Surfactant-dependent contact line dynamics and droplet spreading on textured substrates: derivations and computations

TL;DR

This paper derives and computes the complex dynamics of surfactant-covered droplet spreading on textured substrates, highlighting the dominant role of surfactant-dependent surface tension and providing a numerical scheme for challenging simulations.

Contribution

It presents a comprehensive derivation of droplet dynamics with insoluble surfactant on textured surfaces using Onsager's principle and develops a stable numerical scheme for simulation.

Findings

Surfactant significantly influences droplet deformation.

The derived dynamics include contact line motion and surfactant evolution.

Numerical simulations demonstrate the impact of surfactant on droplet behavior.

Abstract

We study spreading of a droplet, with insoluble surfactant covering its capillary surface, on a textured substrate. In this process, the surfactant-dependent surface tension dominates the behaviors of the whole dynamics, particularly the moving contact lines. This allows us to derive the full dynamics of the droplets laid by the insoluble surfactant: (i) the moving contact lines, (ii) the evolution of the capillary surface, (iii) the surfactant dynamics on this moving surface with a boundary condition at the contact lines and (iv) the incompressible viscous fluids inside the droplet. Our derivations base on Onsager's principle with Rayleigh dissipation functionals for either the viscous flow inside droplets or the motion by mean curvature of the capillary surface. We also prove the Rayleigh dissipation functional for viscous flow case is stronger than the one for the motion by mean curvature. After incorporating the textured substrate profile, we design a numerical scheme based on unconditionally stable explicit boundary updates and moving grids, which enable efficient computations for many challenging examples showing significant impacts of the surfactant to the deformation of droplets.