Implementation of an antitrapping current for a multicomponent multiphase-field ansatz

The benefit of an antitrapping current has been investigated for a multicomponent multiphase-field model based on a double obstacle potential [Eiken et al., Phys. Rev. E 73 (2006) 066122]. Arguments justifying the analytical form of this correction for artificial solute trapping are given using Kim's formalism [Kim, Acta Mat. 55 (2007) 4391]. The validity of the model has been tested by comparing the phase-field results with those obtained by a sharp interface model. In particular, the 1D steady state solutions for solidification of a binary Al-Si and a ternary Al-Si-Mg alloy under isothermal conditions with a constant solute concentration at a finite distance from the solidification front have been used for comparison. The front velocity, the liquid concentration profile, and the concentration in solid predicted by the phase-field model with antitrapping compare well with the sharp interface solutions. In addition, for dendritic growth the convergence of tip velocity and local solute concentration at the tip with decreasing interface thickness is demonstrated.