Steering droplets on substrates using moving steps in wettability

Abstract

We use the boundary element method (BEM) and the Cox–Voinov law to study the motion of droplets on a substrate with a moving wettability profile. Under the right conditions, droplets surf.

Droplets on substrates with oscillating wettability

“…The full details of our boundary element method are provided in Ref. 24 . Briefly, to discretize Eq.…”

“…Furthermore, a droplet may trigger a chemical reaction with the substrate and thereby create a wettability gradient, which moves it forward 23 . Taking into account the switchable substrates introduced above, we have shown recently how a chemically inert droplet responds to moving steps in wettability 24 . Thus, the droplet's motion is under external control.…”

“…Since at small length scales viscous forces dominate inertia within the droplet, the internal fluid flow is described by the Stokes equations 26 . We solve these using the boundary element method, the implementation of which we have described in a previous work 24 . At the edge of the dropletsubstrate interface (the contact line), we use the Cox-Voinov law to calculate the velocity of the contact line 27 .…”

“…At the edge of the dropletsubstrate interface (the contact line), we use the Cox-Voinov law to calculate the velocity of the contact line 27 . We have previously validated and applied our method to droplets that are steered by moving steps in wettability 24 .…”

“…Here, we investigate a droplet on substrates with oscillating uniform wettability by varying minimium and maximum contact angles and frequency. To simulate this situation, we use our previous work [Grawitter and Stark, Soft Matter, 2021, 17, 2454], where we implemented the boundary element method in combination with the Cox-Voinov law for the contactline velocity, to determine the fluid flow inside a droplet. After a transient regime the droplet performs steady oscillations, the amplitude of which decreases with increasing frequency.…”