On the use of happel's model for filtration studies

Payatakes, A. C.; Rajagopalan, R.; Tien, Chi

doi:10.1016/0021-9797(74)90369-5

Cited by 30 publications

(12 citation statements)

References 5 publications

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“…There are more than 10 different CFT mechanistic models, each employing different environmental conditions, model geometries, or force/torque mechanisms [ Yao et al ., ; Payatakes et al ., , b; Rajagopalan and Tien , ; Paraskeva et al ., ; Burganos et al ., , ; Cushing and Lawler , ; Tufenkji and Elimelech , ; Long and Hilpert , ; Ma et al ., ; Nelson and Ginn , ]. Each of these mechanistic models is associated with one or more approximating correlation equations.…”

Section: Mechanistic Prediction Of Retention In Favorable and Unfavormentioning

confidence: 99%

“…This approach, as noted by Yao et al [1971], produced velocity distributions that were likely poor representations of realistic porous media. The isolated-sphere approach was subsequently modified to employ a Happel sphere-in-cell geometry [Happel, 1958] that included porosity, as well as constricted tube geometry [Payatakes et al, 1974a[Payatakes et al, , 1974bParaskeva et al, 1991;Burganos et al, 1992Burganos et al, , 1994. The most popular, the Happel sphere-in-cell approach, considers the collector, otherwise isolated from the influence of other collectors and perfectly spherical, to be surrounded by an envelope of fluid that is associated with the collector.…”

Section: The Geometry Of Mechanistic Modelsmentioning

confidence: 99%

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Predicting colloid transport through saturated porous media: A critical review

et al. 2015

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Understanding and predicting colloid transport and retention in water‐saturated porous media is important for the protection of human and ecological health. Early applications of colloid transport research before the 1990s included the removal of pathogens in granular drinking water filters. Since then, interest has expanded significantly to include such areas as source zone protection of drinking water systems and injection of nanometals for contaminated site remediation. This review summarizes predictive tools for colloid transport from the pore to field scales. First, we review experimental breakthrough and retention of colloids under favorable and unfavorable colloid/collector interactions (i.e., no significant and significant colloid‐surface repulsion, respectively). Second, we review the continuum‐scale modeling strategies used to describe observed transport behavior. Third, we review the following two components of colloid filtration theory: (i) mechanistic force/torque balance models of pore‐scale colloid trajectories and (ii) approximating correlation equations used to predict colloid retention. The successes and limitations of these approaches for favorable conditions are summarized, as are recent developments to predict colloid retention under the unfavorable conditions particularly relevant to environmental applications. Fourth, we summarize the influences of physical and chemical heterogeneities on colloid transport and avenues for their prediction. Fifth, we review the upscaling of mechanistic model results to rate constants for use in continuum models of colloid behavior at the column and field scales. Overall, this paper clarifies the foundation for existing knowledge of colloid transport and retention, features recent advances in the field, critically assesses where existing approaches are successful and the limits of their application, and highlights outstanding challenges and future research opportunities. These challenges and opportunities include improving mechanistic descriptions, and subsequent correlation equations, for nanoparticle (i.e., Brownian particle) transport through soil, developing mechanistic descriptions of colloid retention in so‐called “unfavorable” conditions via methods such as the “discrete heterogeneity” approach, and employing imaging techniques such as X‐ray tomography to develop realistic expressions for grain topology and mineral distribution that can aid the development of these mechanistic approaches.

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Section: Mechanistic Prediction Of Retention In Favorable and Unfavormentioning

confidence: 99%

Section: The Geometry Of Mechanistic Modelsmentioning

confidence: 99%

Predicting colloid transport through saturated porous media: A critical review

et al. 2015

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“…Colloid attachment under saturated conditions is commonly described by colloid filtration theory, originally developed by Yao et al (1971) According to this theory, the attachment rate coefficient is dependent on the mass transfer of colloids to the collector surface and subsequent colloid–surface interactions. The sphere‐in‐cell model was used in filtration theory (Happel, 1958; Payatakes et al, 1974) to study colloid mass transfer due to interception, sedimentation, and diffusion to a single spherical solid collector. At the column scale, filtration theory preserves the overall porosity by representing the liquid as a continuous sheath completely surrounding the collector grains of a porous medium.…”

Section: Collector Scalementioning

confidence: 99%

Colloid Transport and Retention in Unsaturated Porous Media: A Review of Interface‐, Collector‐, and Pore‐Scale Processes and Models

Bradford

Torkzaban

2008

Vadose Zone Journal

308

259

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A: AWI, air-water interface; DLVO, Derjaguin-Landau-Verwey-Overbeek; SWI, solid-water interface.S S : V Z M Our ability to accurately simulate the transport and reten on of colloids in the vadose zone is currently limited by our lack of basic understanding of colloid reten on processes that occur at the pore scale. This review discusses our current knowledge of physical and chemical mechanisms, factors, and models of colloid transport and reten on at the interface, collector, and pore scales. The interface scale is well suited for studying the interac on energy and hydrodynamic forces and torques that act on colloids near interfaces. Solid surface roughness is reported to have a signifi cant infl uence on both adhesive and applied hydrodynamic forces and torques, whereas non-Derjaguin-Landau-Verwey-Overbeek (DLVO) forces such as hydrophobic and capillary forces are likely to play a signifi cant role in colloid interac ons with the air-water interface. The fl ow fi eld can be solved and mass transfer processes can be quan fi ed at the collector scale. Here the potenal for colloid a achment in the presence of hydrodynamic forces is determined from a balance of applied and adhesive torques. The frac on of the collector surface that contributes to a achment has been demonstrated to depend on both physical and chemical condi ons. Processes of colloid mass transfer and reten on can also be calculated at the pore scale. Diff erences in collector-and pore-scale studies occur as a result of the presence of small pore spaces that are associated with mul ple interfaces and zones of rela ve fl ow stagna on. Here a variety of straining processes may occur in saturated and unsaturated systems, as well as colloid size exclusion. Our current knowledge of straining processes is s ll incomplete, but recent research indicates a strong coupling of hydrodynamics, solu on chemistry, and colloid concentra on on these processes, as well as a dependency on the size of the colloid, the solid grain, and the water content.

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“…The total number N of UBEs in series for a bed of height L is N = L/l, or more precisely, N should be taken as the integer closest to the value of L/l. Payatakes et al (1974b) presented the importance of selecting the particular porous media model to be used in trajectory calculations. They discussed the incompatibility between the Happel's model (as the porous media model) and the concept of unit collector and trajectory calculations.…”

Section: Constricted Tube Modelmentioning

confidence: 99%