Stability of immersed viscous liquid threads under electric field

Recognizing the importance of viscosity ratio (λ) in electrified liquid–liquid systems, a linear stability analysis of a liquid thread (jet) immersed in an infinite surrounding medium while being subjected to radial/axial electric fields (Eo) is performed. The relative motion between the thread and medium is considered zero. The stability of threads under axisymmetric (m = 0) and asymmetric (m = 1) modes of perturbation is studied for arbitrary viscosity ratios. The viscosity ratio, in general, was shown to have a damping effect on the two modes of perturbation. However the effect is more pronounced for the m = 1 mode as compared to m = 0 mode in the presence of radial/axial electric fields. Investigating the effect of both Eo and λ simultaneously, an operating diagram is generated, showing the predominance of the two modes at any given value of electric field and viscosity ratio. The operating diagrams provided can be used to foresee the complete stability behavior of liquid–liquid threads under electric fields.