Modelling the dynamics of the flow within freezing water droplets

The flow within freezing water droplets is here numerically modelled assuming fixed shape throughout freezing. Three droplets are studied with equal volume but different contact angles and two cases are considered, one including internal natural convection and one where it is excluded, i.e. a case where the effects of density differences is not considered. The shape of the freezing front is similar to experimental observations in the literature and the freezing time is well predicted for colder substrate temperatures. The latter is found to be clearly dependent on the plate temperature and contact angle. Including density differences has only a minor influence on the freezing time, but it has a considerable effect on the dynamics of the internal flow. To exemplify, in the vicinity of the density maximum for water (4 ∘C) the velocities are about 100 times higher when internal natural convection is considered for as compared to when it is not.