The stability and mixing of a density-stratified horizontal flow in a saturated porous medium

Creators: List, E. John

Abstract

The mixing of two miscible fluids in motion in a saturated isotropic porous medium and the stability of the density interface between them has been studied. The density interface was formed by a line source introducing a denser fluid into a uniform confined horizontal flow. It was shown that the half-body thus formed may be approximated to within the density difference by the shape when the densities are equal. The mixing of the two fluids by lateral dispersion along such an interface was investigated experimentally and it was found that up to density differences of at least 1 per cent there was no observable effect on the lateral dispersion coefficient. A theoretical investigation has been made of the stability of the uniform two-dimensional horizontal motion of two miscible fluids of different density in a saturated, isotropic, homogeneous porous medium. The fluid of higher density overlay the lower density fluid and both were moving with the same seepage velocity in the same direction. The analytical solution for the stability was obtained from the continuity equation, Darcy's law and the dispersion equation by investigating the stability of arbitrary sinusoidal perturbations to the velocity vector and the density profile prescribed by the lateral dispersion of one fluid into the other. A stability equation similar to the Orr-Sommerfeld equation was obtained and a neutral stability curve in a wave number-Rayleigh number plane was found by two approximate methods. The growth rates of instabilities were investigated for a linear density profile and it has been found that although the flow was always unstable the growth rates of unstable waves could be so low as to form a quasi-stable flow; examples of such flows have been demonstrated experimentally.

Additional Information

© 1965 W. M. Keck Laboratory of Hydraulics and Water Resources. California Institute of Technology. To Professor Norman H. Brooks the writer expresses his gratitude and appreciation for the guidance and advice so kindly offered throughout the investigation. The writer is also indebted to Dr. Robert C-Y Koh for numerous discussions on many aspects of the study and to Dr. P. G. Saffman for a discussion during the development of the instability theory. Financial assistance received by the writer in the form of Graduate Teaching Assistantships during 1963 and 1964, and a Graduate Research Assistantship during 1965, from the California Institute of Technology is gratefully acknowledged. The investigation was supported from May, 1964 by Research Grant WP-0068Q from the National Institute of Health, United States Public Health Service. The experiments were carried out in the W. M. Keck Laboratory of Hydraulics and Water Resources at the California Institute of Technology. The writer wishes to thank Mr. Elton F. Daly and Mr. Robert L. Greenway for their invaluable assistance in the design and construction of the laboratory equipment, Mr. Paul Kochendorfer for his willing aid in the laboratory and Mr. Carl Eastvedt for the photography. This report is a minor revision of a thesis of the same title submitted by the writer in May 1965, to the California Institute of Technology in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Applied Mechanics.

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