Mathematical Modelling of Tyndall Star Initiation

TL;DR

This paper presents experimental observations and a mathematical model for the early development of Tyndall stars in ice, focusing on anisotropic effects and free boundary problems during superheating-induced melting.

Contribution

It introduces a novel mathematical model capturing anisotropic kinetic undercooling and free boundary dynamics in Tyndall star formation.

Findings

Experimental visualization of Tyndall stars in ice.

Development of a free boundary model with anisotropic effects.

Insights into the early stages of superheating-induced melting.

Abstract

The superheating that usually occurs when a solid is melted by volumetric heating can produce irregular solid-liquid interfaces. Such interfaces can be visualised in ice, where they are sometimes known as Tyndall stars. This paper describes some of the experimental observations of Tyndall stars and a mathematical model for the early stages of their evolution. The modelling is complicated by the strong crystalline anisotropy, which results in an anisotropic kinetic undercooling at the interface; it leads to an interesting class of free boundary problems that treat the melt region as infinitesimally thin.