Many of the chemicals that move within fluid undergo reactions. Often the reactions convert toxic compounds into harmless by-products. An example is the cleanup of gasoline that has leaked into a groundwater aquifer. It is very difficult, using current models, to predict the duration or rate of the reactions, primarily because of poor mixing of the reactants. This defines a significant theoretical and practical problem, because most current models of reactive transport in hydrologic systems are based on empirical adjustments to classical laws, which are built upon the flawed well-mixed assumption. In order to make reliable predictions in such systems, novel and improved methods are critical for the scientists and engineers, and ultimately decision makers, stakeholders, and policy developers working in fields such environmental contamination and remediation.
However, the problem of mixing-limited reaction goes far beyond the hydrologic examples that motivated this proposal. Recent studies show that mixing-limited reactions play a dominant role in Earth-bound systems across a huge range of scales, including reactions in the atmosphere (e.g., ozone creation), in drinking-water aquifers (e.g., remediation of contaminants), in geologic basins (e.g., petroleum generation), and in magmas, hydrothermal areas, and ore bodies. This project will have application to many fields, including climate-change related atmospheric reactions, ecologic, and micro-biochemical systems.
The investigators have developed new computer models that demonstrate the need for new paradigms of simulating reactions in imperfectly-mixed systems. First, the project will apply the theoretical approach of "time subordination" that accounts for random particle migration time to active reaction sites. Subordination has been successfully applied to simple systems, but it remains to be proven that it can be extended to more complicated reactions, geometries, and flow patterns. Second, the project will develop a random continuum method that tracks the growth of concentration disturbances. These disturbances include low concentration zones that are the key to slower reaction rates. Third, the project will build on the new computer models, shown to be correct, for the purpose of benchmarking theoretical results and facilitating large-scale reactive simulations. All approaches will be unified through detailed mathematical analysis and application to well-studied laboratory and field experiments.
