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Preprint 4-2016

Thin-film models for viscoelastic liquid bi-layers

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Author(s) : Sebastian Jachalski, Andreas Münch, Barbara Wagner

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 4-2016

MSC 2000

35G30 Boundary value problems for nonlinear higher-order PDE
65C20 Models, numerical methods
76A10 Viscoelastic fluids
76T99 None of the above, but in this section

Abstract :
In this work we consider a two-layer system of viscoelastic liquids of corotational Jeffreys type dewetting from a Newtonian liquid substrates. We derive conditions that allow for the first time the asymptotically consistent reduction of the free boundary problem for the two-layer system to a system of coupled thin-film equations that incorporate the full nonlinear viscoelastic rheology. We show that these conditions are controlled by the order of magnitude of the viscosity ratio of the liquid layers and their thickness ratio. For pure Newtonian flow, these conditions lead to a thin-film model that couples a layer with a parabolic flow field to a layer described by elongational flow. For this system we establish asymptotic regimes that relate the viscosity ratio to a corresponding apparent slip. We then use numerical simulations to discuss the characteristic morphological and dynamical properties of viscoelastic films of corotationl Jeffreys type dewetting from a solid as well as liquid substrate.

Keywords : Fluid dynamics, Viscoelasticty, Thin-film models, Two-phase flow, Asymptotic Methods, Numerical Solution

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