Novel Computational Methods for Imperfectly-Mixed Chemical Reactions

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Many chemicals that move within fluids undergo reactions. Often these convert toxic compounds into harmless byproducts. One such example is the cleanup of gasoline that has leaked into a groundwater aquifer. Unfortunately, current mathematical models and computational methods that assume the reactants are well mixed fail to accurately predict the duration or rate of these reactions, primarily due to the poor mixing of associated reactants. Recent studies show that mixing-limited reactions play a dominant role in most Earth-bound systems across a wide range of scales, including reactions in atmospheric plumes, granular and fractured aquifers, sedimentary (e.g., petroleum-generating and carbon-dioxide-sequestering) basins, hydrothermal areas, and ore bodies. Imperfect mixing and modified dynamics also occur at the nanometer to micron scale in space and picosecond to microsecond scale in time, revealing the ubiquity of mixing-limited reaction, from molecular to global scales. Hence imperfect mixing poses a significant theoretical and practical problem because most current models of reactive transport in hydrological 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, improved methods are critical for scientists and engineers, and ultimately decision makers, stakeholders, and policy developers working in fields such as environmental contamination and remediation. This project develops new computational methods to simulate chemical transport and reaction dynamics, with applications to a variety of fields, including climate-change related atmospheric reactions as well as ecological and micro-biochemical systems. Graduate students participate in the research.The investigators recently developed new computational models that demonstrate the need for new methods to simulate reactions in imperfectly-mixed chemical systems. These stochastic Lagrangian methods directly track particle positions and calculate reactions based on the probability that particles are co-located. The methods correspond to perturbation expansions of the classical diffusion-reaction equation and also match several benchmark experiments. In this project, new algorithms are developed that account for random particle migration time and the statistical structure of initial conditions to properly simulate subgrid fluctuations. Preliminary studies show that the methods work well for bimolecular reactions in simple systems, but it remains to be proven that such techniques can be extended to more complicated reactions, geometries, and flow fields. Additionally, the investigators build upon a continuum approach to simulate reactions and track the growth of concentration perturbations. Finally, they construct and extend Lagrangian numerical methods that are known to be accurate and efficient, to benchmark theoretical results and facilitate large-scale reactive simulations. The approaches are unified through detailed mathematical analyses and applications to well-studied laboratory and field experiments. Graduate students participate in the research.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.