Parameters Driving Anomalous Transport in Colloids: Dimensional Analysis

The anomalous transport of identical colloids, characterized by multiexponential and nonmonotonic retention profiles, under unfavorable conditions, has been the subject of significant interest over the past few decades. This study conducts a dimensional analysis of the governing equations for colloid transport to explore the impact of various dimensionless groups on colloid attachment efficiency (α), defined as the ratio of the number of attached colloids to the number intercepted (i.e., those that enter the near-surface zone). The primary objective of this article is to identify the dimensionless groups responsible for explaining potential variation in α. Our analysis revealed that 15 dimensionless groups govern colloid transport in porous media, which we categorized into three groups: (i) hydrodynamic, (ii) DLVO, and (iii) surface charge heterogeneity dimensionless groups. We assessed the impact of each category on the magnitude of α via pore-assembly colloid trajectory simulations. Our findings indicate that the surface charge heterogeneity dimensionless groups exert a dramatic influence on the value of α compared to the mean-field DLVO or hydrodynamic groups. In particular, the surface charge heterogeneity dimensionless group, H_r (the ratio of the heterodomain radius to the radius of the colloid-surface zone of interaction), significantly impacts α in the approximate range of 0.6 < H_r < 2. As a result, within this range, even a slight variation in H_r causes a marked change in α, facilitating the transition between multiexponential and nonmonotonic retention profiles under unfavorable conditions.