Quasi-static relaxation of arbitrarily shaped sessile drops

TL;DR

This paper investigates the quasi-static relaxation dynamics of arbitrarily shaped liquid drops on solid surfaces, emphasizing the role of contact line dissipation and non-local effects, supported by numerical simulations and theoretical analysis.

Contribution

It introduces a rigorous quasi-static relaxation model incorporating contact line dissipation proportional to line length, and develops a 3D numerical code to analyze shape-dependent relaxation behaviors.

Findings

Contact line dissipation leads to a local relation between velocity and contact angle.

Numerical simulations validate asymptotic solutions for relaxation dynamics.

Relaxation at a point is influenced by the entire drop's dynamics, showing non-local effects.

Abstract

We study a spontaneous relaxation dynamics of arbitrarily shaped liquid drops on solid surfaces in the partial wetting regime. It is assumed that the energy dissipated near the contact line is much larger than that in the bulk of the fluid. We have shown rigorously in the case of quasi-static relaxation using the standard mechanical description of dissipative system dynamics that the introduction of a dissipation term proportional to the contact line length leads to the well known local relation between the contact line velocity and the dynamic contact angle at every point of an arbitrary contact line shape. A numerical code is developed for 3D drops to study the dependence of the relaxation dynamics on the initial drop shape. The available asymptotic solutions are tested against the obtained numerical data. We show how the relaxation at a given point of the contact line is influenced by the dynamics of the whole drop which is a manifestation of the non-local