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

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