Hybrid continuum-atomistic simulation of singular corner flow

A hybrid numerical method is used to study cavity flow driven by a moving wall. Continuum equations with no-slip boundary conditions predict singular stresses at the corners between moving and static walls. Molecular dynamics simulations are used to resolve these singular regions, and the flow field in the remainder of the cavity is obtained from the Navier-Stokes (NS) equations. This hybrid solution agrees well with fully atomistic simulations on small systems, and allows calculations to be accelerated by orders of magnitude in larger systems. Fully continuum and hybrid solutions for the stress and velocity also agree over most of the cavity. Both yield a shear stress that scales as the inverse of the distance from the corner over almost two orders of magnitude. However, in the hybrid solution, this divergence is cut off within a distance S from the corners. In the limit of low wall velocities U, S is a few molecular diameters and corresponds to the length over which slip occurs. By comparing the hybrid solution to NS solutions, we show that the slip cannot be quantitatively described by the Navier slip condition. At higher U, non-Newtonian behavior near the corner causes S to rise linearly with U.