On the relation between dynamical density functional theory and Navier-Stokes equation

Abstract

Navier-Stokes equations are widely applied to deal with non-equilibrium fluid dynamics such as the flow field on nanoscale. On the other category, dynamical density functional theory (DDFT) has recently been recognized as a robust tool to investigate the non-equilibrium processes such as molecular diffusion and adsorption dynamics. Both approaches have achieved great success and it’s natural to wonder if there is any intrinsic relation inbetween. Herein, we prove that DDFT can be derived from the general Navier-Stokes equations with approximate evaluation of pressure tensor. Motivated by this procedure, we introduce the flow effect on pressure tensor, and then propose extensions of DDFT for addressing the coupling between dynamic adsorption and fluid flow. This work, revealing the relation between DDFT and Navier-Stokes equations, not only casts novel insights into the extension of DDFT, but also highlights a potential route to overcome the Navier-Stokes analytic solution problem.