Self-propulsion of a Quincke droplet on a superhydrophobic wall under low electric Reynolds number <i>Re</i><sub>E</sub> <bold>≤</bold> 1

Abstract

A rotating object placed on a wall can generate an additional translating motion. Inspired by this phenomenon, we unfold a novel approach to the self-propulsion of a Quincke rotating drop in the current two-dimensional numerical simulation based on the resting wall effect. Accordingly, the impact of two controlling variables, the electric field strength E0* and viscosity ratio lambda, is examined in detail for a Quincke drop resting on a superhydrophobic wall. We consider a fixed conductivity ratio and permittivity ratio to (i) explore the dynamic activities of the droplet to verify the proposed self-propulsion scheme and (ii) reveal the physical propelling mechanism. Our results show that the Quincke drop displays three distinct states. (I) Taylor state (where the symmetry in dynamic behaviors is the primary indicator). (II) Transition stage from a Taylor regime to the Quincke regime, when the symmetry is broken and the created asymmetric flow causes the droplet to detach from the wall. At this stage, the tuned controlling parameters led to diverse droplet detachment processes, significantly influencing the subsequent self-propulsion. Additionally, based on the droplet behaviors in the transition stage for 6.78 < E-0* <= 57.63 at fixed lambda = 50, three distinct propulsion patterns are discovered: one-way propulsion for 6.78 < E-0* < 9.5, round trip propulsion for 9.5 <= E-0* < 33.9, and liquid film-breakup propulsion for 33.9 <= E-0* <= 57.63. (III) Self-propulsion stage. Here, the levitated droplet entrains the bulk fluid into the bottom, preventing its re-depositing on the wall by creating a liquid cushion between the Quincke rotating drop and the wall. This thin liquid cushion generates a higher viscous stress at the droplet's bottom, causing a significant velocity difference between its upper and lower halves. This velocity difference produces the crucial horizontal translation for the rotating droplet, i.e., the self-propulsion. Moreover, the liquid cushion's thickness (h*) affects the translation velocity. A higher E-0* or lambda leads to a smaller h* and expedites the droplet translation.