Dynamical scaling during interfacial growth in the one-sided model

We study the temporal evolution of a planar interface that separates two coexisting phases, after it becomes morphologically unstable. We solve numerically the interface equation of motion of the one-sided model in two dimensions. Evidence is presented for the appearance of a regime of self-similar growth in which the evolving pattern is characterized by a single, time-dependent length scale, R(t), in agreement with earlier similar studies in the two-sided symmetric model. We have implemented a renormalization procedure to obtain the asymptotic time dependence of R(t). We find R(t){~}t at sufficiently long times. We also show that the asymptotic scaling behavior is determined by the driving term in the equations of motion. This term is proportional to the flux externally imposed ahead of the moving interface. The stabilizing contribution, which is proportional to the capillary length, is shown to be irrelevant for the large-scale behavior. We finally study the effects introduced by anisotropic surface tension and show that the asymptotic behavior of the system remains unchanged.