Novel Computational Methods for Imperfectly-Mixed Chemical Reactions

许多在液体中运动的化学物质都会发生反应。它们通常会将有毒化合物转化为无害的副产品。一个这样的例子是清理泄漏到地下水含水层的汽油。不幸的是，目前假设反应物混合良好的数学模型和计算方法无法准确预测这些反应的持续时间或速率，主要原因是伴生反应物混合不良。最近的研究表明，混合限制反应在大多数大尺度的地球系统中起主导作用，包括大气羽流、粒状和裂隙含水层、沉积（例如，石油生成和二氧化碳封存）盆地、热液区和矿体中的反应。在纳米到微米的空间尺度和皮秒到微秒的时间尺度上，也会发生不完美的混合和修饰动力学，揭示了从分子到全局尺度上混合限制反应的普遍性。因此，不完全混合带来了重大的理论和实践问题，因为水文系统中大多数反应输运模型都是基于对经典定律的经验调整，而经典定律是建立在有缺陷的充分混合假设之上的。为了在这样的系统中做出可靠的预测，改进的方法对于科学家和工程师，以及最终在环境污染和补救等领域工作的决策者、利益相关者和政策制定者至关重要。该项目开发了新的计算方法来模拟化学传输和反应动力学，应用于各种领域，包括与气候变化相关的大气反应以及生态和微生化系统。研究生参与研究。研究人员最近开发了新的计算模型，证明需要新的方法来模拟不完全混合化学系统中的反应。这些随机拉格朗日方法直接跟踪粒子的位置，并根据粒子在同一位置的概率计算反应。该方法符合经典扩散反应方程的微扰展开，并与几个基准实验相匹配。在这个项目中，开发了新的算法，考虑随机粒子迁移时间和初始条件的统计结构，以适当地模拟子网格波动。初步研究表明，该方法适用于简单系统中的双分子反应，但仍有待证明，这种技术可以扩展到更复杂的反应，几何形状和流场。此外，研究人员建立了一个连续的方法来模拟反应和跟踪浓度扰动的增长。最后，他们构建并扩展了已知准确高效的拉格朗日数值方法，以对理论结果进行基准测试，并促进大规模反应模拟。这些方法是通过详细的数学分析和应用于充分研究的实验室和现场实验统一的。研究生参与研究。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.