  Phase field models are powerful tools to tackle free boundary problems. For
phase transformations involving diffusion, the evolution of the non conserved
phase field is coupled to the evolution of the conserved diffusion field.
Introducing the kinetic cross coupling between these two fields [E. A. Brener,
G. Boussinot, Phys. Rev. E {\bf 86}, 060601(R) (2012)], we solve the
long-standing problem of a realistic description of interface kinetics when a
diffusional contrast between the phases is taken into account. Using the case
of the solidification of a pure substance, we show how to eliminate the
temperature jump at the interface and to recover full equilibrium boundary
conditions. We confirm our results by numerical simulations.
