Impact of Attractive Interactions on the Rheology of Dense Athermal Particles

Using numerical simulations, the rheological response of an athermal assembly of soft particles with tunable attractive interactions is studied in the vicinity of jamming. At small attractions, a fragile solid develops and a finite yield stress is measured. Moreover, the measured flow curves have unstable regimes, which lead to persistent shear banding. These features are rationalized by establishing a link between the rheology and the interparticle connectivity, which also provides a minimal model to describe the flow curves.

Figure 1

Shear stress $\sigma$ as a function of strain rate $\dot{\gamma }$ for $N={10}^3$: (a) for different attraction strengths $u$ (as specified in the legends) at $\varphi =0.82$; (b) for different packing fractions (from the bottom to top) $\varphi =0.75$, 0.78, 0.80, 0.82, 0.83, 0.84, 0.843, 0.85, 0.9, 0.95, 1.0 for the attraction strength $u=2\times {10}^{-4}$. The solid lines are fits using the fluidity model [Eq. (3)], the dashed lines are Herschel-Bulkley fits, and the dotted lines are guides to the eye.

Figure 2

Variation of yield stress ${\sigma }_y$ with packing fraction $\varphi$ for different attraction strengths (from bottom to top) $u=2\times {10}^{-5}$, $4.5\times {10}^{-5}$, $2\times {10}^{-4}$, $4.5\times {10}^{-4}$, $5\times {10}^{-3}$, $5\times {10}^{-2}$. Solid line: yield stress of the repulsive system ($u\to 0$) is expected to vanish at $\varphi ={\varphi }_J$ as ${\sigma }_y^{(\text{rep})}\propto {(\varphi -{\varphi }_J)}^{\alpha }$; $\alpha =1.04$. (Inset): schematic of the particle interaction force $F(r)$.

Figure 3

Variation of coordination number $z$ as a function of strain rate $\dot{\gamma }$ (a) for different attraction strengths ($u$) at $\varphi =0.82$ and (b) for different $\varphi$ at a fixed $u=2\times {10}^{-4}$. The values of $u$ in (a) and $\varphi$ in (b) are the same as those in Fig. 1. Dashed lines are guides to the eye. (c) Variation of $z_0\equiv z(\dot{\gamma }\to 0)$ with $\varphi$. The solid line denotes ${(\varphi -{\varphi }_J)}^{1/2}$.

Figure 4

Scaling plots: (a) Yield stress ${\sigma }_y$ normalized by $|\delta \varphi {|}^{\alpha }$ as a function of the combination $u^{1/2}\delta z^{3/2}|\delta \varphi {|}^{-\alpha }$. Dashed lines correspond to the two regimes of Eq. (2). (b) Variation of $z_0-z$ with $\dot{\gamma }{\tau }_a$ (where ${\tau }_a=0.5/u$), using data shown in Fig. 3 (closed symbols) and Fig. 3 (open symbols).

Figure 5

At $\varphi =0.82$, $u=2\times {10}^{-5}$ and $\dot{\gamma }=5\times {10}^{-6}$: Spatial profile of (top) local shear rate $\dot{\gamma }(y)$ and (bottom) the corresponding local contact numbers $z(y)$ for $N=2\times {10}^4$.