Steering droplets on substrates using moving steps in wettability

TL;DR

This paper presents a computational study of droplet motion on substrates with moving wettability patterns, demonstrating control of droplet velocity and behavior through step profiles and feedback mechanisms.

Contribution

It introduces a boundary-element method combined with Cox-Voinov law to simulate droplet dynamics on switchable wettability surfaces, revealing new insights into droplet control.

Findings

Droplets move towards higher wettability regions.

Feedback control achieves constant droplet velocity.

Maximum droplet speeds depend on wettability step parameters.

Abstract

Droplets move on substrates with a spatio-temporal wettability pattern as generated, for example, on light-switchable surfaces. To study such cases, we implement the boundary-element method to solve the governing Stokes equations for the fluid flow field inside and on the surface of a droplet and supplement it by the Cox-Voinov law for the dynamics of the contact line. Our approach reproduces the relaxation of an axisymmetric droplet in experiments, which we initiate by instantaneously switching the uniform wettability of a substrate quantified by the equilibrium contact angle. In a step profile of wettability the droplet moves towards higher wettability. Using a feedback loop to keep the distance or offset between step and droplet center constant, induces a constant velocity with which the droplet surfes on the wettability step. We analyze the velocity in terms of droplet offset and step width for typical wetting parameters. Moving instead the wettability step with constant speed, we determine the maximally possible droplet velocities under various conditions. The observed droplet speeds agree with the values from the feedback study for the same positive droplet offset.