Directional shear jamming of frictionless ellipses

In this work we study shear reversals of dense non-Brownian suspensions composed of cohesionless elliptical particles. By numerical simulations, we show that a new fragility appears for frictionless ellipses in the flowing states, where particles can flow indefinitely in one direction at applied shear stresses but shear jam in the other direction upon shear stress reversal. This new fragility, absent in the isotropic particle case, is linked to the directional order of the elongated particles at steady shear and its reorientation at shear stress reversal, which forces the suspensions to pass through a more disordered state with an increased number of contacts in which it might get arrested.

Figure 1

Strain $\gamma$ as a function of the rescaled time $\langle \dot{\gamma }\rangle t$ for 10 independent shear-stress reversals (indicated by various colors) for ellipses with $\alpha =3$. The gray-shaded area indicates prereversal evolution, and the white postreversal (upon an instantaneous shear stress reversal, $\sigma \to -\sigma$). The effect of increasing the packing fraction is shown, from (a) to (d), with $\mathrm{\Delta }\varphi ={\varphi }_c-\varphi$. Proportionality triangles show the slopes $-1$ (left) and 1 (right), respectively. (e) A typical configuration for a flowing state and (f) that of a shear reversed jammed state at $\varphi =0.877$. Arrows indicate the direction of the shear. Gray particles are wall particles, and brown ones flowing particles (the darker, the more contacts). Inset in (d): The strain evolution upon a second shear reversal from the jammed configurations in the figure.

Figure 2

Average particle direction ${\theta }_{\mathbf{e}·\widehat{\mathbf{y}}}$ (in degrees) with respect to $\widehat{\mathbf{y}}$ before (gray-shaded area) and after (white area) shear reversal. Packing fractions (a)–(d) as in Fig. 1. Lines show the average direction of the ellipses $\pm \langle {\theta }_{\mathbf{e}·\widehat{\mathbf{y}}}\rangle$ in steady shear and the zero line. Inset in (a): The evolution of the angle of a single ellipse in a shear flow as a function of the strain. Doing a turn from $-{60}^{\circ }$ to $-{60}^{\circ }$ (indicated by the dashed lines), passing through 0, requires roughly a strain of 2. Inset in (d): As that in Fig. 1, but for the average particle direction evolution.

Figure 3

Nematic order parameter $S_2$ before (gray-shaded area) and after (white area) shear reversal. Packing fractions (a)–(d) as in Fig. 1. Lines show the corresponding averaged value $\langle S_2\rangle$ as obtained at steady state. Inset in (d): As that in Fig. 1, but for $S_2$.

Figure 4

Instantaneous rescaled pressure $P/\langle P\rangle$ at the two walls as a function of the rescaled time $\langle \dot{\gamma }\rangle t$. Packing fractions (a)–(d) as in Fig. 1. Dashed lines show the average pressure $\langle P\rangle$ at steady state. Inset in (d): As that in Fig. 1, i.e., for a second shear reversal, but with $P/\langle P\rangle$.

Figure 5

Instantaneous number of contacts per particle $Z$ as a function of the rescaled time $\langle \dot{\gamma }\rangle t$. Packing fractions (a)–(d) as in Fig. 1. Dashed black lines show the average values of $\langle Z\rangle$ at steady state. Dashed red lines show the critical value at steady-state shear jamming (value from Ref. [23]). Inset in (d): As that in Fig. 1, i.e., for a second shear reversal, but for $Z$.

Figure 6

Jamming phase diagram in the $\alpha \text{−}\varphi$ plane. The diagram shows the fluid, directional shear-jamming (DSJ), and shear-jamming (SJ) regions.

Figure 7

(a) Strain $\gamma$, (b) average particle direction ${\theta }_{\mathbf{e}·\widehat{\mathbf{y}}}$ (in degrees) with respect to $\widehat{\mathbf{y}}$, (c) nematic order parameter $S_2$, (d) instantaneous pressure at the two walls, rescaled by its corresponding steady shear value, and (e) average number of contacts per particle as a function of time for four different aspect ratios as indicated by the legend in (a). Dotted lines in (b), (c), and (e) show the corresponding values at steady shear. Dashed-dotted lines in (e) show the corresponding value of $Z$ at steady-state shear jamming.

Figure 8

As Fig. 1 in the text, with lubrication forces included ($\mathrm{St}=2.5\times {10}^{-3}$).

Figure 9

Strain $\gamma$ as a function of the rescaled time $\langle \dot{\gamma }\rangle t$. (a) Ellipse walls with flowing disks and (b) disk walls with flowing ellipses.

Figure 10

As Fig. 1 in the text, but with (a) twice the wall separation or (b) twice the (periodic) box width.

Figure 11

As Fig. 1 in the text, but with a 10 times larger spring constant.