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Density-driven instabilities of variable-viscosity miscible fluids in a capillary tube.

Abstract：

:A linear stability analysis is presented for variable-viscosity miscible fluids in an unstable configuration; that is, a heavier fluid placed above a lighter one in a vertically oriented capillary tube. The initial interface thickness is treated as a parameter to the problem. The analysis is based on the three-dimensional Stokes equations, coupled to a convection-diffusion equation for the concentration field, in cylindrical coordinates. When both fluids have identical viscosities, the dispersion relations show that for all values of the governing parameters the three-dimensional mode with an azimuthal wave number of one 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. For the variable viscosity case, the growth rate does not depend on which of the two fluids is more viscous. For every parameter combination the maximum of the eigenfunctions tends to shift toward the less viscous fluid. With increasing mobility ratio, the instability is damped uniformly. We observe a crossover of the most unstable mode from azimuthal to axisymmetric perturbations for Rayleigh numbers greater than 10(5) and high mobility ratios. Hence, the damping influence is much stronger on the three-dimensional mode than the corresponding axisymmetric mode for large Rayleigh numbers. For a fixed mobility ratio, similar to the constant viscosity case, the growth rates are seen to reach a plateau for Rayleigh numbers in excess of 10(6). At higher mobility ratios, interestingly, the largest growth rates and unstable wave numbers are obtained for intermediate interface thicknesses. This demonstrates that, for variable viscosities, thicker interfaces can be more unstable than their thinner counterparts, which is in contrast to the constant viscosity result where growth rate was seen to decline monotonically with increasing interface thickness.

journal_name

Ann N Y Acad Sci

journal_title

Annals of the New York Academy of Sciences

authors

Meiburg E,Vanaparthy SH,Payr MD,Wilhelm D

doi

10.1196/annals.1324.032

subject

Has Abstract

pub_date

2004-11-01 00:00:00

pages

383-402

eissn

0077-8923

issn

1749-6632

pii

1027/1/383

journal_volume

1027

pub_type

杂志文章

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Density-driven instabilities of variable-viscosity miscible fluids in a capillary tube.