Modelling the dynamics of the flow within freezing water droplets

Abstract

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.

Experimental study of the internal flow in freezing water droplets on a cold surface

“…6 Magnitude of the velocity along four lines at t = 1, 1.5, 2, 2.5, 3 and 4 s (i.e., from 6% up to 25% of the freezing time of the droplet) surface is much larger in comparison with the droplet, the water should have had time to cool off during this time period. Moreover, the flow in this time period show large similarities with the natural convection dominated flow modeled by Karlsson et al (2018), both regarding direction of the vortices and the shape of the freezing front. Two differences between the simulations in Karlsson et al (2018) and the presented experiments, is the direction of the flow in the first seconds of freezing, as well as the fact that the highest magnitude is retrieved in the absolute beginning of freezing, and not a few seconds into the freezing process as observed in the simulations.…”

“…Moreover, the flow in this time period show large similarities with the natural convection dominated flow modeled by Karlsson et al (2018), both regarding direction of the vortices and the shape of the freezing front. Two differences between the simulations in Karlsson et al (2018) and the presented experiments, is the direction of the flow in the first seconds of freezing, as well as the fact that the highest magnitude is retrieved in the absolute beginning of freezing, and not a few seconds into the freezing process as observed in the simulations. This reasoning suggest that natural convection is not the only mechanism inducing internal flow in the freezing droplet.…”

“…The surface tension for water in contact with air increase with decreasing temperature, which means that the water will be pulled to regions with higher surface tension (hence low temperature). For the case of a freezing droplet, this means that the water Experimental data from present studies: case 10 Experimental data by Jin et al 2013 Simulated data by Karlsson et al 2018 Fig . 3 Height of the freezing front at different times scaled with the corresponding droplet heights and freezing times in three works: from the present experiments (case 1, 5 and 10), experimental data by Jin et al (2013b) and from simulations by Karlsson et al (2018) located higher up in the droplet will be pulled down along the interface towards the cooling surface and then move up again close to the center of the droplet.…”

“…The height of the freezing front, defined as the area, where the water and ice meet in the droplet, is studied in the performed experiments in three cases (case 1, 5 and 10) and compared to experiments by Jin et al (2013b) and simulations by Karlsson et al (2018). Note that the setups are somewhat different and that the volumes of the droplets are not identical.…”

Influence of Substrate Material on Flow in Freezing Water Droplets—An Experimental Study

“…The phenomenon was first visualized by Kawanami et al [27], who concluded that driving forces that have an influence on the internal flow are temperature gradients, buoyancy forces and surface tension resulting in the Marangoni convection. The internal flow of a water droplet was further numerically studied by Karlsson et al [28,29]. They investigated the buoyancy forces and internal natural convection.…”