Stability and dynamics of droplets on patterned substrates: insights from experiments andlattice Boltzmann simulations

Abstract

The stability and dynamics of droplets on solid substrates are studied both theoreticallyand via experiments. Focusing on our recent achievements within the DFG-priorityprogram 1164 (Nano- and Microfluidics), we first consider the case of (large) droplets on theso-called gradient substrates. Here the term gradient refers to both a change ofwettability (chemical gradient) or topography (roughness gradient). While themotion of a droplet on a perfectly flat substrate upon the action of a chemicalgradient appears to be a natural consequence of the considered situation, weshow that the behavior of a droplet on a gradient of topography is less obvious.Nevertheless, if care is taken in the choice of the topographic patterns (in order toreduce hysteresis effects), a motion may be observed. Interestingly, in this case,simple scaling arguments adequately account for the dependence of the dropletvelocity on the roughness gradient (Moradi et al 2010 Europhys. Lett. 89 26006).Another issue addressed in this paper is the behavior of droplets on hydrophobicsubstrates with a periodic arrangement of square shaped pillars. Here, it is possible topropose an analytically solvable model for the case where the droplet size becomescomparable to the roughness scale (Gross et al 2009 Europhys. Lett. 88 26002). Twoimportant predictions of the model are highlighted here. (i) There exists a state with afinite penetration depth, distinct from the full wetting (Wenzel) and suspended(Cassie–Baxter, CB) states. (ii) Upon quasi-static evaporation, a droplet initially on the topof the pillars (CB state) undergoes a transition to this new state with a finitepenetration depth but then (upon further evaporation) climbs up the pillars and goesback to the CB state again. These predictions are confirmed via independentnumerical simulations. Moreover, we also address the fundamental issue of the internaldroplet dynamics and the terminal center of mass velocity on a flat substrate.