Rugotaxis: Droplet motion without external energy supply

¹ Institute of Physics, Polish Academy of Sciences - Al. Lotników 32/46, 02-668 Warsaw, Poland
² Department of Chemistry, University of Virginia - Charlottesville, VA 22901, USA
³ Institut für Physik, Johannes Gutenberg Universität Mainz - 55099 Mainz, Germany
⁴ Leibniz-Institut für Polymerforschung, Institut Theorie der Polymere - Hohe Str. 6, 01069 Dresden, Germany
⁵ Bulgarian Academy of Sciences, Institute of Physical Chemistry - 1113 Sofia, Bulgaria

^(a) panos@ifpan.edu.pl (corresponding author)

Received: 20 October 2021
Accepted: 16 February 2022

Abstract

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).