Gases and Fluids

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

S. O. Shiryaeva, A. I. Grigor'ev, A. R. Paranin

P.G. Demidov Yaroslavl State University

Abstract: The capillary oscillations of a charged drop of a viscous liquid are calculated in terms of the boundary layer theory in an approximation linear in oscillation amplitude. Calculation is accompanied with the estimation of a relative error that arises when the exact solution is replaced by an approximate one. It is shown that, for the calculation accuracy in the framework of the boundary layer theory to be about several percent, the thickness of the boundary layer near the free surface of the drop must be several times larger than that at which the intensity of the eddy flow caused by the oscillating surface decreases by $e$ times. As the viscosity of the liquid grows, so does the thickness of the boundary layer.

Received: 03.11.2009
Accepted: 25.02.2010

 English version: Technical Physics, 2010, 55:10, 1419–1425

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