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Isomorph invariance of Couette shear flows simulated by the SLLOD equations of motion

Non-equilibrium molecular dynamics simulations were performed to study the thermodynamic, structural, and dynamical properties of the single-component Lennard-Jones and the Kob-Andersen binary Lennard-Jones liquids. Both systems are known to be strongly correlating, i.e., have strong correlations between equilibrium thermal fluctuations of virial and potential energy. Such systems have good isomorphs, i.e., curves in the thermodynamic phase diagram along which structural, dynamical, and some thermodynamic quantities are invariant when expressed in reduced units. The SLLOD equations of motion were used to simulate Couette shear flows of the two systems. We show analytically that these equations are isomorph invariant provided the reduced strain rate is fixed along the isomorph. Since isomorph invariance is generally only approximate, a range of shear rates were simulated to test for the predicted invariance, covering both the linear and non-linear regimes. For both systems, when represented in reduced units the radial distribution function and the intermediate scattering function collapse for state points that are isomorphic. The strain-rate dependence of the viscosity, which exhibits shear thinning, is also invariant along an isomorph. Our results extend the isomorph concept to the state-state non-equilibrium situation of a shear flow, in which the phase diagram is three dimensional because the shear rate defines the third dimension.