Pressures and stresses in freezing water drops

Abstract

Calculations of the pressure in the liquid core of a freezing water droplet and stresses in the surrounding ice shell are made. The theory is developed in terms of two mechanical models for the ice. The first model assumes it is elastic and the second that it is linearly viscoelastic. The calculated pressure development is compared with that measured in drops one centimetre in diameter. It is concluded that the viscoelastic theory is sufficient for describing the pressure growth, but overestimates the magnitudes of the stresses in the shell. It is suggested that a treatment using a non-linear dependence of strain rate on stress would yield a more realistic stress distribution.