Date of Award

Spring 5-2016

Embargo Period


Degree Type


Degree Name

Doctor of Philosophy (PhD)


Engineering and Public Policy


Elizabeth A. Casman

Second Advisor

Gregory Lowrey


Mathematical models improve our fundamental understanding of pollutant fate in the environment and facilitate risk assessment, environmental management, and policy development activities. For nearly a decade, researchers have struggled with the question of how to model nanoparticles (NPs), an emerging class of environmental contaminants whose behavior in surface waters and sediments is controlled by complex interactions between particle properties and environmental factors. Population balance models, which track the size distribution of a particle population as it changes due to physicochemical processes, are a promising alternative to classical mass balance models that only track the total NP mass. However, the strengths and weaknesses of different population balance methods have not yet been explored in-depth for NPs. This work introduces three projects that, together, (1) probe the influence of spatiotemporal variation in environmental conditions on NP fate, (2) investigate the influence of common simplifying assumptions on model predictions, and (3) explore population balance for problems of NP dissolution and aggregation in water. Focus is placed on spherical metal and metal oxide NPs. Chapter 1 reviews past and current approaches in NP fate modeling, highlights key challenges, and frames the scope and objectives of this work. Chapter 2 presents a sediment diagenesis model that explores the influence of organic carbon, dissolved oxygen, and naturally-occurring sulfides on the distribution and speciation of antibacterial silver NPs and their reaction by-products in freshwater sediments. Chapter 3 presents a coupled hydrologic, agricultural, and water quality model that predicts silver and zinc oxide NP fate in a freshwater watershed under spatiotemporally variable environmental conditions. This basin-scale model reveals the unintended consequences of simplifying assumptions commonly used in largescale fate models of NPs. Chapter 4 compares alternative population balance modeling frameworks that vary with respect to runtimes, accuracy, and extensibility to environmentally relevant systems and complex particle types. Chapter 5 summarizes key findings and identifies high-priority research vii areas for experimentalists and modelers interested in the development of next-generation models with greater relevance for scientific investigations at the laboratory scale as well as risk management and regulation at the river or watershed scale.