Interface and contact line motion in a two phase fluid under shear flow

TL;DR

This paper investigates the steady-state behavior of a two-phase fluid under shear flow, focusing on interface configuration and contact line motion, revealing interfacial slip due to dissipative relaxation at the contact line.

Contribution

It introduces a coarse-grained model capturing interfacial slip caused by order parameter relaxation, deriving scaling laws and validating them through numerical solutions.

Findings

Interfacial slip occurs even with no-slip boundary conditions.

Scaling laws involving the ratio l/L and capillary number are established.

Numerical results confirm the theoretical scaling predictions.

Abstract

A coarse grained description of a two phase fluid is used to study the steady state configuration of the interface separating the coexisting phases, and the motion of the contact line at which the interface intersects a solid boundary. The fluid is set in motion by displacing two parallel, infinite solid boundaries along their own plane. Dissipative relaxation of the order parameter leads to interfacial slip at the contact line, even when no-slip boundary conditions for the fluid velocity are considered. This relaxation occurs within a characteristic length scale l that depends on the order parameter mobility, the equilibrium interfacial tension, the imposed wall velocity, the thermal correlation length, the equilibrium miscibility gap, and the mutual diffusion coefficient. Steady-state interface equations which describe the system on a length scale large compared to the correlation length are derived. Scaling forms which involve the ratio l/L, where L is the width of the fluid layer, and the capillary number follow from the interface equations. The scaling results are verified by direct numerical solution of the governing equations.