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This study introduces a novel theoretical model for upscaling colloid transport from the grain scale to the Darcy scale under both favorable and unfavorable conditions. The model integrates colloid interception history, where an interception occurs when colloids enter the near-surface zone within 200 nm of a collector, to capture the traditional exponential retention profile, as well as the anomalous, non-exponential behaviors observed under unfavorable conditions. The development of this theoretical model is based on a two-stage framework: first, upscaling from the grain scale to the single-interception scale, followed by upscaling from the single-interception scale to the Darcy scale. The initial stage addresses the distribution of colloids corresponding to a given interception order. The second stage focuses on the distribution of colloids across multiple interception orders. The key innovation of this work is the inclusion of the colloid removal process, where a fraction, denoted by $$\alpha$$, is removed at each encountered interception, rather than with each grain passed, as specified by classical colloid filtration theory. Our model accounts for scenarios under unfavorable conditions wherein if $$\alpha$$ remains constant, the distribution is exponential, albeit shallower relative to favorable conditions. Additionally, the model considers cases where $$\alpha$$ varies with interceptions, leading to multi-exponential and nonmonotonic retention profile shapes. In both scenarios, the proposed theoretical model offers a mathematical representation of colloid retention profiles under favorable and unfavorable conditions, including those exhibiting anomalous shapes.
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Retention Site Contribution Toward Silver Particle Immobilization in Porous Media
Abstract This work investigates the role that pore structure plays in colloid retention across scales with a novel methodology based on image analysis. Experiments were designed to quantify–with robust statistics–the contribution from commonly proposed retention sites toward colloid immobilization. Specific retention sites include solid‐water interface, air‐water interface, air‐water‐solid triple point, grain‐to‐grain contacts, and thin films. Variable conditions for pore‐water content, velocity, and chemistry were tested in a model glass bead porous medium with silver microspheres. Concentration signals from effluent breakthrough and spatial profiles of retained particles from micro X‐ray Computed Tomography were used to compute mass balances and enumerate pore‐scale regions of interest in three dimensions. At the Darcy‐scale, retained colloids follow non‐monotonic deposition profiles, which implicates effects from flow‐stagnation zones. The spatial distribution of immobilized colloids along the porous medium depth was analyzed by retention site, revealing depth‐independent partitioning of colloids. At the pore‐scale, dominance and overall saturation of all retention sites considered indicated that the solid‐water interface and wedge‐shaped regions associated with flow‐stagnation (grain‐to‐grain contacts in saturated and air‐water‐solid triple points in unsaturated conditions) are the greatest contributors toward retention under the tested conditions. At the interface‐scale, xDLVO energy profiles were in agreement with pore‐scale observations. Our calculations suggest favorable interactions for colloids and solid‐water interfaces and for weak flocculation (e.g., at flow‐stagnation zones), but unfavorable interactions between colloids and air‐water interfaces. Overall, we demonstrate that pore‐structure plays a critical role in colloid immobilization and that Darcy‐, pore‐ and interface‐scales are consistent when the pore structure is taken into account.
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- Award ID(s):
- 1847689
- PAR ID:
- 10445350
- Publisher / Repository:
- DOI PREFIX: 10.1029
- Date Published:
- Journal Name:
- Water Resources Research
- Volume:
- 58
- Issue:
- 5
- ISSN:
- 0043-1397
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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