Stokes and Navier–Stokes models for describing the instability of the charged boundary of a conducting liquid

N. M. Zubarev<sup>ab

a</sup> Institute of Electrophysics, Ural Branch, Russian Academy of Sciences, Ekaterinburg
^b P. N. Lebedev Physical Institute, Russian Academy of Sciences, Moscow

Abstract: We consider the developed stages of the Tonks–Frenkel instability of the free charged surface of a conducting liquid, when, due to the sharpening of the boundary, the scale of the problem is reduced to the microscopic one, and viscous effects begin to play a decisive role. In such a situation, the Stokes approximation is often used to study the flow of fluids. However, as demonstrated, a feature of the Tonks–Frenkel instability with its characteristic explosive behavior of a number of physical quantities is the incorrectness of its analysis within the framework of this approximation. A correct description of the fluid dynamics during the singularity formation requires the use of the full Navier–Stokes equations.

Keywords: Tonks–Frenkel instability, Taylor cone, Navier–Stokes model, Stokes approximation.

Received: 21.05.2025
Revised: 04.07.2025
Accepted: 04.07.2025

DOI: 10.61011/PJTF.2025.19.61148.20378

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