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

Ice growth in aqueous suspensions widely exists in natural and industrial settings where freezing of water occurs with a porous medium and results in the spatiotemporal evolution of a solid/liquid interface. Physical models have been proposed in previous efforts to describe the dynamic behaviours of interfaces in the unidirectional freezing of particle suspensions. Most previous models dealt with this process at the single-particle level, and the growth of a particle compacted layer coupled with ice growth was hardly addressed. Here, based on the fundamental momentum theorem, we propose a consistent theoretical framework to address the unidirectional freezing process in particle suspensions free of solute, which focuses exclusively on the effect of water permeation. We first propose a constant compacted layer model, in which an interface undercooling-dependent pushing force exerted on the compacted layer is derived based on surface tension. Subsequently, a dynamically growing compacted layer is established and analysed. Numerical solutions of the nonlinear models reveal the dependence of the system dynamics on some typical physical parameters, such as particle radius, initial particle concentration in the suspensions, and freezing velocity. The system dynamics are characterized by interface velocity, interface undercooling, and interface recoil as functions of time. The models allow us to reconsider the dynamic ice growth during the freezing of particle suspensions in a simple 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.