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

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