Labyrinthine Instability in Dielectric Fluids

The dual to recent work of the labyrinthine instability in magnetic fluids is demonstrated with analysis and measurements using dielectric fluids. Here polarizable fluid layers are placed within an initially uniform electric field tangential to the fluid interface separating two dielectric fluid layers. To eliminate electric space charge effects, alternating electric fields must be applied at a frequency much greater than the larger reciprocal dielectric relaxation time of the fluids. Past theory and measurements have shown that a flat interface in a uniform tangential field is stable if the interface is of infinite extent. If the fluid interface has a finite thickness in the direction of the applied field, reaction fields cause nonuniform field components tangential to the fluid interface. Above a critical magnitude the resultant field destabilizes the fluid interface forming labyrinthine patterns. An interfacial stability analysis and an energy minimization method are compared to measurements.