  Solute trapping is an important phenomenon in rapid solidification of alloys,
for which the continuous growth model (CGM) is a popular sharp interface
theory. Using matched asymptotic analysis, we show how to quantitatively map
the sharp interface behavior of a binary alloy phase field model onto the CGM
kinetics of Aziz et al. [1], with a controllable partition coefficient k(V ).
We demonstrate the parameterizations that allow the phase field model to map
onto the corresponding CGM or classical sharp interface models. We also
demonstrate that the mapping is convergent for different interface widths.
Finally we present the effect that solute trapping can have on cellular growth
in a directional solidification simulation. The treatment presented for solute
trapping can be easily implemented in different phase field models, and is
expected to be an important feature in future studies of quantitative phase
field modeling in rapid solidification regimes, such as those relevant to
additive manufacturing.
