Mass conserving Allen-Cahn equation and volume preserving mean curvature flow

We consider a mass conserving Allen-Cahn equation u(t) = Delta u + epsilon(-2)(f (u) - epsilon lambda(t)) in a bounded domain with no flux boundary condition, where epsilon lambda(t) is the average of f(u(., t)) and -f is the derivative of a double equal well potential. Given a smooth hypersurface gamma(0) contained in the domain, we show that the solution u(epsilon) with appropriate initial data tends, as epsilon (sic) 0, to a limit which takes only two values, with the jump occurring at the hypersurface obtained from the volume preserving mean curvature flow starting from gamma(0).