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 non-equilibrium molecular simulations of flow in a nanochannel. Results are compared with viscosity profiles obtained by integrating the conservation of momentum across the channel width and close agreement is found. Viscosity can vary widely, particularly near the channel boundaries, indicating that a uniform viscosity is no longer appropriate. The variation of the viscosity and velocity near the channel surfaces with different mineral surfaces and solution compositions implies that solution and surface chemistry may need to be considered to rigorously understand molecular-scale flows in nanochannels.