Comment on: Nonequilibrium molecular dynamics calculation of self-diffusion in a non-Newtonian fluid subject to a Couette strain field

When a non-Newtonian fluid is subjected to a large strain field, nonlinear effects become important and Curie’s principle breaks down. It consequently becomes possible for the strain field to modify the diffusive mass current and the self-diffusion coefficient becomes a second rank tensor with field dependent components. This behavior can be of importance in some chemical engineering applications such as mixing and stirring. In order to study the self-diffusion tensor (SDT) in more detail, Cummings et al.’ performed an extensive nonequilibrium molecular dynamics (NEMD) study of a Lennard-Jones fluid undergoing Couette flow. Their work will hereinafter be referred to as I. The strain field was simulated by employing the Sllod equations of motion.2 Starting from a microscopic definition of the particle density which is equivalent to the selfpart of the van Hove space time correlation function they obtained a statistical mechanical expression for the mean square displacements (MSDs) of the molecules in the fluid. By inspection of the functional form of the MSDs they postulated Green-Kubo (GK) relations and a NEMD color conductivity algorithm for the various components of the SDT. The GK relations have later been proved rigorously by Evans3 but the color conductivity algorithm has been found to be wrong.4 The connection between the statistical mechanical expressions for the SDT and the experimentally measurable diffusion coefficients was established by comparing the microscopic MSDs and the MSDs obtained from the solution of the convective diffusion equation, where the SDT was assumed to be diagonal. The lack of a solution of the macroscopic convective diffusion equation for a diffusion tensor of arbitrary symmetry was a restriction of the analysis in I. The statistical mechanical MSDs include off diagonal elements and the GK simulations in Ref. 4 also imply that there should be small but nonzero off diagonal elements.