Thin-film models for viscoelastic liquid bi-layers
- Jachalski, Sebastian
- Münch, Andreas
- Wagner, Barbara
2010 Mathematics Subject Classification
- 76A20 76Mxx
- fluid dynamics, viscoelasticty, thin-film models, two-phase flow, asymptotic methods, numerical solution
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 corotational Jeffreys' type dewetting from a solid as well as liquid substrate.