Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-19T12:36:45.147Z Has data issue: false hasContentIssue false
  • English
  • Français

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]
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Adda-Bedia, M., Mahadevan, L.. Crack-front instability in a confined elastic film. Proc. R. Soc. Lond. A, 462 (2006) 3233-3251. CrossRefGoogle Scholar
Asaro, R. J., Tiller, W. A.. Interface morphology development during stress corrosion cracking : Part I. Via surface diffusion. Metall. Trans. B 3 (1972), 1789-1796. CrossRefGoogle Scholar
Barbero, D. R., Steiner, U.. Nonequilibrium Polymer Rheology in Spin-Cast Films. Phys. Rev. Lett. 102 (2009), 248303, 1-4. CrossRefGoogle ScholarPubMed
Bodiguel, H., Fretigny, C.. Viscoelastic dewetting of a polymer film on a liquid substrate. Eur. Phys. J. E, 19 (2006), 185-193. CrossRefGoogle ScholarPubMed
Bureau, L., Léger, L.. Sliding Friction at a Rubber/Brush Interface. Langmuir 20 (2004), 4523-4529. CrossRefGoogle Scholar
Closa, F., Ziebert, F., Raphaël, E.. Interplay of internal stresses, electric stresses, and surface diffusion in polymer films. Phys. Rev. E, 83 (2011), 051603, 1-13. CrossRefGoogle ScholarPubMed
Ghatak, A.. Confinement-induced instability of thin elastic film. Phys. Rev. E, 73 (2006), 041601, 1-7. CrossRefGoogle ScholarPubMed
Ghatak, A., Chaudhury, M. K.. Critical Confinement and Elastic Instability in Thin Solid Films. J. Adh., 83 (2007), 679-704. CrossRefGoogle Scholar
Ghatak, A., Chaudhury, M. K., Shenoy, V., Sharma, A.. Meniscus instability in a thin elastic film. Phys. Rev. Lett., 85 (2000), 4329-4332. CrossRefGoogle Scholar
Grinfeld, M. A.. Instability of the interface between a nonhydrostatically stressed elastic body and a melt. Dok. Akad. Nauk SSSR 290 (1986), 1358-1363 [Sov. Phys. Dokl. 31 (1986), 831-834]. Google Scholar
J. D. Jackson. Classical Electrodynamics. Wiley, New York (1998).
L. D. Landau, E. M. Lifshitz. Theory of Elasticity. Pergamon Press, New York, 1986.
Melcher, J. R.. Electrohydrodynamic and Magnetohydrodynamic Surface Waves and Instabilities . Phys. Fluids, 4 (1961), 1348-1354. CrossRefGoogle Scholar
C. W. Macosko. Rheology : Principles, Measurements, and Applications. Wiley, New York (1994).
Norrman, K., Ghanbari-Siahkali, A., Larsen, N. B.. Studies of spin-coated polymer films. Annu. Rep. Prog. Chem., Sect. C, 101 (2005), 174-201. CrossRefGoogle Scholar
Onuki, A.. Interface instability induced by an electric field in fluids . Physica A 217 (1995), 38-52. CrossRefGoogle Scholar
Rajagopal, K. R., Saccomandi, G.. Shear Waves in a Class of Nonlinear Viscoelastic Solids. Q. J. Mechanics Appl. Math. 56 (2003), 311-326. CrossRefGoogle Scholar
Reiter, G., Hamieh, M., Damman, P., Sclavons, S., Gabriele, S., Vilmin, T., Raphaël, E.. Residual stresses in thin polymer films cause rupture and dominate early stages of dewetting. Nature Mat., 4 (2005), 754-758. CrossRefGoogle ScholarPubMed
Schäffer, E., Thurn-Albrecht, T., Russell, T. P., Steiner, U.. Electrohydrodynamic instabilities in polymer films. Europhys. Lett. 53 (2001), 518-524. CrossRefGoogle Scholar
Shenoy, V., Sharma, A.. Stability of a thin elastic film interacting with a contactor. J. Mech. Phys. Solids 50 (2002), 1155-1173. CrossRefGoogle Scholar
Taylor, G. I., McEwan, A. D.. The stability of a horizontal fluid interface in a vertical electric field. J. Fluid Mech., 22 (1965), 1-15. CrossRefGoogle Scholar
Tomar, G., Shankar, V., Sharma, A., Biswas, G.. Electrohydrodynamic instability of a confined viscoelastic liquid film. J. Non-Newtonian Fluid Mech. 143 (2007), 120-130. CrossRefGoogle Scholar
Tsori, Y.. Phase transitions in polymers and liquids in electric fields. Rev. Mod. Phys. 81 (2009), 1471-1494. CrossRefGoogle Scholar
Vilmin, T., Raphaël, E., Damman, P., Sclavons, S., Gabriele, S., Hamieh, M., Reiter, G.. The role of nonlinear friction in the dewetting of thin polymer films. Europhys. Lett. 73 (2006), 906-912. CrossRefGoogle Scholar
Vilmin, T., Ziebert, F., Raphaël, E.. Simple View on Fingering Instability of Debonding Soft Elastic Adhesives. Langmuir, 26 (2010), 3257-3260. CrossRefGoogle ScholarPubMed
Ziebert, F., Raphaël, E.. Dewetting of thin polymer films : Influence of interface evolution. EPL 86 (2009), 46001, p1-p6. Google Scholar
Ziebert, F., Raphaël, E.. Dewetting dynamics of stressed viscoelastic thin polymer films. Phys. Rev. E, 79 (2009), 031605, 1-10. CrossRefGoogle ScholarPubMed
Ziebert, F., Zimmermann, W.. Comment on “Instabilities of Isotropic Solutions of Active Polar Filaments”. Phys. Rev. Lett. 93 (2004), 159801-1. CrossRefGoogle Scholar
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.