Renormalization group calculation of late stage interface dynamics

Abstract. The temporal evolution of an interface separating two phases is studied for its large time behavior. The calculation involves adaptation of methodology known in the physics literature as renormalization group and scaling theory. We consider the fully dynamic set of equations, i.e., the sharp interface model incorporating surface tension and kinetic undercooling. This extends earlier results and those of Jasnow and Vinals that were obtained for the quasi-static regime. The characteristic length, R(t), governing the morphology of late stage growth is found to vary as t 1/2, while the total surface area of the interface, S(t), varies as t (d−1)/2. Thus the growth exponents in this fully dynamic analysis differ from the R(t) ∼ t found for the quasi-static regime by Jasnow and Vinals. In both cases, however, the capillarity length arising from surface tension is irrelevant for large time behavior, even though it is a crucial factor for the initial growth velocity and the linear stability of the interface