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Water freezing in particle suspensions widely exists in nature. As a typicalphysical system of free boundary problem, the spatiotemporal evolution of thesolid/liquid interface not only origins from phase transformation but also frompermeation flow in front of ice. Physical models have been proposed in previousefforts to describe the interface dynamic behaviors in unidirectional freezingof particle suspensions. However, there are several physical parametersdifficult to be determined in previous investigations dedicated to describingthe spatiotemporal evolution in unidirectional freezing of particlesuspensions. Here, based on the fundamental momentum theorem, we propose aconsistent theoretical framework to address the unidirectional freezing processin the particle suspensions coupled with the effect of water permeation. Aninterface undercooling-dependent pushing force exerted on the compacted layerwith a specific formula is derived based on the surface tension. Then a dynamiccompacted layer is considered and analyzed. Numerical solutions of thenonlinear models reveal the dependence of system dynamics on some typicalphysical parameters, particle radius, initial particle concentration in thesuspensions, freezing velocity and so on. The system dynamics are characterizedby interface velocity, interface undercooling and interface recoil as functionsof time. The models allow us to reconsider the formation mechanism of icespears in freezing of particle suspensions in a simpler but novel way, withpotential implications for both understanding and controlling not only iceformation in porous media but also crystallization processes in other complexsystems.

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