Theory and experiments on the ice-water front propagation in droplets freezing on a subzero surface

TL;DR

This paper presents an approximate theory and experimental validation of ice-water front propagation in freezing water droplets on various subzero surfaces, highlighting the influence of substrate heat conductivity and challenging previous assumptions.

Contribution

The study introduces a new approximate theoretical model for droplet freezing and provides experimental data comparing different substrates, revealing limitations of prior constant-temperature assumptions.

Findings

The heat conductivity of the substrate affects freezing dynamics.

Experimental results show the base temperature varies during freezing.

Previous models assuming constant base temperature are not accurate.

Abstract

An approximate theory is presented describing the propagation of the ice-water front that develops in droplets of water that are deposited on a planar surface at a temperature below the melting point of ice. A calculation based on this theory is compared with our experimental observations of the time evolution of this front. The results of calculations of this front by Schultz et al7, obtained by integrating numerically the exact differential equations for this problem, were published graphically, but only for the time-dependent velocity of this front. Unfortunately, these theoretical results cannot be compared directly with our experimental observations. Our experiments were performed by freezing water droplets directly on a block of dry ice, and in order to examine the effects of the heat conductivity of a substrate during the freezing process, such droplets were also deposited on a glass plate and on a copper plate placed on dry ice. The temperature at the base of these droplets, and the dependence of the freezing time on their size was also investigated ex perimentally, and compared with our analytic approximation of the theory. Such experiment have not been published previously, and reveal that the usual assumption that the temperature at the base of the droplets is a constant, made in all previous theoretical papers on this subject, cannot be implemented in practice.