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

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Abstract
The van der Waals driven rupture of a freely suspended thin viscous sheet is examined using a long-wavelength model. Dimensional analysis shows the possibility of first-type similarity solutions in which the dominant physical balance is between inertia, extensional viscous stresses and the van der Waals disjoining pressure, while surface tension is negligible. For both line rupture and point rupture the film thickness decreases like (t*−t)1/3 and the lateral length scale like (t*−t)1/2, where t*−t is the time remaining until rupture. In each geometry these scalings are confirmed by numerical simulations of the time-dependent behavior, and a discrete family of similarity solutions is found. The “lowest-order” mode in the family is the one selected by the time-dependent dynamics.

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