Electric field and van der Waals force induced instabilities in thin viscoelastic bilayers

Abstract

A unified theory is presented for the field-induced spinodal instabilities of thin viscoelastic bilayers composed of the Maxwell fluids or of the soft solids obeying the Kelvin-Voigt model. The analysis includes the different important mechanisms by which a bilayer is rendered unstable: (1) the wetting instability engendered by the excess van der Waals forces in an ultrathin (<100 nm) bilayer (Figure (1a)); (2) the electric field induced instability caused by an external electrostatic field across the bilayer (Figure (1b)); (3) the contact instability caused by the attractive interactions with another surface in the contact proximity of the upper film (Figure (1c)). The key features of the short-, long-, and finite-wavenumber instabilities are compared and contrasted for a host of bilayers having purely viscous, purely elastic, viscoelastic-viscous, and viscoelastic rheological properties. Linear stability analysis shows: (i) controlling mode of instability can shift from one interface to the other, which is accompanied by an abrupt shift in the time and the length scales of the instabilities with the change in the interfacial tensions, relaxation times, and elastic moduli of the films; (ii) purely elastomeric bilayers show a finite wavenumber bifurcation only beyond a critical destabilizing force due to their elastic stiffness; (iii) bilayers with at least one viscous or Maxwell layer show zero elastic-stiffness against the destabilizing influences; (iv) wetting viscoelastic bilayer is unstable only when it is ultrathin and elastically very soft or if one of the layers is purely viscous; (v) Maxwell (elastomer) bilayers show a faster (slower) growth of instability with the increase in relaxation time (elastic modulus).