Publication type: Article in scientific journal
Type of review: Peer review (publication)
Title: Density-driven instabilities of miscible fluids in a capillary tube : linear stability analysis
Authors : Vanaparthy, Surya Harith
Meiburg, E.
Wilhelm, Dirk
DOI : 10.1017/S0022112003006499
Published in : Journal of Fluid Mechanics
Volume(Issue) : 497
Pages : 99
Pages to: 121
Issue Date: 25-Dec-2003
Publisher / Ed. Institution : Cambridge University Press
ISSN: 0022-1120
Language : English
Subject (DDC) : 530: Physics
Abstract: A linear stability analysis is presented for the miscible interface formed by placing a heavier fluid above a lighter one in a vertically oriented capillary tube. The analysis is based on the three-dimensional Stokes equations, coupled to a convection-diffusion equation for the concentration field, in cylindrical coordinates. A generalized eigenvalue problem is formulated, whose numerical solution yields both the growth rate and the two-dimensional eigenmodes as functions of the governing parameters in the form of a Rayleigh number and a dimensionless interfacial thickness. The dispersion relations show that for all values of the governing parameters the three-dimensional mode with an azimuthal wavenumber of 1 represents the most unstable disturbance. The stability results also indicate the existence of a critical Rayleigh number of about 920, below which all perturbations are stable. The growth rates are seen to reach a plateau for Rayleigh numbers in excess of 10^6 . In order to analyse the experimental observations by Kuang et al.(2002), which show that a small amount of net flow can stabilize the azimuthal instability mode and maintain an axisymmetric evolution, a base flow of Poiseuille type is included in the linear stability analysis. Results show that a weak base flow leads to a slight reduction of the growth rates of both axisymmetric and azimuthal modes. However, within the velocity interval that could be analysed in the present investigation, there is no indication that the axisymmetric mode overtakes its azimuthal counterpart.
Fulltext version : Published version
License (according to publishing contract) : Licence according to publishing contract
Departement: School of Engineering
Organisational Unit: Institute of Applied Mathematics and Physics (IAMP)
Appears in Collections:Publikationen School of Engineering

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