Instability of Slender Liquid Jet in AC Electric Field of Arbitrary Frequency

In the present work stability of capillary micro-jet of electrolyte solution in alternating longitudinal electric field is investigated theoretically. The gravity effects are neglected. The problem is described by strongly coupled nonlinear system of PDEs for ion transport, electric field and fluid flow under assumption of a viscous Newtonian liquid. The Debye layer thickness is supposed to be small compared with initial jet radius. The Peclet number based on the Debye layer thickness is assumed to be small. These assumptions lead to substantial simplification of the problem. Slender-body theory is used to further simplification of initial statement. Used asymptotic method allows to reduce initially infinite system to three-dimensional ODE with time-periodic coefficients. It is shown that monodromy operator has the only real unstable multiplier. In the case of high-frequency alternating electric field the results showed good agreement with the ones provided by averaging theory.