  A new diffuse interface model has been proposed in this study for simulating
binary alloy solidification under universal cooling conditions, involving both
equilibrium and non-equilibrium solute partitioning. Starting from the
Gibbs-Thomson equation, which is the classical theory that describes the
dynamics of a sharp interface, the phase-field equation is derived using a
traveling wave solution that represents a diffuse interface. To tackle the
spurious effects caused by the variation of liquid concentration within the
diffuse interface with artificial width, a middle obstacle is introduced to
sharpen the diffuse interface and an invariant liquid concentration can be
found for determining a constant undercooling in the interface normal
direction. For slow solidification under equilibrium conditions, the
convergence performance of the dendrite tip shows superior invulnerability to
the width effect of the diffuse interface. For rapid solidification under
non-equilibrium conditions, the output partition coefficients obtained from the
steady-state concentration profiles agree with the input velocity-dependent
function. The proposed model is promising to be an indispensable tool for the
development of advanced alloy materials through the microstructure control of
solidification under a wide range of cooling conditions.
