Orientational Ordering in Athermally Sheared, Aspherical, Frictionless Particles

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 $\alpha \to 0$ and particles approach spherical. We find that the nematic order parameter $S_2$ is nonmonotonic in the packing fraction $\varphi$ and that, as $\alpha \to 0$, $S_2$ 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 $\alpha \to 0$.

Figure 1

Nematic order parameter $S_2$ vs packing $\varphi$ at different shear strain rates $\dot{\gamma }$. (a) 2D spherocylinders at asphericity $\alpha =0.01$ and (b) 3D ellipsoids at $\alpha =0.02$. Vertical dashed lines locate the jamming transition of $\alpha =0$ spherical particles, ${\varphi }_J^{(0)}=0.8433$ for 2D [28, 29, 30] and 0.649 for 3D [31].

Figure 2

Nematic order parameter $S_2$ for (a) 2D spherocylinders and (b) 3D ellipsoids vs packing $\varphi$ for different asphericities $\alpha$, at two different small strain rates ${\dot{\gamma }}_1$ (solid symbols) $<{\dot{\gamma }}_2$ (open symbols); see Table 1 for values. Vertical dashed lines locate the jamming ${\varphi }_J^{(0)}$ of spherical particles.

Figure 3

Component of the average particle angular velocity in the direction of the system vorticity, scaled by the strain rate, $-⟨{\omega }_{zi}⟩/\dot{\gamma }$ for (a) 2D spherocylinders and (b) 3D ellipsoids vs packing $\varphi$ for different asphericities $\alpha$, at two different small strain rates ${\dot{\gamma }}_1$ (solid symbols) $<{\dot{\gamma }}_2$ (open symbols); see Table 1 for values. Vertical dashed lines locate the jamming ${\varphi }_J^{(0)}$ of spherical particles.

Figure 4

For 2D spherocylinders and 3D ellipsoids. (a) $S_{2\max }$ vs $\alpha$. Solid lines are fits to $S_0+c{\alpha }^{\beta }$, using the five smallest $\alpha$ points. Dropping the point at $\alpha =0.001$, dashed lines show power law fits. (b) ${\varphi }_J^{(0)}-{\varphi }_{\max }$ vs $\alpha$, with ${\varphi }_J^{(0)}$ the $\alpha =0$ jamming point. Solid lines connect the data points; the dashed line for the 2D spherocylinders is a power law fit to the five smallest $\alpha$ points.

Figure 5

Probability $\mathcal{P}(\vartheta )$ for a particle to have a contact at polar angle $\vartheta$ on its surface, for different asphericities $\alpha$ at fixed $\varphi$ near ${\varphi }_J^{(0)}$. (a) 2D spherocylinders at $\varphi =0.843$ and (b) 3D ellipsoids at $\varphi =0.648$, for sufficiently small $\dot{\gamma }$ that $\mathcal{P}(\vartheta )$ becomes independent of $\dot{\gamma }$. In (a), the sharp peaks near $\vartheta =\pi /6$ and $5\pi /6$ are shadow effects from particles in contact at $\vartheta =\pi /2$.