Viscoelasticity in two dimensions

Abstract

We present the first nonequilibrium molecular-dynamics simulations of viscoelasticity in two-dimensional fluids. The shear viscosity is found to depend logarithmically upon the frequency; however, the divergence at low frequencies is shielded by a ‘‘turnover regime’’ where the shear viscosity becomes independent of frequency. The stress-stress autocorrelation function is shown to have a $t^{\mathrm{-}1}$ long-time tail, and the coefficient matches the coefficient of the logarithmic frequency dependence of the shear viscosity. The Goddard-Miller relation between the frequency and strain-rate dependence of the shear viscosity is shown to be incorrect. Superharmonic excitations are observed in both the shear stress and the pressure.