Model for predicting pressure drop and filtration efficiency in fibrous media

Spielman, Lloyd A.; Goren, Simon L.

doi:10.1021/es60016a003

Cited by 321 publications

(187 citation statements)

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“…2). This was in contrast to the shear stresses on the ECM fibers, which were higher overall on a perpendicularly aligned matrix than on those aligned in a random or parallel direction, as expected (Spielman and Goren, 1968;Jackson and James, 1986). In addition, both the pressure and shear drag on the cell were lower in perpendicularly aligned (vs. cubic) matrices (Fig.…”

Section: Resultsmentioning

confidence: 76%

“…Spielman and Goren presented permeability relationships for random and aligned fibrous matrices which have been substantiated by, or compare well with, later work by other groups (Spielman and Goren, 1968;Jackson and James, 1986;Higdon and Ford, 1996;Chernyakov, 1998). Their computations resulted in implicit relationships between a dimensionless permeability (K/ r f 2 , where r f is the fiber diameter) and the solid volume fraction of the medium, j s , for matrices with fibers aligned randomly, parallel to flow, or perpendicular to flow, respectively:…”

Section: Theorymentioning

confidence: 61%

“…Thus, by remodeling its local matrix in a perpendicular alignment to interstitial flow, the cell reduces its shear stress and drag forces, and slows the local flow around it. We can expect from Darcy's Law that K À 1 reflects the overall drag of the fibers (Spielman and Goren, 1968), and thus the drag on the matrix fibers in a perpendicularly aligned matrix is higher than that on fibers in the same matrix if it is aligned parallel to flow (Eqs. 2 and 3).…”

Section: Resultsmentioning

confidence: 99%

See 2 more Smart Citations

Cells in 3D matrices under interstitial flow: Effects of extracellular matrix alignment on cell shear stress and drag forces

Pedersen

Lichter

Swartz

2010

Journal of Biomechanics

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a b s t r a c tInterstitial flow is an important regulator of various cell behaviors both in vitro and in vivo, yet the forces that fluid flow imposes on cells embedded in a 3D extracellular matrix (ECM), and the effects of matrix architecture on those forces, are not well understood. Here, we demonstrate how fiber alignment can affect the shear and pressure forces on the cell and ECM. Using computational fluid dynamics simulations, we show that while the solutions of the Brinkman equation accurately estimate the average fluid shear stress and the drag forces on a cell within a 3D fibrous medium, the distribution of shear stress on the cellular surface as well as the peak shear stresses remain intimately related to the pericellular fiber architecture and cannot be estimated using bulk-averaged properties. We demonstrate that perpendicular fiber alignment of the ECM yields lower shear stress and pressure forces on the cells and higher stresses on the ECM, leading to decreased permeability, while parallel fiber alignment leads to higher stresses on cells and increased permeability, as compared to a cubic lattice arrangement. The Spielman-Goren permeability relationships for fibrous media agreed well with CFD simulations of flow with explicitly considered fibers. These results suggest that the experimentally observed active remodeling of ECM fibers by fibroblasts under interstitial flow to a perpendicular alignment could serve to decrease the shear and drag forces on the cell.

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Section: Resultsmentioning

confidence: 76%

Section: Theorymentioning

confidence: 61%

Section: Resultsmentioning

confidence: 99%

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Cells in 3D matrices under interstitial flow: Effects of extracellular matrix alignment on cell shear stress and drag forces

Pedersen

Lichter

Swartz

2010

Journal of Biomechanics

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“…Electrospun mats can be approximated as planar fibrous networks. From the review by Jackson and James [21], analytical permeability models for flow perpendicular to a 2-D array of cylinders developed by Happel [12] and by Spielman and Goren [15] fit the experimental data well in the solidity range ~0.05 to 0.3 (where solidity is defined as 1-porosity). Since Happel's equation is considerably simpler and does not involve implicit functions of permeability, Happel's model is chosen for this work.…”

Section: Introductionmentioning

confidence: 95%

“…Equations for permeability constants that account for the drag forces exerted on the liquid by the solid medium have been developed for flow through a 2-D array of cylinders that are aligned parallel [12,13] or perpendicular [12,13,14] to the direction of the flow, as well as through 3-D random arrays of cylinders [15]. Mao and Russell [16,17] included the effect of fiber orientation in both 2-D and 3-D arrays.…”

Section: Introductionmentioning

confidence: 99%

Permeability of electrospun fiber mats under hydraulic flow

Choong

Khan

2014

Journal of Membrane Science

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Hydraulic permeability of electrospun fiber mats under flow-induced compression has been modeled and verified experimentally. The permeation model accurately estimates the changes in solidity, and hence the permeability of the electrospun mats, over a range of pressure differentials. The model is based on Darcy's law applied to a compressible, porous medium, using Happel's equation for the permeability and Toll's equation for the compressibility of fiber mats. Hydraulic permeability of electrospun mats of bis-phenol A polysulfone (PSU) comprising fibers of different mean diameter, annealed at temperatures at and above the glass transition of the polymer, was measured for feed water pressures ranging from 5 kPa to 140 kPa. The electrospun mats are found to experience a decrease of more than 60% in permeability constant between 5 and 140 kPa due to the loss of porosity resulting from the flow-induced compression.

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The Effective Transmissivity of a Plane‐Walled Fracture With Circular Cylindrical Obstacles

Jasinski

Dąbrowski

2018

JGR Solid Earth

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Stimulated and propped fractures provide the conductive pathways in low matrix permeability rocks. We study the impact of fracture aperture and proppant size and fraction on the effective transmissivity of a stimulated fracture filled with a partial monolayer of proppant grains. The proppant grains are treated as circular cylindrical obstacles, and the fracture walls are planar. The key geometric parameters are the obstacle fraction f and the ratio between the fracture aperture and the obstacle diameter α. We use three‐dimensional Stokes flow numerical simulations to demonstrate that the fracture flow model given by the Reynolds equations may largely overestimate the flow rate. To circumvent the inability of the Reynolds model to fulfill the no‐slip boundary condition at the rims of the obstacles, we use the Brinkman flow model adapted to the case of fracture flow. The relative difference between the effective transmissivities computed with the Stokes and Brinkman models for systems with multiple obstacles is below 10% for fractions up to 0.5. We use the Brinkman model to study the effective transmissivity of a plane‐walled fracture with circular cylindrical obstacles. Systematic numerical simulations show that the normalized effective transmissivity is predominantly dependent on f and α, and the effects of obstacle ordering are minor. The presented numerical results can be used by petroleum engineers for estimating transmissivities of propped fractures under in situ conditions. The model can also be applied to microfluidic systems and for deriving first‐order estimates of the effective transmissivity of rough‐walled, natural fractures with load‐bearing contact areas.

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Model for predicting pressure drop and filtration efficiency in fibrous media

Cited by 321 publications

References 13 publications

Cells in 3D matrices under interstitial flow: Effects of extracellular matrix alignment on cell shear stress and drag forces

Cells in 3D matrices under interstitial flow: Effects of extracellular matrix alignment on cell shear stress and drag forces

Permeability of electrospun fiber mats under hydraulic flow

The Effective Transmissivity of a Plane‐Walled Fracture With Circular Cylindrical Obstacles

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