Spatio-temporal instability in free ultra-thin films

The linear evolution of an initially localized disturbance is investigated for a free ultra-thin film of viscous liquid, which is subjected to capillary and long range intermolecular forces. The analysis is based on the long-wave model proposed by Erneux and Davis (1993, Phys. Fluids A, 5, 1117), which is reformulated in an equivalent form by means of the disjoining pressure approach. A negative disjoining pressure due to the van der Waals attraction strongly promotes instability. Both the growth rate along rays x = Ut and speed of the disturbance edges increase as the thickness of the undisturbed film decreases. The estimated film rupture time is larger than that found from linear temporal stability analysis. (C) Elsevier, Paris.