Phase separation dynamics in a concentration gradient

Phase separation dynamics with an initially nonuniform concentration are studied. Critical and off-critical behavior is observed simultaneously. A mechanism for an expanding phase-separated region is demonstrated and the time dependence of the concentration is determined. The final equilibrium state consists of a planar interface separating one phase from the other. The evolution to this state is characterized by an experimentally observable flux, j, crossing this interface. We find that j∼t^−2/3 if patterns are formed in the bulk and j∼t^−1/2 if the bulk remains homogeneous. The results are explained in terms of scaling arguments which are confirmed numerically.