Reaction rate scaling in porous media in the transport controlled regime

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This research applies a theory of solute transport in porous media developed by the investigator to predict the time dependence of chemical reaction rates near the earth's surface. Chemical weathering rates, for example, of silicate minerals, have significant impacts on the global carbon cycle, with implications for climate change, extinctions, and soil production. It is well known that chemical weathering rates in the earth's crust decrease rapidly with increasing time, diminishing by as much as seven orders of magnitude (a factor of 10 million) as the time scale for observation increases from hours to millions of years. These weathering processes are complex. A full solution would require simultaneous treatment of the chemical equilibration of various compounds on particle surfaces and in solution, the movement of reagents and reaction products through the porous media, and changes in the nature of the particle surfaces. Researchers apply the greatly simplifying assumption that weathering rates are proportional to solute transport velocities, which they know how to predict. Without reagents, the reactions do not occur; without removal of the weathering products, reactions reach equilibrium and cease. As the weathered layer of the surface deepens, the transport paths that bring reacting species together become longer and more tortuous (i.e., they exhibit frequent changes in direction). This research clarifies the degree to which the paths become more tortuous and thus how drastically the reactions are slowed. In addition, it provides insight into how the tortuosity of paths relevant for solute transport can be altered. Investigators' results may also applicable to rates of deposition and leaching of toxic chemicals in the subsurface, making them relevant to a wide range of threats to our environment. Nutrient transport in agricultural run-off can be a serious threat to streams, estuaries, and near-shore environments. On the other hand, efficient nutrient transport in the shallow subsurface enhances the success of industrial agriculture. Understanding of how to influence the tortuosity of such paths can thus aid in the optimization of agricultural and environmental needs. The present research is relevant not only for solute transport in fluid flow, but also for applications as diverse as cellular mitosis, blood perfusion in the brain, chromatography, filtration, secondary oil recovery, catalysis, the behavior of packed bed reactors, degradation of building materials, tissue physiology, migration and epidemiology, heat dispersion in foams and the internal dynamics of the atom.