Comparison of Analytical and Numerical Simulations for Underwater Ice Evolution and Nonlinear Dynamics of False Bottoms

In the present work, a comparative study of a model of the nonlinear solidification of a binary melt in the presence of a quasi-equilibrium mushy region and a binary phase field model of an aqueous solution of NaCl in water is performed. Nonlinear model is solved analytically in integral form with the effective coefficients of heat and mass transfer. Temperature and concentration distributions in the mushy zone are interpolated in the consideration of quasi-stationery boundary propagation. The binary phase field model introduces the temperature- and concentration-dependent mobility coefficients and allows the simultaneous solution of heat and solute transfer. The quantitative agreement between the analytical nonlinear model solved in integral form and the phase field model is shown. The applicability of the methods and details of the numerical implementation are discussed.