Unraveling Anomalous Transport in Colloids: Why Does It Happen and How Can We Parsimoniously Model It?

The study of colloid transport in porous media has been a subject of significant interest since the early 1970s. Colloids are commonly found in natural environments in the form of clay minerals, metal oxides, bacteria, viruses, and organic macromolecules. Their movement within groundwater and surface water systems plays a crucial role in the distribution of contaminants, as colloids themselves may be considered contaminants. Consequently, a thorough understanding of colloid transport mechanisms and the ability to predict their migration into groundwater are essential for safeguarding both ecological and human health, as well as for the effective protection of groundwater aquifers. The terms "favorable" and "unfavorable" conditions in colloid attachment refer to the absence and presence, respectively, of a repulsive energy barrier between colloids and the grains of the porous medium. Under favorable conditions, colloid filtration theory has been successfully employed to describe colloid retention profiles, quantified as the number of attached colloids as a function of downstream distance, using an exponential distribution. This exponential form corresponds to a first-order decay rate in the advection-dispersion equation. However, colloid filtration theory fails to accurately predict retention profiles under unfavorable conditions, particularly when experimental data exhibit anomalous (non-exponential) behaviors, such as multi-exponential or nonmonotonic retention profiles. This thesis, through numerical simulations of colloid transport under unfavorable conditions, aims to (i) investigate and propose potential explanations for the observed anomalous non-exponential retention profiles under unfavorable conditions, manifested as multi-exponential and nonmonotonic shapes, and (ii) develop upscaled models capable of predicting colloid transport and retention under unfavorable conditions, including the ability to capture these anomalous non-exponential shapes. In pursuit of these objectives, we examine the influence of initial injection conditions on colloid retention profiles under unfavorable conditions. The findings indicate that differences in injection conditions, specifically uniform versus flux-weighted injection, offer a plausible explanation for the experimental observation of anomalous retention profiles under such conditions. Furthermore, we introduce both empirical (random walk) and theoretical upscaling models designed to predict anomalous retention profiles under unfavorable conditions. To complement these efforts, a dimensional analysis of the governing equations for colloid transport is conducted to identify key parameters influencing the manifestation of anomalous retention behaviors. Overall, this research establishes a theoretical and empirical framework for predicting anomalous colloid transport under unfavorable conditions. Additionally, it raises new questions regarding the governing parameters that drive this anomalous behavior, thereby paving the way for future investigations to explore these aspects in greater detail.