An energy-stable phase-field model for droplet icing simulations

TL;DR

This paper introduces an energy-stable phase-field model for droplet icing that combines fluid dynamics and phase change equations, validated through numerical simulations and physical experiments, revealing key factors influencing droplet freezing.

Contribution

The paper develops a novel energy-stable phase-field model for droplet icing that accurately captures phase change dynamics and is validated against physical experiments.

Findings

Droplet tip formation is mainly due to vertical expansion during freezing.

Lower substrate temperatures accelerate droplet freezing.

The ice front shape transitions from horizontal to concave during solidification.

Abstract

A phase-field model for three-phase flows is established by combining the Navier-Stokes (NS) and the energy equations, with the Allen-Cahn (AC) and Cahn-Hilliard (CH) equations and is demonstrated analytically to satisfy the energy dissipation law. A finite difference scheme is then established to discretize the model and this numerical scheme is proved to be unconditionally stable. Based on this scheme, the droplet icing process with phase changing is numerically simulated and the pointy tip of the icy droplet is obtained and analyzed. The influence of the temperature of the supercooled substrate and the ambient air on the droplet freezing process is studied. The results indicate that the formation of the droplet pointy tip is primarily due to the expansion in the vertical direction during the freezing process. Lower substrate temperatures can accelerate this process. Changes in air temperature have a relatively minor impact on the freezing process, mainly affecting its early stages. Moreover, our results demonstrate that the ice front transitions from an approximately horizontal shape to a concave one. Dedicated physical experiments were conducted and the measured solidification process matches the results of the proposed phase-field method very well.