This article concerns reading the nanoscale heterogeneity thought responsible for colloid retention on surfaces in the presence of energy barriers (unfavorable attachment conditions). We back out this heterogeneity on glass surfaces by comparing mechanistic simulations incorporating discrete heterogeneity with colloid deposition experiments performed across a comprehensive set of experimental conditions. Original data is presented for attachment to soda lime glass for three colloid sizes (0.25, 1.1, and 1.95 μm microspheres) under a variety of ionic strengths and fluid velocities in an impinging jet system. A comparison of mechanistic particle trajectory simulations incorporating discrete surface heterogeneity represented by nanoscale zones of positive charge (heterodomains) indicates that a power law size distribution of heterodomains ranging in size from 120 to 60 nm in radius was able to explain the observed retention for all conditions examined. In contrast, uniform and random placement of single-sized heterodomains failed to capture experimentally observed colloid retention across the range of conditions examined.

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Surface roughness has been reported to both increase as well as decrease colloid retention. In order to better understand the boundaries within which roughness operates, attachment of a range of colloid sizes to glass with three levels of roughness was examined under both favorable (energy barrier absent) and unfavorable (energy barrier present) conditions in an impinging jet system. Smooth glass was found to provide the upper and lower bounds for attachment under favorable and unfavorable conditions, respectively. Surface roughness decreased, or even eliminated, the gap between favorable and unfavorable attachment and did so by two mechanisms: (1) under favorable conditions attachment decreased via increased hydrodynamic slip length and reduced attraction and (2) under unfavorable conditions attachment increased via reduced colloid-collector repulsion (reduced radius of curvature) and increased attraction (multiple points of contact, and possibly increased surface charge heterogeneity). Absence of a gap where these forces most strongly operate for smaller (<200 nm) and larger (>2 μm) colloids was observed and discussed. These observations elucidate the role of roughness in colloid attachment under both favorable and unfavorable conditions.

Many mechanisms of colloid retention in porous media under unfavorable conditions have been identified from experiments or theory, such as attachment at surface heterogeneities, wedging at grain to grain contacts, retention via secondary energy minimum association in zones of low flow drag, and straining in pore throats too small to pass. However, no previously published model is capable of representing all of these mechanisms of colloid retention. In this work, we demonstrate that incorporation of surface heterogeneity into our hemispheres-in-cell model yields all experimentally observed non-straining retention mechanisms in porous media under unfavorable conditions. We also demonstrate that the predominance of any given retention mechanism depends on the coupled colloid-collector-flow interactions that are governed by parameters such as the size and spatial frequency of heterogeneous attractive domains, colloid size, and solution ionic strength. The force/torque balance-simulated retention is shown to decrease gradually with decreasing solution ionic strength, in agreement with experimental observations. This gradual decrease stands in sharp contrast to predictions from mean field theory that does not account for discrete surface heterogeneity.

We herein demonstrate the cause of well-observed variant transport behaviors for apparently identical colloids in porous media under conditions of colloid-collector repulsion (unfavorable attachment conditions). We demonstrate that variant colloid transport behavior under unfavorable conditions can be explained by inherently variable colloid residence times prior to arrest on grains (collectors). We demonstrate that the residence time distributions derived from particle trajectory simulations incorporating representative nanoscale heterogeneity provide quantitative prediction of colloid transport under unfavorable conditions. We quantitatively predict hyper-exponential retention profiles in glass beads from representative nanoscale heterogeneity determined for glass, and we qualitatively predict nonmonotonic retention profiles in quartz sand from an estimated representative nanoscale heterogeneity for quartz. We also demonstrate that the transition from hyper-exponential to nonmonotonic profiles among glass beads versus quartz sand under otherwise equivalent conditions is primarily driven by greater grain angularity and consequent greater length and number of grain to grain contacts in quartz sand relative to glass beads. That continuum-scale transport behaviors emerge from upscaling of simulated pore-scale colloid residence times corroborates the utility of representative nanoscale heterogeneity for quantitative prediction of colloid transport under unfavorable conditions.