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In recent decades novel solid substrates have been designed which changetheir wettability in response to light or an electrostatic field. Here, weinvestigate a droplet on substrates with oscillating uniform wettability byvarying minimium and maximum contact angles and frequency. To simulate thissituation, we use our previous work [Grawitter and Stark, Soft Matter 17, 2454(2021)], where we implemented the boundary element method in combination withthe Cox-Voinov law for the contact-line velocity, to determine the fluid flowinside a droplet. After a transient regime the droplet performs steadyoscillations, the amplitude of which decreases with increasing frequency. Forslow oscillations our numerical results agree well with the linearizedspherical-cap model. They collapse on a master curve when we rescale frequencyby a characteristic relaxation time. In contrast, for fast oscillations weobserve significant deviations from the master curve. The decay of thesusceptibility is weaker and the phase shift between oscillations inwettability and contact angle stays below the predicted $\pi/2$. The reasonbecomes obvious when studying the combined dynamics of droplet height andcontact angle. It reveals non-reciprocal shape changes during one oscillationperiod even at low frequencies due to the induced fluid flow inside thedroplet, which are not captured by the spherical-cap model. Similar periodicnon-reciprocal shape changes occur at low frequencies when the droplet isplaced on an oscillating nonuniform wettability profile with six-fold symmetry.Such profiles are inspired by the light intensity pattern of Laguerre-Gausslaser modes. Since the non-reciprocal shape changes induce fluid circulation,which is controllable from the outside, our findings envisage to designtargeted microfluidic transport of solutes inside the droplet.

Droplets on substrates with oscillating wettability