A comprehensive review of modeling water solidification for droplet freezing applications

Various mathematical approaches undertaken to model all stages of droplet freezing are reviewed. The literature is rife with theoretical, experimental, and numerical treatments of the phase-change process in pure substances. With the water droplet solidification research finding its ever-increasing application in a vast array of industrial and natural applications of interest, there is a critical need to exhaustively review the mathematical treatment of multi-physics solidification stages occurring over a wide spatio-temporal range. This research analyzes key studies surrounding the treatment of the water droplet solidification mechanisms in the broader context of pharmaceutical, food, energy storage, meteorology, and process industry applications. Different formulations of Stefan problem in the spherical coordinates are reviewed followed by a critical evaluation of other macro-scale solidification modeling approaches such as the front-tracking, volume of fluid, level-set, and phase-field methods. The discussion of Stefan problem is followed by reviewing nucleation models during the freezing of water. Lastly, a review of dendritic growth modeling is presented with a particular focus on the progress made during the last decade. The review understands that the scientific community has come a long way in modeling the thermal physics of each droplet solidification stage, especially incorporating the atomic-scale interface kinetics effects within the macro-scale representation of droplet freezing. However, there is still significant progress to be made to develop holistic mathematical models that can rigorously incorporate nucleation dynamics within the macro-scale solidification formulation. The authors believe that these holistic models will allow for improved solidification dynamics predictions in many engineering applications.