Surface tension and domain growth in nonuniform electric fields

Abstract

We look at the surface tension in a binary mixture of two dielectric liquids placed inside a concentric capacitor. This is a model for systems with long range electrostatic forces lacking translational symmetry. For an initially homogeneous mixture above the bulk binodal curve, when the potential across the cylinders is small, smooth composition variations exist. When the voltage exceeds a critical value, however, there is a demixing transition whereby the more polar mixture component is found near the inner walls and the less polar liquid migrates to the outer boundary. We further look at the interface and calculate its location as a function of the system parameters. This allows us to calculate the surface tension. We then extend these to the dynamical evolution of the demixing phase transition. We define the surface tension in a way which is valid for slow dynamics, that is, late-time relaxation close to equilibrium. Contrary to infinite (bulk) systems, the surface tension depends on the location of the interface. We find that its value can increase or decrease with interface location, and point out that this implies a new type of interfacial instability where the field stabilizes a smooth interface and surface tension destabilizes it.