Effects of In-plane Elastic Stress and Normal External Stress on Viscoelastic Thin Film Stability

F. Closa¹ ; F. Ziebert^2, 3 ; E. Raphaël¹

¹ Laboratoire de Physico–Chimie Théorique – UMR CNRS Gulliver 7083, ESPCI 10 rue Vauquelin, F-75231 Paris, France
² Physikalisches Institut, Albert–Ludwigs–Universität, 79104 Freiburg, Germany
³ Institut Charles Sadron, 23 rue du Loess, 67034 Strasbourg, France

Mathematical modelling of natural phenomena, Tome 7 (2012) no. 4, pp. 6-19

Résumé

Motivated by recent experiments on the electro-hydrodynamic instability of spin-cast polymer films, we study the undulation instability of a thin viscoelastic polymer film under in-plane stress and in the presence of either a close by contactor or an electric field, both inducing a normal stress on the film surface. We find that the in-plane stress affects both the typical timescale of the instability and the unstable wavelengths. The film stability is also sensitive to the boundary conditions used at the film-substrate interface. We have considered two conditions, either rigidly attaching the film to the substrate or allowing for slip.

Détail

DOI : 10.1051/mmnp/20127402

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[29] Note that Yc, Kc and Kfg are determined by elasticity, the viscosity does not play a role. However, Kfg can exist only if η ≠ 0, else, the problem is a static problem and Kfg is not defined.