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 $\lambda$ and temperature $\lambda _t$ fields, across various values of aspect ratio $\Lambda$ (defined as the ratio of the film thickness $h$ to the structure’s periodic length $l$ ) and gas–liquid fraction $\phi$ . Asymptotic solutions of $\lambda$ and $\lambda _t$ for $\Lambda \ll 1$ and $\Lambda \gg 1$ are derived and summarised for different surface structures, interface shapes and $\Lambda$ , which reveal a different trend of $\lambda$ for $\Lambda \ll 1$ 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 $\Lambda \lesssim 0.1$ and $\phi \lt 1 - 0.5^{2/3} \approx 0.37$ . For gravity-driven CCM, the parameters of $l$ and $\phi$ determine whether the melting rate is enhanced, reduced or nearly unaffected. We construct a phase diagram based on the parameter matrix $(\log _{10} l, \phi )$ to delineate these three regimes. Lastly, we derive two asymptotic solutions for predicting the variation in time of the unmelted solid height.