Rupture of thin viscous films by van der Waals forces: Evolution and self-similarity

The van der Waals driven rupture of a freely suspended thin viscous sheet i s examined using a long-wavelength model. Dimensional analysis shows the po ssibility of first-type similarity solutions in which the dominant physical balance is between inertia, extensional viscous stresses and the van der W aals disjoining pressure, while surface tension is negligible. For both lin e rupture and point rupture the film thickness decreases like (t*-t)(1/3) a nd the lateral length scale like (t*-t)(1/2), where t*-t is the time remain ing until rupture. In each geometry these scalings are confirmed by numeric al simulations of the time-dependent behavior, and a discrete family of sim ilarity solutions is found. The "lowest-order" mode in the family is the on e selected by the time-dependent dynamics. (C) 2001 American Institute of P hysics.