Viscosity calculations of simple liquids using the transient time correlation function formalism
István Borzsák
Calculation of the strain rate dependent shear viscosity is of considerable theoretical and industrial interest. Most fluids, subjected to planar Couette flow (the velocity gradient is perpendicular to the flow direction), exhibit Newtonian behaviour, which means the shear viscosity is independent of strain rate up to a certain crossover strain rate, typically given by the inverse of the longest relaxation time in the fluid, which for simple fluids is the translational relaxation time. Beyond the crossover strain rate, shear thinning occurs: the viscosity decreases with increasing strain rate. This crossover point is usually at a strain rate which is too high to be accessed by experimental measurement, but also – due to the poor signal-to-noise ratio at low strain rates – too low to calculate using steady state (SS) nonequilibrium molecular dynamics (NEMD) simulation.
The calculation of the strain rate dependent shear viscosity is reported here for several simple model fluids using the transient time correlation function (TTCF) formalism. The TTCF formalism is perhaps the simplest nonlinear generalization of the Green-Kubo relations. Its numerical accuracy is similar to the Green-Kubo calculations at equilibrium, but the TTCF method is capable of calculating the viscosity over several orders of magnitude in strain rates with the same level of accuracy. The particles of the model fluids interact via a Lennard-Jones type of potential. Both the TTCF method and the resulting viscosities for the fluids are discussed in detail.