Nonlinear viscous flow in two-dimensional systems

Abstract

Nonequilibrium molecular dynamics calculations have been performed for soft disks. It was found that the strain-rate dependence $\ensuremath{\gamma}$ of shear viscosity $\ensuremath{\eta}$ and hydrostatic pressure $p$ could be described by the following functional forms: $\ensuremath{\eta}(\ensuremath{\gamma})={A}_{\ensuremath{\eta}}{log}_{10}|\ensuremath{\gamma}{T}_{\ensuremath{\eta}}|$ and $p(\ensuremath{\gamma})=p(0)+{A}_{p}|\ensuremath{\gamma}{T}_{p}|{log}_{10}|\ensuremath{\gamma}{T}_{p}|$. These functional forms are the same as ones that have been predicted using asymptotic "long-time-tail" theories. The numerical values of the coefficients as determined from the simulations are several orders of magnitude greater than theory predicts. If the equation above for the effective shear viscosity is valid in the limit of small strain rates, then Navier-Stokes hydrodynamics does not exist in two-dimensional fluids.