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Finite-time singularity formation in lubrication models of thin-film flows


Friday 16th September, at 4pm, in A2-002

Dr Michael Dallaston (Imperial College Longdon)

Contact Dr Iain Moyles (iain.moyles@ul.ie)

Abstract: The evolution of thin viscous liquid films is typically governed by the competition between a high order stabilising mechanism, often associated with surface tension and a second, destabilising mechanism, e.g. disjoining pressure due to van der Waals forces. The archetype is finite-time rupture, but other examples include the Rayleigh-Taylor instability of a thin film, destabilisation of a heated film due to thermocapillary Marangoni effects, and singular behaviour of the Benney equation, used to model falling films with finite inertia In the lubrication approximation, the thin-film governing equation in each case is almost identical, differing only in the form of the coefficient functions on each term. In this talk we examine the different behaviours that occur for different exponents in the coefficient function of the destabilising term. These behaviours range from finite-time rupture, to cascades of increasingly short wavelength perturbations, to finite-time blow up. One striking feature is that stable self-similarity is lost due to the merging of solution branches at saddle-node bifurcations. Some work in progress on the stability analysis of self-similar solutions will also be discussed.

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