Nonequilibrium dynamics and fluctuation-dissipation relation in a sheared fluid

The nonequilibrium dynamics of a binary Lennard-Jones mixture in a simple shear flow is investigated by means of molecular dynamics simulations. The range of temperature T investigated covers both the liquid, supercooled, and glassy states, while the shear rate γ covers both the linear and nonlinear regimes of rheology. The results can be interpreted in the context of a nonequilibrium, schematic mode-coupling theory developed recently, which makes the theory applicable to a wide range of soft glassy materials. The behavior of the viscosity $\mathrm{\eta (T,\gamma )}$ is first investigated. In the nonlinear regime, strong shear-thinning is obtained, ${\mathrm{\eta \sim \gamma }}^{\mathrm{-\alpha (T)}},$ with $\mathrm{\alpha (T)\simeq }\frac{2}{3}$ in the supercooled regime. Scaling properties of the intermediate scattering functions are studied. Standard “mode-coupling properties” of factorization and time superposition hold in this nonequilibrium situation. The fluctuation-dissipation relation is violated in the shear flow in a way very similar to that predicted theoretically, allowing for the definition of an effective temperature $T_{\mathrm{eff}}$ for the slow modes of the fluid. Temperature and shear rate dependencies of $T_{\mathrm{eff}}$ are studied using density fluctuations as an observable. The observable dependence of $T_{\mathrm{eff}}$ is also investigated. Many different observables are found to lead to the same value of $T_{\mathrm{eff}},$ suggesting several experimental procedures to access $T_{\mathrm{eff}}.$ It is proposed that a tracer particle of large mass $m_{\mathrm{tr}}$ may play the role of an “effective thermometer.” When the Einstein frequency of the tracers becomes smaller than the inverse relaxation time of the fluid, a nonequilibrium equipartition theorem holds with ${\mathrm{〈m}}_{\mathrm{tr}}{v}_z^2{\mathrm{〉=k}}_B{T}_{\mathrm{eff}},$ where $v_z$ is the velocity in the direction transverse to the flow. This last result gives strong support to the thermodynamic interpretation of $T_{\mathrm{eff}}$ and makes it experimentally accessible in a very direct way.