Close-contact melting on hydrophobic textured surfaces: Confinement and meniscus effects

We investigate the dynamics of close-contact melting (CCM) on 'gas-trapped' hydrophobic surfaces, with specific focus on the effects of geometrical confinement and the liquid-air meniscus below the liquid film. By employing dual-series and perturbation methods under the assumption of small meniscus deflections, we obtain numerical solutions for the effective slip lengths associated with velocity and temperature fields, across various values of aspect ratio (defined as the ratio of the film thickness to the structure's periodic length) and gas-liquid fraction. Asymptotic solutions of and for and are derived and summarised for different surface structures, interface shapes and, which reveal a different trend of for and depending on the presence of a meniscus. In the context of constant-pressure CCM, our results indicate that longitudinal grooves can enhance heat transfer under the effects of confinement and a meniscus when and. For gravity-driven CCM, the parameters of and determine whether the melting rate is enhanced, reduced or nearly unaffected. We construct a phase diagram based on the parameter matrix to delineate these three regimes. Lastly, we derive two asymptotic solutions for predicting the variation in time of the unmelted solid height.