The influence of boundary conditions and interfacial slip on the time taken to achieve a nonequilibrium steady-state for boundary-driven flows

In this study, we investigate the equilibration time to attain steady-state for a system of liquid molecules under boundary-driven planar Couette flow via nonequilibrium molecular dynamics (NEMD) simulation. In particular, we examine the equilibration time for the two common types of boundary-driven flow: one in which both walls slide with equal and opposite velocity (±û/2), and the other in which one wall is fixed and the other moves with twice the velocity (û). Both flows give identical steady-state strain rates and, hence, flow properties, but the transient behavior is completely different. We find that in the case of no-slip boundary conditions, the equilibration times for the counter-sliding walls flow are exactly four times faster than those of the single-sliding wall system, and this is independent of the atomistic nature of the fluid, i.e., it is an entirely hydrodynamic feature. We also find that systems that exhibit slip have longer equilibration times in general, and the ratio of equilibration times for the two types of boundary-driven flow is even more pronounced. We analyze the problem by decomposing a generic planar Couette flow into a linear sum of purely symmetric and antisymmetric flows. We find that the no-slip equilibration time is dominated by the slowest decaying eigenvalue of the solution to the Navier–Stokes equation. In the case of slip, the longest relaxation time is now dominated by the transient slip velocity response, which is longer than the no-slip response time. In the case of a high-slip system of water confined to graphene channels, the enhancement is over two orders of magnitude. We propose a simple universal relation that predicts the enhanced equilibration time, which agrees well with our NEMD results for simple Lennard-Jones fluids and the water–graphene system. The implications of this significant speed-up in attaining steady-state, which is especially pronounced in the presence of slip, are discussed in general.