Renormalization and scaling methods for quasi-static interface problems Original Research Article

We study the temporal evolution of an interface separating two phases for its large-time behavior by adapting renormalization group methods and scaling theory. We consider a full two-phase model in the quasi-static regime and implement a renormalization procedure in order to calculate the characteristic length of a self-similar system, R(t)R(t), that is the time-dependent length scale characterizing the pattern growth. When the dynamical undercooling is non-zero (α≠0)(α≠0), we find that R(t)R(t) increases as t-1/λt-1/λ, where λλ can take on values in the continuous spectrum, [-3,-2][-3,-2]. For α=0α=0 the spectrum is [-3,0)[-3,0) so that the single value of λ=-1λ=-1 is selected by the plane wave imposed by Jasnow and Vinals. It is also shown that in almost all of these cases, the capillarity length, d0d0, (arising from the surface tension, σ0σ0) is not relevant for the large-time behavior even though it has a crucial role at the early stage evolution of an interface. The exception is λ=-3λ=-3, i.e., R(t)∼t1/3R(t)∼t1/3, for which d0d0 is invariant.