Slip, immiscibility and boundary conditions at the liquid-liquid interface

TL;DR

This study uses molecular dynamics simulations to investigate the validity of conventional boundary conditions at liquid-liquid interfaces, revealing slip behavior when density drops near the interface.

Contribution

It demonstrates that the traditional assumption of continuous tangential velocity may not hold when density decreases significantly at the interface, leading to slip described by a Navier boundary condition.

Findings

Tangential velocity can appear discontinuous at the interface.

Slip behavior correlates with local density drops.

Navier boundary condition describes the apparent slip.

Abstract

The conventional boundary conditions at the interface between two flowing liquids include continuity of the tangential velocity. We have tested this assumption with molecular dynamics simulations of Couette and Poiseuille flows of two-layered liquid systems, with various molecular structures and interactions. When the total liquid density near the interface drops significantly compared to the bulk values, the tangential velocity varies very rapidly there, and would appear discontinuous at continuum resolution. The value of this apparent slip is given by a Navier boundary condition.