Electro-hydrodynamic instability of stressed viscoelastic polymer films

We study the stability of a viscoelastic thin polymer film under two destabilization factors: the application of an electric field normal to the surface--as in typical electro-hydrodynamic destabilization experiments--and the presence of a frozen-in internal residual stress, stemming from the preparation process of the film, typically spin-coating. At the film-substrate interface we consider a general boundary condition, containing perfect gliding on slippery substrates, as well as perfect sticking of the film to the substrate as limiting cases. We show that the interplay of the two sources of stress, the viscoelasticity and the boundary condition, leads to a rich behavior, especially as far as the fastest growing wave number (or wavelength) is concerned. The latter determines the initial growth of the instability, and often also the final pattern obtained in small capacitor gaps, and is the main experimental observable.