CNCS Graduate Certificate Recipient

Mark Frederick Steen

Thesis Title: The Convection of Binary Fluids in Porous Media

Ph.D. Final Defense Date:  March 21, 1999

Ph.D. Dissertation Committee:

Robert P. Behringer (Chair)
Henry S. Greensided
Laurens Howle
Roxanne Springer
Stephen Teitsworth

Abstract:

Currently, physics does not have answers for even some of the simplest questions related to pattern formation - the creation of spontaneous, non-trivial, spatial regularity in otherwise homogeneous systems. This dissertation describes experiments which use binary-fluid. porous-medium convection (BF-PMC) as a pattern-forming system. The experimental results do not support a commonly-used theoretical description in which all of the medium effects are included by using velocity equations based on Darcy's law. However, the introduction of the physically intuitive dispersion or "enhancing mixing" effect into a simple model produces results which are qualitatively consistent with the experiment. This indicates that enhanced mixing is a crucial piece of the description of BF-PMC. Moreover, BF-PMC may be a rare example of a physical system in which a forward bifurcation to time-dependent behavior can be effectively studied.

In these experiments, a small aspect ratio porous medium is filled with a mixture of alcohol and water, heated from below and cooled from the top. The heat transfer efficiency (Nusselt number) and the convective pattern are recorded. For separation ratios less than zero, a primary bifurcation to a novel, low-amplitude, time-dependent state is observed through Nusselt measurements. A secondary, subcritical bifurcation to large-amplitude, steady, overturning convection is also observed. This state is stable for long times and displays significant hysteresis.

An eight-mode, Lorenz-type model shows that when the effect of the medium is included through the permeability in Darcy's law, the nonlinear state above bifucation is finite-amplitude, oscillatory convection, which is not seen in the experiments. However, if a term representing enhanced solutal mixing due to the medium is included, the model results are qualitatively consistent with the experiment. Quantitative comparisons indicate that the enhanced mixing coefficient for the experimental medium is very large, which may result in significant secondary effects not included in the present model.

We conclude that enhanced solutal mixing must be included in any BF-PMC description and that BF-PMC may be a good candidate for further studies of a supercritical, time-dependent bifurcation.