Bella, Davide; (2021) Stochastic Solidification Growth in Supercooled Water Droplets. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

Ranging over different phenomena, the matter of nucleation is for sure one of the oldest and richest in terms of human empirical experience and yet it is still a subject with many gray areas. Analytical methods are able to avoid the computational workload needed by molecular dynamic simulations (notwithstanding the great success of the simulations) and can help in choosing the correct simulation’s environment and parameters. This work aims at finding a unifying analytical description of the two aspects of the phenomenon: the initial stochastic behaviour and its deterministic solidification regime. Here we provide the solution of a stochastic Stefan problem and describe the evolution of the interface of the growing nucleus together with the stability conditions with kinetic undercooling. We then express the solution in a probabilistic form providing an expression for the transition probabilities of the nucleus of reaching a final state given a known starting one. By sampling these probability distributions one can obtain insight into the morphology of the growing ice nucleus. Understanding the morphology of the nucleus is also found to provide useful insight in the context of heterogeneous nucleation, which in turn has considerable scientific value in understanding the formation of ice and it can have interesting implications in the development of icephobic coatings for engineering applications, such as on airborne and other vehicles.

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