Cox–Voinov theory with slip

Tak Shing Chan,Jens Eggers,James E Sprittles,Catherine Kamal,Jacco H Snoeijer

doi:10.1017/jfm.2020.499

Abstract

Highlights

The theory of the moving contact line at small capillary numbers was founded by Voinov (1976) and generalized to arbitrary viscosity ratios M by Cox (1986)
The simplest, and often physically realistic, such choice is the introduction of a Navier slip length λ (Lauga, Brenner & Stone 2008), over which a fluid may slip past a solid interface
One of the main aims is to calculate the apparent contact angle as well as the critical capillary number at which fluid 1 is entrained into fluid 2

Summary

Introduction

The theory of the moving contact line at small capillary numbers was founded by Voinov (1976) and generalized to arbitrary viscosity ratios M by Cox (1986). In contrast to the approach of asymptotic matching between micro and macroscales adopted by Cox (1986) or Hocking & Rivers (1982), the GL equation (1.4), for small Ca, gives a full representation of the interfacial profile, given that boundary conditions at the contact line and the far field are properly imposed, for arbitrary contact angles and viscosity ratios. We calculate c for arbitrary angles θeq and arbitrary viscosity ratios M, based on earlier work by Hocking (1977), who calculates the stress on a slip wall, assuming a straight interface h = s sin θeq.

A single phase

Two phases

Discussion