Dynamical Heterogeneity in a Highly Supercooled Liquid under a Sheared Situation

In the present study, we performed molecular-dynamics simulations and investigated dynamical heterogeneity in a supercooled liquid under a steady shear flow. Dynamical heterogeneity can be characterized by three quantities: the correlation length $\xi_4(t)$, the intensity $\chi_4(t)$, and the lifetime $\tau_\text{hetero}(t)$. We quantified all three quantities by means of the correlation functions of the particle dynamics, i.e., the four-point correlation functions, which are extended to the sheared condition. Here, to define the local dynamics, we used two time intervals $t=\tau_\alpha$ and $\tau_{\text{ngp}}$; $\tau_\alpha$ is the $\alpha$-relaxation time, and $\tau_{\text{ngp}}$ is the time at which the non-Gaussian parameter of the Van Hove self-correlation function is maximized. We discovered that all three quantities ($\xi_4(t)$, $\chi_4(t)$, and $\tau_\text{hetero}(t)$) decrease as the shear rate $\dot{\gamma}$ of the steady shear flow increases. For the time interval $t=\tau_\alpha$, the scalings $\xi_4(\tau_\alpha) \sim \dot{\gamma}^{-0.08}$, $\chi_4(\tau_\alpha) \sim \dot{\gamma}^{-0.26}$, and $\tau_\text{hetero}(\tau_\alpha) \sim \dot{\gamma}^{-0.88}$ were obtained. The steady shear flow suppresses the heterogeneous structure as well as the lifetime of the dynamical heterogeneity. In addition, our results demonstrated that the $\alpha$-relaxation time $\tau_\alpha$ dependences of three quantities coincide with those at equilibrium. This means that all three quantities of the dynamical heterogeneity can be mapped onto those in the equilibrium state through $\tau_\alpha$.