Numerical simulation of the freezing process of a water drop attached to a cold plate

This paper presents a direct numerical work on the freezing process of a water drop that is either sessile on or pendant from a cold plate. The numerical technique used is an axisymmetric front-tracking method to represent interfaces that separate different phases. The sessile drop corresponds to positive Bond numbers Bo (i.e., Bo > 0), and the pendant drop represents the other values of Bo. Numerical results show that pendant drops break up into liquid drops when gravity dominates the force induced by surface tension at Bo < 0. That is, a decrease in Bo enhances the breakup of the freezing drop. The breakup also depends significantly on the initial shape of the drop in terms of the contact angle at the plate ϕ0, that is, increasing ϕ0 induces breakup. In addition, the drop rapidly completes freezing due to breakup. In the case of non-breakup, the increase in Bo reduces the solidified drop height and decreases the time to complete solidification. The freezing process also consumes minimal time with small ϕ0. The solidified drop after solidification has a cone near the axis of symmetry due to volume expansion of water upon solidification. This shape of the solidified drop is in accordance with the experimental observation.