On the thickness of a boundary layer related to the oscillating free surface of a charged drop of a viscous liquid

Shiryaeva, S. O.; Григорьев, А. И.; Paranin, A. R.

doi:10.1134/s106378421010004x

Cited by 1 publication

(3 citation statements)

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“…In the low viscosity approximation, the mathemat ical statement of the model problem can be simplified using the same procedures as those used in the con ventional theory of boundary layers associated with the presence of a free surface or a solid wall [1][2][3][4][5][6][7]23].…”

Section: Simplification Of the Model Problem In Terms Of The Boundarymentioning

confidence: 99%

“…Based on the concepts of the boundary layer structure of a low viscosity liquid flow in a surface layer [1][2][3][4][5][6][7]23], we will formulate a model problem to approximate an exact solution, as was done in [1][2][3][4][5][6][7]. We proceed from the assumptions (see above) that the potential flow covers the entire volume of the drop and vanishes at the center of the drop and that the eddy part of the flow concentrates in the boundary (subsur face) layer with thickness δ.…”

Section: Statement and Solution Of A Model Problemmentioning

confidence: 99%

“…A series of works has been accomplished in recent years in which the theory of a boundary layer near the flat, cylindrical, and spherical charged free surface of a conducting incompressible liquid executing periodic motion was elaborated [1][2][3][4][5][6][7]. In these works, the shape of the equilibrium liquid surface was assumed to be independent of environmental conditions.…”

Section: Introductionmentioning

confidence: 99%

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Modification of the boundary layer theory for calculating viscous drop oscillations in a uniform electrostatic field

Григорьев¹,

Paranin²,

Shiryaeva³

2012

Tech. Phys.

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Capillary oscillations on the free surface of a viscous conductive liquid drop placed in an electrostatic field are calculated. In an approximation linear in stationary deformation amplitude, the drop in this field has the shape of a spheroid extended along the field. The initial problem is modified and simplified in terms of the boundary layer theory by applying an approximation that is linear in the oscillation amplitude and quadratic in the eccentricity of the drop. The accuracy of the approximate solution relative to an exact one is estimated. It is shown that, with a rise in the electrostatic field strength (with an increase in the eccentricity of the drop) and in the viscosity of the liquid, the boundary layer at the free surface of the drop becomes thicker.

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