Ratcheted rings for leidenfrost self-propulsion and droplet mixing

Abstract

Liquid droplets deposited on a saw-tooth ratcheted surface will move spontaneously in a unique direction attaining a reasonable terminal velocity (typically, 10 cm/s) provided that the droplets are in the Leidenfrost state. Here, the droplet levitates above the surface on top of a vapour cushion produced by the evaporating liquid. This work aims to explore the potentials of the phenomenon in the field of droplet mixing. New ratcheted surfaces in the shape of a ring were manufactured to constrain empirical studies in a shorter footprint (enabling more conditions to be studied). Experiments were also used to gain new insights into the mechanism, with the purpose of superseding the limited scaling analysis previously given in the literature. (1) A high-speed camera was used to capture the droplet motion (e.g. droplet velocity) and droplet mixing process (e.g. colour distribution). A custom programme in MATLAB refined these images to isolate a region of interest (ROI) corresponding to the droplet field. The efficiency of the programme was tested by comparing the results against time-consuming manual measurements performed in ImageJ (Fiji); differences of just 0.75–3.82% were observed. (2) A new analytical model was developed on the basis of a Leidenfrost droplet, where the deformable nature of the liquid is taken into account for the first time. Droplet deformation was theoretically analysed through a pressure balance, by considering the dynamic pressure (produced by the fast droplet motion), the static hydrodynamic pressure (produced by gravity), and the Laplace pressure (produced by the surface tension). The model indicates that the acceleration and driving force are sensitive to the deformation of the liquid and the geometry of the ratcheted surface (height and length of the ratchets), but shows little dependence on the droplet size and surface temperature. (3) Four aluminium ratcheted ring designs were employed to study the self-propelled droplets, in a difference of ratchet parameters, ratchet shape and diameter scale. Meanwhile, the droplet deformation around the ratchets was observed via a microscopic lens. These measurements were used to validate the model with respect to different ratchet parameters, surface temperatures (between 300°C and 400°C) and droplet sizes (from 30 µL to 1500µL). ii The model fitted the experimental measurements better than previous reports, having a maximum of 23% deviation. Additionally, it was found that the annular ring design enabled higher terminal velocities than other linear ratchet designs in the literature, up to 0.39 m/s, which is potentially beneficial to energy harvesting and flow chemistry applications. (4) The four ratcheted rings and a flat substrate were then used to study mixing inside the droplets under the Leidenfrost state. Measurements were collected for a range of different droplet volumes (from 400µL to 1200µL) and surface temperatures (from 300°C to 400 °C). The result shows that it takes a maximum of 5 s for mixing to reach completion under the selfpropulsion Leidenfrost state compared to several minutes for the room temperature diffusion benchmark. Therefore, the mixing efficiency has been significantly improved using these Leidenfrost propulsion devices