The wetting problem of fluids on solid surfaces. Part 2: the contact angle hysteresis

TL;DR

This paper models the dynamic contact angle and hysteresis phenomena of fluids on solid surfaces, explaining stick-slip motion and maximum wetting speed through a microscopic to macroscopic analysis.

Contribution

It introduces a new model linking microscopic interfacial energy oscillations to macroscopic contact line dynamics, capturing hysteresis and speed limits.

Findings

Derived a macroscopic equation for contact line motion.

Reproduced contact angle hysteresis and its dependence on line celerity.

Provided a qualitative explanation for maximum wetting speed.

Abstract

In part 1, we proposed a model of dynamics of wetting for slow movements near a contact line formed at the interface of two immiscible fluids and a solid when viscous dissipation remains bounded. The contact line is not a material line and a Young-Dupr\'e equation for the apparent dynamic contact angle taking into account the line celerity was proposed. In this paper we consider a form of the interfacial energy of a solid surface in which many small oscillations are superposed on a slowly varying function. For a capillary tube, a scaling analysis of the microscopic law associated with the Young-Dupr\'e dynamic equation yields a macroscopic equation for the motion of the contact line. The value of the deduced apparent dynamic contact angle yields for the average response of the line motion a phenomenon akin to the stick-slip motion of the contact line on the solid wall. The contact angle hysteresis phenomenon and the modelling of experimentally well-known results expressing the dependence of the apparent dynamic contact angle on the celerity of the line are obtained. Furthermore, a qualitative explanation of the maximum speed of wetting (and dewetting) can be given.