Collisional dissipation rate in shearing flows of granular liquid crystals

We make use of discrete-element-method numerical simulations of inelastic frictionless cylinders in simple shearing at different length-to-diameter ratios and solid volume fractions to analyze the rate of collisional dissipation of the fluctuation kinetic energy. We show that the nonspherical geometry of the particles is responsible, by inducing rotation, for increasing the dissipation rate of the fluctuation kinetic energy with respect to that for frictionless spheres. We also suggest that the partial alignment of the cylinders induced by shearing concurs with the particle inelasticity in generating correlation in the velocity fluctuations and thus affecting the collisional dissipation rate as the solid volume fraction increases. Finally, we propose simple phenomenological modifications to the expression of the collisional dissipation rate of kinetic theory of granular gases to take into account our findings.

Figure 1

Snapshots of the shear flows of (a) flat $\left(l/d=0.25\right)$ and (b) elongated $\left(l/d=4\right)$ cylinders at $\nu =0.4$.

Figure 2

Numerical (symbols) and theoretical (dashed lines) (using the effective coefficient of restitution) dimensionless collisional dissipation rate versus solid volume fraction for (a) elongated and (b) flat cylinders when $\nu \le 0.35$ and $l/d=0.17$ (closed down triangles), $l/d=0.25$ (closed up triangles), $l/d=0.5$ (closed squares), $l/d=0.8$ (open diamonds), $l/d=1$ (open circles), $l/d=2$ (open squares), $l/d=4$ (open up triangles), and $l/d=6$ (open down triangles). Also shown are the numerical (closed circles) (after [20]) and theoretical (solid line) results for simple shearing of frictionless spheres having $e=0.95$.

Figure 3

Normalized effective coefficient of restitution versus aspect ratio.

Figure 4

Same as in Fig. 2, but for $\nu \ge 0.35$.

Figure 5

Numerical (same symbols as in Fig. 2) dimensionless correlation length as a function of the solid volume fraction. The solid and dashed lines represent Eq. (10) when $e_{\mathrm{eff}}=0.9$ (i.e., $l/d=1)$ and 0.86 (i.e., $l/d=2)$, respectively.

Figure 6

Numerical (same symbols as in Fig. 2) dimensionless correlation length as a function of the order parameter. The solid line represents Eq. (11).