  In recent decades novel solid substrates have been designed which change
their wettability in response to light or an electrostatic field. 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 17, 2454
(2021)], where we implemented the boundary element method in combination with
the Cox-Voinov law for the contact-line 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. For
slow oscillations our numerical results agree well with the linearized
spherical-cap model. They collapse on a master curve when we rescale frequency
by a characteristic relaxation time. In contrast, for fast oscillations we
observe significant deviations from the master curve. The decay of the
susceptibility is weaker and the phase shift between oscillations in
wettability and contact angle stays below the predicted $\pi/2$. The reason
becomes obvious when studying the combined dynamics of droplet height and
contact angle. It reveals non-reciprocal shape changes during one oscillation
period even at low frequencies due to the induced fluid flow inside the
droplet, which are not captured by the spherical-cap model. Similar periodic
non-reciprocal shape changes occur at low frequencies when the droplet is
placed on an oscillating nonuniform wettability profile with six-fold symmetry.
Such profiles are inspired by the light intensity pattern of Laguerre-Gauss
laser modes. Since the non-reciprocal shape changes induce fluid circulation,
which is controllable from the outside, our findings envisage to design
targeted microfluidic transport of solutes inside the droplet.
