Molecular dynamics study of shear-induced long-range correlations in simple fluids

We investigate long-range correlations (LRCs) induced by shear flow using the molecular dynamics (MD) simulation. We observe the LRCs by comparing the MD results with the linearized fluctuating hydrodynamics (LFH). We find that the MD result has large finite-size effects, and it prevents the occurrence of LRCs in small systems. We examine the finite-size effects using a sufficiently large system consisting of more than ten million particles, and verify the existence of shear-induced LRCs without ambiguity. Furthermore, we show that MD result is quantitatively consistent with the LFH solution for the large system. As we reduce the system size $L$ or increase the shear rate $\dot{\gamma}$, the hydrodynamic description gradually breaks down in the long-wavelength region. We define a characteristic wavenumber $k^{\rm vio}$ associated with the breakdown and find the nontrivial scaling relations $k^{\rm vio} \propto L^{-\omega}$ and $k^{\rm vio} \propto \dot{\gamma}$, where $\omega$ is an exponent depending on $\dot{\gamma}$. These relations enable us to estimate the finite-size effects in a larger-size simulation from a smaller system.