Wetting failure and contact line dynamics in a Couette flow

TL;DR

This paper investigates liquid-liquid wetting failure in a two-dimensional Couette flow, analyzing critical velocities and comparing sharp and diffuse interface models to understand contact line dynamics.

Contribution

It provides an exact solution for wetting failure in Couette flow using lubrication theory and introduces a numerical method based on diffuse interface models for comparison.

Findings

Identification of critical velocities for wetting failure

Quantitative comparison between sharp and diffuse interface models

Analysis of parameter effects on contact line dynamics

Abstract

Liquid-liquid wetting failure is investigated in a two-dimensional Couette system with two immiscible fluids of arbitrary viscosity. The problem is solved exactly using a sharp interface treatment of hydrodynamics (lubrication theory) as a function of the capillary number, viscous ratio and separation of scale, i.e. slip length versus macroscopic scale of the system. The existence of critical velocities, above which no stationary solutions are found, is analyzed in detail in terms of the relevant parameters of the system. Comparisons with existing analysis for other geometries are also carried out. A numerical method of analysis is also presented, based on diffuse interface models obtained from multiphase extensions of the lattice Boltzmann equation (LBE). Sharp interface and diffuse interface models are quantitatively compared face to face indicating the correct limit of applicability of the diffuse interface models.