A spline-based method to obtain spatially dependent viscosity in confined flows

Coupling chemical physics to continuum theories is a critical step to understanding multi-scale phenomena. This paper will connect non-equilibrium molecular dynamics simulations to a continuum-based Navier-Stokes equation that has relaxed the assumption of spatial uniformity in viscosity. Using a form for the viscosity based on spline interpolation, the viscosity as a function of position is obtained from a least squares fit of the velocity profile measured from molecular simulations of flow in a nanochannel. Viscosity can vary widely, particularly near the channel boundaries, indicating that a uniform viscosity is no longer appropriate. Variations of the viscosity near the channel surfaces implies that considering solution and surface chemistry could be necessary to rigorously understand molecular-scale flows in nanochannels.