A one dimensional modal approach for flows controlled by contact line motion

TL;DR

This paper develops a simplified one-dimensional model to analyze how nanoscale surface defects influence contact line motion, providing a tractable framework for studying complex interfacial flows and thermal effects.

Contribution

It derives the response function of the contact line to perturbations, enabling the creation of reduced models that incorporate nanoscale defect effects and thermal fluctuations.

Findings

Response function characterizes contact line behavior under perturbations

Model facilitates analysis of thermally activated contact line motion

Framework integrates nanoscale defect effects into interfacial flow models

Abstract

The hydrodynamics of a liquid-vapour interface in contact with an heterogeneous surface is largely impacted by the presence of defects at the smaller scales. Such defects introduce morphological disturbances on the contact line and ultimately determine the force exerted on the wedge of liquid in contact with the surface. From the mathematical point of view, defects introduce perturbation modes, whose space-time evolution is governed by the interfacial hydrodynamic equations of the contact line. In this paper we derive the response function of the contact line to such generic perturbations. The contact line response may be used to design simplified 1+1 dimensional models accounting for the complexity of interfacial flows coupled to nanoscale defects, yet offering a more tractable mathematical framework to include thermal fluctuations and explore thermally activated contact line motion through a disordered energy landscape.