Prediction of nonlinear interface dynamics in the unidirectional freezing of particle suspensions with rigid compacted layer

Water freezing in particle suspensions widely exists in nature. As a typical physical system of free boundary problem, the spatiotemporal evolution of the solid/liquid interface not only origins from phase transformation but also from permeation flow in front of ice. Physical models have been proposed in previous efforts to describe the interface dynamic behaviors in unidirectional freezing of particle suspensions. However, there are several physical parameters difficult to be determined in previous investigations dedicated to describing the spatiotemporal evolution in unidirectional freezing of particle suspensions. Here, based on the fundamental momentum theorem, we propose a consistent theoretical framework to address the unidirectional freezing process in the particle suspensions coupled with the effect of water permeation. An interface undercooling-dependent pushing force exerted on the compacted layer with a specific formula is derived based on the surface tension. Then a dynamic compacted layer is considered and analyzed. Numerical solutions of the nonlinear models reveal the dependence of system dynamics on some typical physical parameters, particle radius, initial particle concentration in the suspensions, freezing velocity and so on. The system dynamics are characterized by interface velocity, interface undercooling and interface recoil as functions of time. The models allow us to reconsider the formation mechanism of ice spears in freezing of particle suspensions in a simpler but novel way, with potential implications for both understanding and controlling not only ice formation in porous media but also crystallization processes in other complex systems