Unified study of glass and jamming rheology in soft particle systems

We explore numerically the shear rheology of soft repulsive particles at large volume fraction. The interplay between viscous dissipation and thermal motion results in multiple rheological regimes encompassing Newtonian, shear-thinning, and yield stress regimes near the “colloidal” glass transition when thermal fluctuations are important, crossing over to qualitatively similar regimes near the “jamming” transition when dissipation dominates. In the crossover regime, glass and jamming sectors coexist and give complex flow curves. Although glass and jamming limits are characterized by similar macroscopic flow curves, we show that they occur over distinct time and stress scales and correspond to distinct microscopic dynamics. We propose a simple rheological model describing the glass-to-jamming crossover in the flow curves, and discuss the experimental implications of our results.

Figure 1

Flow curves at different temperatures and densities, shown as $\sigma (\dot{\gamma })$ (left) or $\eta (\dot{\gamma })$ (right). Diamonds (left) mark the state points analyzed in Fig. 3. Circles (right) indicate thermal (closed) and athermal (open) viscosities reported in Fig. 2. Flow curves are shown in blue (dot-dashed) when thermal Newtonian behavior is observed, in red (dashed) when thermal effects are negligible, and in black otherwise.

Figure 2

(a) Shear viscosities ${\eta }_T$ and ${\eta }_0$ and their distinct hard sphere limits $G(\phi )$ [17] and $J(\phi )$ [21]. (b) Density dependence of yield stress for different temperatures, including the $T=0$ limit. (c) Same data as in (b) in a glass-jamming phase diagram.

Figure 3

Mean-square displacement at $\phi =0.62$ and $\dot{\gamma }={10}^{-3}\cdots {10}^{-7}$ and different temperatures. Caged dynamics (dashed curve) is only observed at finite $T$ and $P_e\ll 1$.