Abstract
Electrohydrodynamic flows in which there are zones of abrupt changes in the electric charge (while remaining bounded, by assumption) are investigated. In a diffusionless approximation such flows are characterized by a discontinuity in the electric charge q. Examples of such motions are nonstationary flows with moving electrical charge fronts [1], stationary flows in which the electrical charge is lumped in just part of the hydrodynamic stream [2, 3], flows with discontinuity in q [4–7], boundary layers near an electrode grid mounted perpendicularly to the electrohydrodynamic stream. Diffusion effects of charged particles should cause smoothing of the electrical charge discontinuities. The diffusion structure of such discontinuities is studied for high electrical Peclet numbers. The distribution of q in gasdynamic jumps is analyzed taking account of the viscous and diffusion structure of the discontinuities in the small parameter approximation of the electrogasdynamic interaction. Three problems about flows with charged particle diffusion are examined: the problem of scattering of a finite electric charge in a medium at rest, initially concentrated at a point on a line of unit length; the boundary layer on an electrode grid perpendicular to the direction of the charged fluid stream; electrogasdynamic flows with an abrupt change in velocity not accompanied by the appearance of a surface charge.
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Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 59–67, January–February, 1975.
The author is grateful to V. I. Grabovskii and O. K. Varentsov for carrying out the calculations.
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Vatazhin, A.B. Smoothing the discontinuities of an electrical charge in electrodynamics as a result of diffusion processes. Fluid Dyn 10, 49–56 (1975). https://doi.org/10.1007/BF01023779
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DOI: https://doi.org/10.1007/BF01023779