Fluid Simulations with Atomistic Resolution: Multiscale Model with Account of Nonlocal Momentum Transfer

Abstract

Nano- and microscale flow phenomena turn out to be highly non-trivial for simulation and require the use of heterogeneous modeling approaches. While the continuum Navier-Stokes equations and related boundary conditions quickly break down at those scales, various direct simulation methods and hybrid models have been applied, such as Molecular Dynamics and Dissipative Particle Dynamics. Nonetheless, a continuum model for nanoscale flow is still an unsolved problem. We present a model taking into account nonlocal momentum transfer. Instead of a bulk viscosity an improved system of parameters of liquid properties, represented by a spatial scalar function for momentum transfer rate between neighboring volumes, is used. Our model does not require boundary conditions on the channel walls. Common nanoflow models relying on a bulk viscosity in combination with a slip boundary condition can be obtained from the model. The required model parameters can be calculated from momentum density fluctuations obtained by Molecular Dynamics simulations. Thus, our model is multiscale, however, the continuum model is applied in the whole region of the simulation. We demonstrate good agreed with nanoflow in a tube as obtained by complete Molecular Dynamics.