) and oriented close to the flow direction. For the α = 0.01 configuration, which has a smaller global S 2 ≈ 0.23, the S 2 (r) look more disordered, with a greater variation in magnitudes and directions fluctuating about the global orientation θ 2 ≈ 45 • [8].…”