Dynamics of small bubble interface perturbations in vertical hele-shaw cell with magnetic liquid under the action of normal magnetic field

A linearized problem of dynamics for small perturbations of the gas bubble rising in the Hele-Shaw cell filled with magnetic liquid is considered. It is reduced to searching of eigenvalues and eigenfunctions for a linear operator with periodic boundary conditions. The obtained operator is presented...

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Bibliographic Details
Published in:Mathematical modelling and analysis Vol. 9; no. 4; pp. 287 - 298
Main Authors: Cirulis, T., Lietuvietis, O., Cēbers, A.
Format: Journal Article
Language:English
Published: Taylor & Francis Group 01.01.2004
Subjects:
Chebyshev polynomials
eigenvalues and eigenfunctions problem
gas bubble
Hele-Shaw cell
magnetic liquid
the Degenerate Matrices method
ISSN:1392-6292, 1648-3510
Online Access:Get full text
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Summary:A linearized problem of dynamics for small perturbations of the gas bubble rising in the Hele-Shaw cell filled with magnetic liquid is considered. It is reduced to searching of eigenvalues and eigenfunctions for a linear operator with periodic boundary conditions. The obtained operator is presented as a sum of two linear operators: the second order differential operator with varying coefficients and the integro - differential operator with the singularity of the Cauchy type. The spectral problem is solved by the Degenerate Matrices (DM) method using Chebyshev polynomials of the first and second kind.
ISSN:1392-6292
1648-3510
DOI:10.1080/13926292.2004.9637260