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Natural Damped Frequencies of an Infinitely Long Column of Immiscible Viscous Liquids
Author(s) -
Bauer H. F.
Publication year - 1984
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19840641113
Subject(s) - viscous liquid , rotational symmetry , surface tension , viscosity , instability , mechanics , free surface , materials science , surface (topology) , thermodynamics , natural frequency , physics , vibration , geometry , mathematics , quantum mechanics
The determination of the damped natural frequencies of an infinitely long liquid column consisting of immiscible viscous liquids has been performed for various systems such as a single liquid column, two immiscible liquids in a rigid container, having an interfacial surface, a liquid around a rigid cylindrical center core, as well as two immiscible liquids with free liquid surface and interfacial surface. The frequency equation for the damped and coupled natural frequencies yields a complex determinant, from which the complex frequency has to be determined. It was noticed that besides the damped oscillatory root, which corresponds for vanishing viscosity to the undamped frequency of the frictionless liquid system, additional decayroots appear. Only the simple viscous infinite liquid column the frequency equation has been evaluated numerically. It could be shown that viscosity decreases the instability region for the axisymmetric (m = 0) case, and that this region depends upon the surface tension parameter.