Technique for calculating streamwise local fluxes in general flows

Abstract

This paper presents a new technique for calculating microscopic local fluxes that provides a robust and accessible way to obtain the streamwise fluxes in general flows. Flux calculation is one of the fundamental elements in molecular simulations. Several-decades-long research efforts on the subject made significant progresses since the pioneering work of Irving and Kirkwood [J. Chem. Phys, (1950) 18, 817–829]. However, some issues remain regarding the fluxes in the flow direction. The streaming velocity (SV) and the fluxes independent of SV are difficult to manage during computation. For example, the local fluxes and SV that vary in more than one direction are not well represented despite being prevalent in the microscopic phenomena such as nanofluidics, biotechnologies, and energy conversions. The technique presented in this paper is based on the instantaneous microscopic conservation equations and depends only on the total fluxes that include the convective contributions. This allows a calculation of all the fluxes at the end of a simulation run, with no complication arising in terms of defining and collecting SV, pressure tensor, and heat flux vector. Widely-used methods such as the method of planes and volume-average method were adapted, respectively. This study then investigated a planar shear flow in a highly confined channel, where a flow is unknown at the beginning of a simulation, and the controversial streamwise heat flux with no temperature gradient was present. The flow and fluxes were structured, and the streamwise heat flux evolved significantly and slowly over a few tens of nano-seconds even with steady boundary conditions.