Mixing and Removal Processes in Complex Environmental Flow Systems

This dissertation investigates the roles of mixing and removal processes in complex environmental flow systems exhibiting anomalous transport, focusing on three distinct applications: porous media, fracture networks, and streams. Anomalous transport, characterized by deviations from classical advection-diffusion models, is explored through numerical and analytical models to address challenges in predicting solute behavior at multiple scales. In porous media, pore-scale simulations of solute transport under varying P\'eclet numbers reveal mechanisms governing the evolution of mixing interfaces, highlighting equilibrium conditions dictated by the interplay of advection and diffusion. For discrete fracture networks, simulations demonstrate that mixing dynamics are influenced by unique splitting events at fracture intersections, leading to novel temporal scaling laws. Finally, the study develops models to capture the transport and removal of environmental DNA (eDNA) and antibiotic-resistant genes (ARGs) in streams, providing tools for predicting decay rates and spatial distribution. The findings contribute to advancing predictive capabilities for mixing-limited reactions and improving models for subsurface transport, fracture dynamics, and environmental monitoring in stream systems. The developed methodologies and insights have broad implications for environmental engineering, hydrology, and reactive transport modeling.