  Nano-patterned substrates offer possibilities for controlling the motion of
fluids without external energy supply in novel technologies in microfluidics,
coatings, etc. Here, we report on the rugotaxial motion of droplets on wrinkled
substrates with gradient in the wavelength of the wrinkles by exploring a broad
range of parameters, such as amplitude of the wrinkles, substrate wettability,
droplet size and wavelength gradient. Adopting a theoretical and molecular
dynamics approach, we determine the Cassie-Baxter and Wenzel states of the
droplets, investigate the efficiency of rugotaxis as a function of different
parameters, and discuss additional effects, such as pinning. We find that
shallow wrinkles characterised by small wavelength gradients, and moderate
adhesion of the droplet to the substrate favour the rugotaxis motion with
growing droplet size, when pinning is avoided. We also find that the driving
force in rugotaxis is the gain in interfacial energy between the droplet and
the substrate as the droplet enters regions of denser wrinkles (smaller
wavelengths of the wrinkles).
