Non-equilibrium melting of ice in contact with salty water

This paper presents a numerical analysis of the melting process when a pure ice slab suddenly in contact with salty water. Because the equilibrium freezing temperature of the salt solution is a function of the salt concentration, the ice at the ice/liquid interface is constitutionally overheated even when the ice is at the same temperature as the solution. Such a solid overheating provides a driving force for ice melting, leading to a non-equilibrium melting process. A linear phase-change kinetics, relating the interface velocity to the interface temperature and the salt concentration at the interface, is then introduced into the mathematical formulation to account for such a non-equilibrium behavior of the melting. A NaCO₃ solution is used as the model material in the calculations. Computational results show three melting regimes. The initial non-equilibrium melting regime is characterized by continuous variations in the interface parameters (velocity, temperature and the salt concentration). The interface velocity drops significantly as the constitutional overheating of the ice diminishes, The process is then followed by the second regime during which both the interface temperature and the salt concentration at the interface approach a constant, and the interface velocity follows the classic diffusion law, V_i ∝ t^-1/2. The local equilibrium condition is satisfied at the interface, and the similarity solution for infinite domain can be used to describe the melting behavior during this regime. In the third regime, the effect of the finite dimension of the system becomes important, the temperature of the entire slab becomes uniform, and the solute diffusion becomes the rate-limiting process. The third regime is characterized by a low melting velocity.