Orientational Ordering in Athermally Sheared, Aspherical, Frictionless Particles

Abstract

We numerically simulate the uniform athermal shearing of bidisperse, frictionless, two dimensional spherocylinders and three dimensional prolate ellipsoids. We focus on the orientational ordering of particles as an asphericity parameter α → 0 and particles approach spherical. We find that the nematic order parameter S2 is non-monotonic in the packing fraction φ, and that as α → 0 S2 stays finite at jamming and above. The approach to spherical particles thus appears to be singular. We also find that sheared particles continue to rotate above jamming, and that particle contacts preferentially lie along the narrowest width of the particles, even as α → 0.Models of athermal (T = 0) granular materials have often focused on the simplest case of spherical particles. Recently, however, more attention has been paid to the case of elongated particles with lower rotational symmetry [1]. The question then arises whether such elongated particles will orientationally order as the particle density increases, so as to pack more efficiently. While elongated particles in thermal equilibrium are known to have a nematic orientational ordering transition [2, 3], recent works have found that such particles do not orientationally order upon athermal isotropic compression [4][5][6][7][8].Orientational ordering is, however, found when elongated particles are placed in an athermal uniform shear flow. In this case, drag forces between the particle and the flow will cause the particle to tumble [9]. If the particle is asymmetrical, with unequal eigenvalues of its moment of inertia tensor, tumbling will have a non-uniform rotational velocity; the torque from drag forces will vary with the particle's orientation, and the particle will on average align with the flow direction. For a finite density of colliding particles, nematic ordering remains but the nematic director becomes oriented at a finite angle with respect to the flow direction [10][11][12][13][14][15][16][17][18].Here we investigate the nematic ordering of frictionless, aspherically shaped particles, athermally sheared at constant strain rateγ, putting the system into a steady state of simple shear flow. We consider behavior as an asphericity parameter α → 0, and the particles approach spherical. We find the surprising result that a finite nematic ordering persists even as α → 0, suggesting that the shear driven jamming of aspherical particles has a singular limit as α → 0. Since most particles in nature are not truly spherical, our result may have broad implications for granular shear flows.Models: We consider two different numerical models: (i) spherocylinders in two dimensions (2D), and (ii) prolate ellipsoids in three dimensions (3D). In both cases we take a bidisperse distribution of particle sizes, with equal numbers of big and small particles. We use softcore particles with a one-sided harmonic elastic repulsion. The system length is L in all directions, with periodic boundary conditions along the flow directionx, and Lees-Edwards boundary conditions [19] with a uniform stra...

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

“…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.…”

“…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.…”

Athermal shearing of frictionless cross-shaped particles of varying aspect ratio

“…The non-convex shape of the crosses allows for particles to interlock and create gear-like effects in their interactions. We study the rotational motion of such particles and their orientational ordering in the shear flow, making comparison to previous work we have done on non-convex U-shaped particles ("staples") [4] and convex elongated rods [5][6][7]. We will see that the lack of convexity plays a significant role in such particle orientational effects.…”

“…6 we plot the average particle rotational veloc- ity, scaled by the strain rate, − θ i /γ vs φ for crosses with aspect ratio β = 0.25, 0.5, and 1. For comparison we include our earlier results for staples [4] and spherocylinders with α = 4 [5,7]. In each case, here and in subsequent Figs.…”

Shear thickening of suspensions of dimeric particles

“…In simple shear, from symmetry considerations one expects the eigenvectors, and in particular the so-called director u 1 , to lie either in the shear plane, or along the vorticity direction. To represent the director u 1 , I will follow earlier literature and use its spherical coordinates with the vorticity as the zenith direction, with ϕ the angle between the director and the vorticity direction and θ the angle between the flow direction and the projection of the director on the flow plane [Campbell, 2011;Guo et al, 2012;Nagy et al, 2017;Nath and Heussinger, 2019;Marschall et al, 2019]. Because the order is nematic, I use directors such that 0 < θ < π.…”