Equation of motion of the triple contact line along an inhomogeneous surface

TL;DR

This paper derives an equation describing the slow evolution of the triple contact line on inhomogeneous surfaces, accounting for surface defects, and provides an exact solution for a single defect case.

Contribution

It introduces a new equation for contact line dynamics on inhomogeneous surfaces and solves it exactly for a simple defect scenario.

Findings

Equation accurately models contact line evolution with defects

Exact solution for a single defect case

Provides insights into wetting flow control

Abstract

Wetting flows are controlled by the contact line motion. We derive an equation that describes the slow time evolution of the triple solid-liquid-fluid contact line for an arbitrary distribution of defects on a solid surface. The capillary rise along a partially wetted infinite vertical wall is considered. The contact line is assumed to be only slightly deformed by the defects. The derived equation is solved exactly for a simple example of a single defect. Introduction.