Electric field Induced Patterns in Soft Visco-elastic films: From Long Waves of Viscous Liquids to Short Waves of Elastic Solids

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We show that the electric field driven surface instability of visco-elastic films has two distinct regimes: (1) The visco-elastic films behaving like a liquid display long wavelengths governed by applied voltage and surface tension, independent of its elastic storage and viscous loss moduli, and (2) the films behaving like a solid require a threshold voltage for the instability whose wavelength always scales as 4 x film thickness, independent of its surface tension, applied voltage, loss and storage moduli. Wavelength in a narrow transition zone between these regimes depends on the storage modulus.