A thermodynamic consistent multi-phase-field model base on the maximal entropy production princip

Abstract

The maximal entropy production principle (MEPP) based on which the additional constrains can be incorporated conveniently by the Lagrange method is applied to propose a new multi-phase-field model. The phase-field and diffusion equations follow the classical Onsanger reciprocal law which means that the present work is thermodynamic consistent with the classical irreversible thermodynamics. The bulk and interface contributions can be separated completely both at equilibrium condition and highly non-equilibrium condition where complete solute trapping happens. For medium growth velocities, the interaction between the bulk and interface contributions can be suppressed by increasing the order of a new interpolation function, which makes a quantitative modeling of rapid solidifications possible. For the one-sided growth model, the driving force for the phase field is not the grand potential but the model with solute drag as is in the classical sharp interface model. This means that the grand potential function which does not incorporate the additional constrains rightly is not thermodynamics consistent. Application to rapid solidification Si-9at.%As alloy shows that a good agreement between the model prediction and experimental results can be found.