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

Published online by Cambridge University Press:  09 July 2012

F. Closa ,
F. Ziebert  and
E. Raphaël
F. Closa
Affiliation:
Laboratoire de Physico–Chimie Théorique – UMR CNRS Gulliver 7083, ESPCI 10 rue Vauquelin, F-75231 Paris, France
F. Ziebert
Affiliation:
Physikalisches Institut, Albert–Ludwigs–Universität, 79104 Freiburg, Germany Institut Charles Sadron, 23 rue du Loess, 67034 Strasbourg, France
E. Raphaël*
Affiliation:
Laboratoire de Physico–Chimie Théorique – UMR CNRS Gulliver 7083, ESPCI 10 rue Vauquelin, F-75231 Paris, France
*
∗ Corresponding author. E-mail: [email protected]
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Abstract

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

Keywords

thin filmspolymersinstabilitymechanics(visco)elasticityinternalresidual stress
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 7 , Issue 4: Modelling phenomena on micro- and nanoscale , 2012 , pp. 6 - 19
Copyright
© EDP Sciences, 2012

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Note that Y c, K c and K fg are determined by elasticity, the viscosity does not play a role. However, K fg can exist only if η ≠ 0, else, the problem is a static problem and K fg is not defined.