  We present a phase field model for isothermal transformations of two
component alloys that includes Onsager kinetic cross coupling between the
non-conserved phase field and the conserved concentration field. We also
provide the reduction of the phase field model to the corresponding macroscopic
description of the free boundary problem. The reduction is given in a general
form. Additionally we use an explicit example of a phase field model and check
that the reduced macroscopic description, in the range of its applicability, is
in excellent agreement with direct phase field simulations. The relevance of
the newly introduced terms to solute trapping is also discussed.
