How Phase Coexistence affects the mechanical properties of heterogeneous 2D suspensions

Abstract

Although numerical simulations of rheological measurements typically focus on homogeneous systems, heterogeneity can profoundly impact material properties. We report on the rheological properties of a suspension of two-dimensional Lennard-Jones particles across the gas/liquid and the gas/solid coexistence lines of the system. We show how the presence of multiple coexisting states has a significant impact on the mechanical properties of these systems when compared with their homogeneous reference counterparts. Our results establish an extended map to navigate a landscape where not only density and temperature, but also phase coexistence, dictate the transition from viscous to elastic-dominated behavior under shear. These results provides a benchmark for future research into heterogeneous fluids where the coexistence of complex dynamic states is frequently observed.

Figures (4)

• Figure 1: Phase diagram of a two-dimensional Lennard-Jones potential cutoff at $2.5\sigma$. The ashed line corresponds to the liquid/gas coexistence binodal, the star indicates the location of the critical point $(\rho_\text{c}, \, T_\text{c})=(0.355, \, 0.515)$ and the circle shows the location of the triple point $(\rho_\text{TP}, \, T_\text{TP})=(0.75, \, 0.415)$barker1981phasestepanov2013modelling. G+L labels the gas/liquid coexistence region, while G+S labels the gas/solid coexistence region. Snapshots are shown for $\rho \in \left\{ 0.3, 0.5, 0.7 \right\}$ and $T \in \left\{ 0.25, 0.35, 0.45, 0.55 \right\}$.
• Figure 2: Two dimensional relaxation modulus $G(t)$ computed from Eq. \ref{['eq:gt2d']} at different temperatures $T$ for (a) $\rho=0.3$, (b) $\rho=0.5$ and (c) $\rho=0.7$. The relaxation modulus decays monotonially as a function of time $t$.
• Figure 3: Real $G'(\omega)$ (thick lines) and imaginary $G"(\omega)$ (thin lines) parts of the complex shear modulus at different temperatures, for: (a) $\rho =0.3$, (b) $\rho =0.5$ and (c) $\rho =0.7$. The red, dark orange, orange and yellow symbols in panels a (squares), b (circles) and c (stars) represent the crossover frequency where $G^{'}$=$G^{"}$
• Figure 4: (a-c) Effective viscosity $\eta$ from Eq. \ref{['eq:visc']} for a range of frequencies $\omega$ at different temperatures $T$ and density $\rho$. (d-f) The steady-state (st. st.) viscosity as measured by the average out-of-diagonal stress component $\left\langle \sigma_{xy} \right\rangle$ over strain rate $\dot{\gamma}$ in the steady-state after applying a constant strain on the system for different values of temperature and densities. Densities: $\rho=0.3$ (a,d), $\rho=0.5$ (b,e) and $0.7$ (c,f). Inset: Snapshot of a typical sheared system at $\rho=0.5$ and T=0.45.