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

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.

Charge Leakage Mediated Pattern Miniaturization in the Electric Field Induced Instabilities of an Elastic Membrane

“…The accuracy of the LSA performed for the simplified LPL model has been verified in the asymptotic limits in Figure . The solid and the broken line in this figure show the variation in the growth rate (ω) with the wavenumber ( k ) plot for two different unstable modes of the existing study on the PPP trilayer . The circular symbols indicate that the LSA discussed in the present work can reproduce these unstable modes in the limit with zero conductivities at the liquid layers (σ 1 = σ 3 = 0) together with zero surface charge densities at the interface ( q 10 = q 20 = 0).…”

“…A previous study showed that the interfaces of a purely dielectric trilayer can readily deform into a bending mode when exposed to a small destabilizing electric field . In comparison, threshold field intensity is essential to initiate the squeezing mode of instability.…”

“…Interfacial instabilities of elastically soft polymer films often result in interesting patterns under the influence of intermolecular interactions − or electric field. − These patterns find important applications in the microelectronic or microfluidic devices, sensors, electrochemical cells, solar panels, and drug delivery modules. − The field-induced deformation of a thin elastic film is also a model in vitro prototype − to investigate the dynamics of biomembranes. − Thus, the deformations of thin membranes have been extensively explored in recent years to scrutinize various fundamental and technological aspects.…”

“…In particular, when the gap between the electrodes are of the order or a few micrometers or less, the field intensity can only be increased to a certain limit, which hinders the applicability of this process toward the fabrication of submicrometer patterns. An alternative then would be the use of multiple layers − in which the lesser stabilizing interfacial tension at the embedded interface(s) not only reduces the requirement for the field intensity but also helps in controlling the periodicity of the EFL patterns. − Apart from the use of multiple layers, introduction of leaky dielectric layers , could be another alternative to enhance the intensity of the electric field stress at the interfaces. Recent works predicted a much lower length scales for the EFL instabilities of single layer, ,, confined bilayers, − and free bilayers , composed of leaky dielectric films.…”

“…Linear stability analysis (LSA) is performed after taking into consideration the full descriptions of the Maxwell’s and hydrodynamic stresses for the electric field and flow, respectively. A pair of coupled elastic-viscous interfaces was found to deform either in a long-wave bending mode or in a finite-wavenumber squeezing mode with a short wave characteristic . Here we investigate the role of the charge leakage in the surrounding liquid layers on the mode selection, the amplitudes of deformation at the interfaces, and the length scale of instability.…”