M.V. Knysh1, V.V. Моrоzоv2, S.N. Razinkov3

1 Yaroslavl Higher Military School of Air Defense named after Marshal of the Soviet Union L.A. Govorov (Yaroslavl, Russia)

2 Yaroslavl State Agrarian University (Yaroslavl, Russia)

3 Military educational-scientific center of Air Force of the «Military-air academy named after professor N.E. Zhukovsky and Yu.A. Gagarin» (Voronezh, Russia)

1 mariku2713@ mail.ru, 2 info@yarcx.ru, 3 razinkovsergey@rambler.ru

To assess the stability of artificial aerosol formations, it is necessary to establish the patterns of capillary oscillations and the stability conditions for incompressible conductive droplets with surface electric charges in an external electric field. Analysis of drop transformation at movement in dielectric medium under action of external electric field on the basis of joint solution of Laplace equations for its hydrodynamic and electric potentials at control of integral conditions of center of mass immobility, preservation of volume and charge is carried out. The evolutionary equation and conditions for the stability of the droplet under the influence of electric forces are effectively found using the asymptotic method of analytical representation of capillary oscillations when setting their amplitudes and the deviation of the equilibrium shape from the spherical surface of a unit radius as small parameters. Analysis of transformation patterns and determination of stability conditions for nearby aerosol cloud droplets in an external field. On the basis of solution of Laplace equations for hydrodynamic and electric potentials of drop in external electric field of point charge at zero or-der of smallness of surface oscillation amplitudes, expressions for its equilibrium form are obtained. Given the first order of smallness of oscillation amplitudes, an evolutionary equation is obtained and stability conditions of the disturbed liquid surface are established. Revealed regularities of capillary oscillations and stability conditions of charged drop surface of incompressible non-viscous con-ducting liquid in external electric field make it possible to evaluate stability of artificial aerosol formations and to substantiate parameters of ion-cluster-droplet beams at spraying of liquid-droplet aerosol.

Knysh M.V., Моrоzоv V.V., Razinkov S.N. Analysis of oscillations and stability of charged incompressible conductive droplet of an aerosol cloud in an external electric field. Electromagnetic waves and electronic systems. 2025. V. 30. № 6. P. 84−97. DOI: https://doi.org/10.18127/j15604128-202506-08 (in Russian)

1. Knysh M.V., Моrоzоv V.V., Razinkov S.N. Analysis of decay of droplets with electric charges in an aerosol cloud under the influence of an electrostatic field. Nonlinear World. 2025. V. 23. № 2. P. 77–82. DOI 10.18127/j20700970-202501-08. (in Russian)
2. Shiryaeva S.O., Grigoriev A.I. Patterns of Rayleigh decay of a drop in a sharply inhomogeneous electric field. Journal of Technical Physics. 1992. V. 62. № 3. P. 35–39. (in Russian)
3. Koromyslov V.A., Grigoriev A.I., Rybakova M.V. Instability of a moving charged droplet in an external electric field. Electronic processing of materials. 2002. № 4. P. 50–53. (in Russian)
4. Grigoriev A.I., Shiryaeva S.O., Belavina E.I. The equilibrium shape of a charged drop in electric and gravitational fields. Journal of Technical Physics. 1989. V. 59. № 6. P. 27–34. (in Russian)
5. Mukhina E.I., Grigoriev A.I. Equilibrium forms and critical conditions of electrohydrodynamic instability of droplet particles in an electric field. Journal of Technical Physics. 1992. V. 62. № 2. P. 18–26. (in Russian)
6. Grigoriev A.I., Koromyslov V.A., Rybakova M.V. On the shape of a charged drop in crossed electric and hydrodynamic fields. Electronic processing of materials. 2002. № 6. P. 22–25. (in Russian)
7. Karyappa R.B., Naik A.V., Thaokar R.M. Electroemulsification in a uniform electric field. Langmuir. 2015. V. 32. № 1. P. 46–54. DOI 10.1021/acs.langmuir.5b03188.
8. Tikhonov A.N., Arsenin V.Ya. Methods of solving ill-posed problems. Moscow: Nauka. 1986. 288 p. (in Russian)
9. Grimm R.L., Beauchamp J.L. Dynamics of Field-Induced Droplet Ionization: Time-Resolved Studies of Distortion, Jetting, and Progeny Formation from Charged and Neutral Methanol Droplets Exposed to Strong Electric Fields. The journal of physical chemistry. B. 2005. V. 109. № 16. P. 8244–8250. DOI 10.1021/jp0450540.