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

TL;DR

This paper studies the effects of geometrical confinement and meniscus shape on close-contact melting on hydrophobic textured surfaces, revealing how surface structure and parameters influence heat transfer and melting rates.

Contribution

It provides new analytical and numerical solutions for slip lengths and melting dynamics considering confinement and meniscus effects on textured surfaces.

Findings

Longitudinal grooves can enhance heat transfer under certain confinement conditions.

Transverse grooves generally reduce heat transfer in constant-pressure melting.

A phase diagram delineates regimes of melting rate enhancement, reduction, or neutrality based on surface parameters.

Abstract

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, 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 summarized for different surface structures, interface shapes and $\Lambda$, which reveal a different trend for $\lambda$ and $\Lambda \ll 1$ and the presence of a meniscus. In the context of constant-pressure CCM, our results indicate that transverse-grooves surfaces consistently reduced the heat transfer. However, longitudinal grooves can enhance heat transfer under the effects of confinement and meniscus when $\Lambda \lessapprox 0.1$ and $\phi < 1 - 0.5^{2/3} \approx 0.37$. 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 derived two asymptotic solutions for predicting the variation in time of the unmelted solid height.