On the Critical Conditions for Realization of Instability of Azimuthal Modes of Conducting Liquid Jets Carrying Uniform and Nonuniform Induced Surface Charges and Their Electrodispersion

• Published in: Colloid journal of the Russian Academy of Sciences 2022-06, Vol.84 (3), p.254-264
• Main Authors: Grigor’ev, A. I., Shiryaeva, S. O.
• Format: Article
• Language: English
• Subjects: Amplitudes; Asymptotic methods; Capillary waves; Chemistry; Chemistry and Materials Science; Cross-sections; Electric fields; Initial conditions; Polymer Sciences; Stability; Surface tension; Surfaces and Interfaces; Symmetry; Thin Films
• ISSN: 1061-933X; 1608-3067
• DOI: 10.1134/S1061933X22030061

Analytical asymptotic methods are used to study the critical conditions for realization of electrostatic instability of various azimuthal modes of electrically conducting liquids with respect to external electrostatic fields, in which a liquid jet surface acquires induced charges. A uniform electrostatic fields, which is directed perpendicularly to the symmetry axis of an unperturbed liquid jet and impart an elliptical shape to the jet cross section, and a radial axially symmetric field have been selected as such external fields. An analytical expression has been derived for an arbitrary azimuthal mode of capillary waves on the surface of an elliptical jet. It has turned out that the critical conditions for the realization of the electrostatic instability of azimuthal modes are independent of the initial amplitudes of the waves (despite the existence of an intermode interaction), but rather are determined by the jet radius, the surface tension coefficient of the liquid, the strength of the external electrostatic field, and the presence of a stationary deformation of the equilibrium jet shape relative to a jet with a circular cross section. For an elliptical jet, the time dependences of the amplitudes of unstable azimuthal waves have been plotted under different initial conditions.