Asymptotic regimes of ridge and rift formation in a thin viscous sheet model

PERAZZO, CARLOS ALBERTO; GRATTON, JULIO

PHYSICS OF FLUIDS

Año: 2008 vol. 20 p. 431031 - 431038

1070-6631

We numerically and theoretically investigate the evolution of the ridges and rifts produced by the convergent and divergent motions of two substrates over which an initially uniform layer of a Newtonian liquid rests. We put particular emphasis on the various asymptotic self-similar and quasi-self-similar regimes that occur in these processes. During the growth of a ridge, two self-similar stages occur; the first takes place in the initial linear phase, and the second is obtained for a large time. Initially, the width and the height of the ridge increase as t1/2. For a very large time, the width grows as t3/4, while the height increases as t1/4. On the other hand, in the process of formation of a rift, there are three self-similar asymptotics. The initial linear phase is similar to that for ridges. The second stage corresponds to the separation of the current in two parts, leaving a dry region in between. Last, for a very large t, each of the two parts in which the current has separated approaches the self-similar viscous dam break solution.