Effect of Surface Tension Relaxation on the Stability of a Charged Jet

Abstract

In the asymptotic calculations of the first order of smallness by the dimensionless amplitude of capillary waves on the surface of charged jets of a polar liquid, the effect of the relaxation effect of surface tension on the regularities of their implementation is studied. Calculations are carried out on the model of an ideal incompressible electrically conductive fluid. It is shown that taking into account the effect of dynamic surface tension leads to an increase in the order of the dispersion equation, which has another damping root, describing the oscillations of the jet surface related to the destruction of the near-surface double electric layer (destruction of the ordering of polar molecules in the near-surface layer). At sufficiently large charges (prebreakdown in the sense of the ignition of a corona discharge in a gaseous medium), this solution becomes unstable, as a result of which the entire surface undergoes electrostatic instability. In the used mathematical model of an ideal fluid, the motion of the jet surface that occurs when the surface tension relaxation effect is turned on and the attenuation decrements of the capillary wave motions are purely of a relaxation nature.