Dynamic modeling of deep‐bed filtration

Mackie, R. I.; Horne, R.M.; Jarvis, R. J.

doi:10.1002/aic.690331102

Cited by 56 publications

(24 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Choo and Tien 1995a developed a mathematical model Ž . similar to that of Mackie et al 1987 , again based on the concept of the sphere-in-cell model. Their model predicts that the deposited layer has nonuniform thickness and covers the entire surface of the grains.…”

Section: Introductionmentioning

confidence: 96%

See 1 more Smart Citation

Simulation of the dynamics of depth filtration of non‐Brownian particles

Burganos¹,

Skouras²,

Paraskeva³

et al. 2001

AIChE Journal

View full text Add to dashboard Cite

show abstract

Section: Introductionmentioning

confidence: 96%

“…Mackie et al 1987 developed a mathematical model to describe the evolution of the deposit on spherical grains. Calculated effluent concentration profiles and overall filter coefficients were found to be in qualitative agreement with experimental data for the initial stages of deposition.…”

Section: Introductionmentioning

confidence: 99%

Simulation of the dynamics of depth filtration of non‐Brownian particles

Burganos¹,

Skouras²,

Paraskeva³

et al. 2001

AIChE Journal

View full text Add to dashboard Cite

show abstract

“…The probability of binding is not constant over the support surface because the shear rate (the force per unit area that a cell must counteract to remain bound) is a strong function of position and greatly affects cell binding. Also taken into account is the fact that the probability of contact with a particular position on the support is not constant across the support surface (Jung and Tien, 1993;Mackie et al, 1987). Following the approach of Vaidyanathan and Tien (1991), we can show that, for streamline flow around the support, the relationship between the expected value of the probability of binding (adhesion efficiency) and the critical angular position, C , on the support past which binding will not occur is…”

Section: Theoretical Modelmentioning

confidence: 99%

Cell affinity separations using magnetically stabilized fluidized beds: Erythrocyte subpopulation fractionation utilizing a lectin‐magnetite support

Putnam

Namasivayam

Burns

2003

Biotech & Bioengineering

View full text Add to dashboard Cite

A magnetically stabilized fluidized bed is used to separate erythrocyte subpopulations. Binding specificity was obtained by immobilizing the lectin Helix pomatia Agglutinin (HpA) or Griffonia simplicifolia I (GSI) onto a magnetite-containing support. Separation of type A and type O erythrocytes with the lectin HpA was particularly effective, leading to a 94% purity of retained type A erythrocytes. A 3.1 +/- 0.6 log removal of type A erythrocytes was also accomplished leading to a 99.7% +/- 0.4% purity and 95% +/- 7% yield of type O erythrocytes in the collected effluent. Elution of the purified cells was accomplished using fluidization in the presence of a sugar competing for the lectin-erythrocyte binding site. A mathematical model based on the depth filtration model of Putnam and Burns (Chem Eng Sci 1997;52(1):93-105) was extended to include multicomponent cell adhesion. This filtration model is the first to take into account the finite binding capacity of the chromatographic support and is used to characterize the cell binding behavior and to determine optimal parameters and conditions that lead to high capacities and selectivities. Model parameter values and observations from in situ adsorption studies suggest that the non-spherical shape of the magnetite-based support allows for a more efficient utilization of the support surface area than the spherical shape. Using a 1.5-cm diameter laboratory column and realistic parameter values, the processing rates of the system are predicted to be at least an order of magnitude greater than the 10(8)/h cells that can typically be processed in packed bed cell affinity chromatography (CAC) systems.

show abstract

“…There have been some theoretical developments that account for the accumulation of particles in UBE models (e.g., Mackie et al, 1987;Choo and Tien, 1995;Putnam and Burns, 1997), and other simplified models that relate particle accumulation to changes in pore transmissivity (e.g., Hunt et al, 1993;Boller and Kavanaugh, 1995;Stephan and Chase, 2000). However, in general it is difficult to represent processes of particle mounding using trajectory analyses and hence, these types of analyses are best suited to modeling the efficiency of clean filter beds.…”

Section: Introductionmentioning

confidence: 98%

“…For example, the spherein-cell model (i.e., a solid spherical grain surrounded by a fluid envelope) referred to as Happel's model (Happel, 1958) is a popular choice of UBE. Mackie et al (1987) compute the 'collection efficiency' (i.e., ratio of particle mass collected on the filter to the total mass transported through the UBE) for Happel's model, using a particle trajectory analysis that accounts for gravitational and hydrodynamic drag forces (that are of most importance in non-colloidal systems), while Rajagopalan and Tien (1976) also include van der Waals forces between particles. Elimelech and coworkers (Elimelech and O'Melia, 1990;Song and Elimelech, 1995;Ryan and Elimelech, 1996;Ko and Elimelech, 2000) have combined trajectory analysis with detailed experimental investigations focusing on particle-to-grain surface interactions.…”

Section: Introductionmentioning

confidence: 99%

Filtration in a Porous Granular Medium: 1. Simulation of Pore-Scale Particle Deposition and Clogging

Kim

Whittle

2006

Transp Porous Med

View full text Add to dashboard Cite

This paper presents a numerical model for simulating the pore-scale transport and infiltration of dilute suspensions of particles in a granular porous medium under the action of hydrodynamic and gravitational forces. The formulation solves the Stokes' flow equations for an incompressible fluid using a fixed grid, multigrid finite difference method and an embedded boundary technique for modeling particle-fluid coupling. The analyses simulate a constant flux of the fluid suspension through a cylindrical model pore. Randomly generated particles are collected within the model pore, initially through contact and attachment at the grain surface (pore wall) and later through mounding close to the pore inlet. Simple correlations have been derived from extensive numerical simulations in order to estimate the volume of filtered particles that accumulate in the pore and the differential pressure needed to maintain a constant flux through the pore. The results show that particle collection efficiency is correlated with the Stokes' settling velocity and indirectly through the attachment probability with the particle-grain surface roughness. The differential pressure is correlated directly with the maximum mound height and indirectly with particle size and settling velocity that affect mound packing density. Simple modification factors are introduced to account for pore length and dip angle. These parameters are used to characterize pore-scale infiltration processes within larger scale network models of particle transport in granular porous media in a companion paper.

show abstract

Dynamic modeling of deep‐bed filtration

Cited by 56 publications

References 22 publications

Simulation of the dynamics of depth filtration of non‐Brownian particles

Simulation of the dynamics of depth filtration of non‐Brownian particles

Cell affinity separations using magnetically stabilized fluidized beds: Erythrocyte subpopulation fractionation utilizing a lectin‐magnetite support

Filtration in a Porous Granular Medium: 1. Simulation of Pore-Scale Particle Deposition and Clogging

Contact Info

Product

Resources

About