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Electric-field-induced interfacial instabilities of a soft elastic membrane confined between viscous layers

Mohar Dey1, Dipankar Bandyopadhyay2, Ashutosh Sharma1,3,*, Shizhi Qian1,4, and Sang Woo Joo1,†

  • 1School of Mechanical Engineering, Yeungnam University, Gyeongsan 712-749, South Korea
  • 2Department of Chemical Engineering, Indian Institute of Technology Guwahati, 781039, Assam, India
  • 3Department of Chemical Engineering, Indian Institute of Technology Kanpur, UP 208016, India
  • 4Institute of Micro/Nanotechnology, Old Dominion University, Norfolk, Virginia 23529, USA

  • *ashutos@iitk.ac.in
  • †Author to whom correspondence should be addressed: swjoo@yu.ac.kr
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Phys. Rev. E 86, 041602 – Published 10 October, 2012

DOI: https://doi.org/10.1103/PhysRevE.86.041602

Abstract

We explore the electric-field-induced interfacial instabilities of a trilayer composed of a thin elastic film confined between two viscous layers. A linear stability analysis (LSA) is performed to uncover the growth rate and length scale of the different unstable modes. Application of a normal external electric field on such a configuration can deform the two coupled elastic-viscous interfaces either by an in-phase bending or an antiphase squeezing mode. The bending mode has a long-wave nature, and is present even at a vanishingly small destabilizing field. In contrast, the squeezing mode has finite wave-number characteristics and originates only beyond a threshold strength of the electric field. This is in contrast to the instabilities of the viscous films with multiple interfaces where both modes are found to possess long-wave characteristics. The elastic film is unstable by bending mode when the stabilizing forces due to the in-plane curvature and the elastic stiffness are strong and the destabilizing electric field is relatively weak. In comparison, as the electric field increases, a subdominant squeezing mode can also appear beyond a threshold destabilizing field. A dominant squeezing mode is observed when the destabilizing field is significantly strong and the elastic films are relatively softer with lower elastic modulus. In the absence of liquid layers, a free elastic film is also found to be unstable by long-wave bending and finite wave-number squeezing modes. The LSA asymptotically recovers the results obtained by the previous formulations where the membrane bending elasticity is approximately incorporated as a correction term in the normal stress boundary condition. Interestingly, the presence of a very weak stabilizing influence due to a smaller interfacial tension at the elastic-viscous interfaces opens up the possibility of fabricating submicron patterns exploiting the instabilities of a trilayer.

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Phys. Rev. E 86, 041602– Published 10 October, 2012
  • Received 12 July 2012

©2012 American Physical Society

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