Dimensionless Permeability Research Articles

Variable permeability effect on convection in binary mixtures saturating a porous layer

The Darcy Model with the Boussinesq approximation is used to study natural convection in a shallow porous layer, with variable permeability, filled with a binary fluid. The permeability of the medium is assumed to vary exponentially with the depth of the layer. The two horizontal walls of the cavity are subject to con- stant fluxes of heat and solute while the two vertical ones are impermeable and adiabatic. The governing parameters for the problem are the thermal Rayleigh number, RT, the Lewis number, Le, the buoyancy ratio, u, the aspect ratio of the cavity, A, the normalized porosity, e, the vari- able permeability constant, c, and parameter a defining double-diffusive convection (a = 0) or Soret induced convection (a = 1). For convection in an infinite layer, an analytical solution of the steady form of the governing equations is obtained on the basis of the parallel flow approximation. The onset of supercritical convection, R sub ; or subcritical, R sub ; convection are predicted by the present theory. A linear stability analysis of the parallel flow model is conducted and the critical Rayleigh number for the onset of Hopf's bifurcation is predicted numerically. Numerical solutions of the full governing equations are found to be in excellent agreement with the analytical predictions. List of symbols A Aspect ratio of the cavity (L 0 /H 0 ) D Mass diffusivity of species (m 2 /K) D 0 Thermodiffusion coefficient (m 2 /s K) g Gravitational acceleration (m/s 2 ) H 0 Height of porous layer (m) j 0 Constant mass flux per unit area (kg/m s) K Dimensionless permeability of the porous medium K 0 Reference permeability of the porous medium (m 2 ) k Thermal conductivity (W/(m K)) L 0 Width of fluid layer (m)

Permeability of aqueous foams

We perform forced-drainage experiments in aqueous foams and compare the results with data available in the literature. We show that all the data can be accurately compared together if the dimensionless permeability of the foam is plotted as a function of liquid fraction. Using this set of coordinates highlights the fact that a large part of the published experimental results corresponds to relatively wet foams (epsilon approximately 0.1). Yet, most of the foam drainage models are based on geometrical considerations only valid for dry foams. We therefore discuss the range of validity of the different models in the literature and their comparison to experimental data. We propose extensions of these models considering the geometry of foam in the relatively wet-foam limit. We eventually show that if the foam geometry is correctly described, forced drainage experiments can be understood using a unique parameter --the Boussinesq number.

On the motion of a porous sphere in a Stokes flow parallel to a planar confining boundary

An analysis is presented of the three-dimensional creeping flow in and around a porous sphere, modelled as a generalized Brinkman medium, near a smooth plane where the sphere (i) translates uniformly without rotating in an otherwise quiescent Newtonian fluid, (ii) rotates uniformly without translating in an otherwise quiescent Newtonian fluid, and (iii) is fixed in a shear field, which is uniform in the far field and has a linearly increasing velocity profile with increasing distance from the plane. The linear superposition of these three flow regimes is also considered for the special case of the free translational and rotational motion of a neutrally buoyant porous sphere in a shear field that is uniform in the far field. Exact series solutions to the momentum equations are derived for the velocity and pressure fields in the Brinkman and Stokes-flow regions. Coefficients in the series solutions for each flow regime are determined using recursion relations derived from the continuity equations in the Brinkman and Stokes-flow regions, from the interfacial boundary conditions on the porous spherical surface, and from the no-slip condition on the plane. Results are presented in terms of the drag force on the porous sphere and torque about the sphere centre as a function of the dimensionless clearance distance between the sphere and the rigid plane for several values of the dimensionless hydraulic permeability of the Brinkman medium. The free motion of the neutrally buoyant sphere is calculated by requiring that the net hydrodynamic drag force and torque acting on the sphere vanish. Results for this case are presented in terms of the dimensionless translational and rotational speeds of the porous sphere relative to the far-field shear rate as a function of the dimensionless clearance distance for several values of the dimensionless hydraulic permeability. The work is motivated by insights it offers into the behaviour of porous agglomerates, and by its potential utility in industrial, biological, biophysical, medicinal and environmental applications wherever gas or liquid suspensions of porous agglomerates might arise.

Smoothed Particle Hydrodynamics Modeling of Transverse Flow in Randomly Aligned Fibrous Porous Media

The Lagrangian smoothed particle hydrodynamics (SPH) method is employed to obtain a meso-/micro-scopic pore-scale insight into the transverse flow across the randomly aligned fibrous porous media in a 2D domain. Fluid is driven by an external body force, and a square domain with periodic boundary conditions imposed at both the streamwise and transverse flow direction is assumed. The porous matrix is established by randomly embedding a certain number of fibers in the square domain. Fibers are represented by position-fixed SPH particles, which exert viscous forces upon, and contribute to the density variations of, the nearby fluid particles. An additional repulsive force, similar in form to the 12-6 Lennard-Jones potential between atoms, is introduced to consider the no-penetrating restraint prescribed by the solid pore structure. This force is initiated from the fixed solid material particle and may act on its neighboring moving fluid particles. Fluid flow is visualized by plotting the local velocity vector field; the meandering fluid flow around the porous microstructures always follow the paths of least resistance. The simulated steady-state flow field is further used to calculate the macroscopic permeability. The dimensionless permeability (normalized by the squared characteristic dimension of the fiber cross section) exhibits an exponential dependence on the porosity within the intermediate porosity range, and the derived dimensionless permeability—porosity relation is found to have only minor dependence on either the relative arrangement condition among fibers or the fiber cross section (shape or area).

Simulating permeability of 3-D calendered fibrous structures

Many fibrous materials such as nonwoven materials are often consolidated by means of hot calenders, i.e., hot compaction rolls. Hot calendering compresses the fiber assembly and can cause changes in the structure. In nonwovens, calendering has an added function of thermally bonding the fibers at their respective crossovers to form a strong but yet somewhat porous material. Calendering causes a significant increase in the solid volume fraction (SVF) of the media and therefore, affects their permeability. To our knowledge, no work in the literature has been dedicated to modeling the permeability of calendered nonwovens. In this study, virtual nonwoven structures are generated and compressed from top and bottom to resemble the hot calendering process. In agreement with our experimental observations, it was found that the average SVF profile across the material's thickness turns into a U-shape profile after the calendering. In this work, the dimensionless permeability of the calendered media is computed using CFD tools and reported for different compaction ratios. Results of our simulations are compared with the experiment as well as the available empirical and/or analytical permeability models in the literature and good agreement, depending upon the SVF, is observed. We also studied the influence of orientation distribution of the fibers on the dimensionless permeability of the fabric and noticed that permeability decreases by increasing the directionality of the fibers. This is found to be primarily due to the fact that highly oriented uncompressed fiber-webs tend to have a higher SVF. Fiber-webs of identical SVF, however, exhibited almost identical permeabilities regardless of their fiber orientations.

Developing a new form of permeability and Kozeny–Carman constant for homogeneous porous media by means of fractal geometry

The semi-empirical Kozeny–Carman (KC) equation is the most famous permeability–porosity relation, which is widely used in the field of flow in porous media and is the starting point for many other permeability models. However, this relation has many limitations from its inception, and the KC constant is an empirical parameter which was proved to be not a constant. In this paper, we briefly reviewed the KC equation, its modifications and various models for the KC constant. We then derived an analytical expression for the permeability in homogeneous porous media based on the fractal characters of porous media and capillary model. The proposed model is expressed as a function of fractal dimensions, porosity and maximum pore size. The analytical KC constant with no empirical constant is obtained from the assumption of square geometrical model. Furthermore, a distinct linear scaling law between the dimensionless permeability and porosity is found. It is also shown that our analytical permeability is more closely related to the microstructures (fractal dimensions, porosity and maximum pore size), compared to those obtained from conventional methods and models.

Fractal-like tree networks increasing the permeability

The effective permeability of composites embedded with self-similar fractal-like tree networks is studied. The effective permeability tensor of the composites is derived and is found to be related to microstructures of the networks. The present results show that the larger the ratio of successive branching channel diameters, the higher the effective permeability; the higher the relative surface porosity of the tree networks and matrix, the higher the effective permeability; the denser the tree networks, the lower the effective permeability; the longer the branches, the lower the effective permeability. It is found that the dimensionless effective permeability of composites scales as the diameter exponent by K+(e,y) approximately beta alpham, with alpha approximately 4. It is also found that when m>1 and nbeta4/gamma<1, the effective permeability K+(e,y) scales as the iteration m, ln K+(e,y)/m approximately ln (nbeta4/gamma). The fractal-like tree networks can significantly increase the effective permeability of the composites compared to the traditional parallel nets under properly chosen structural parameters.

Stability of natural convection in superposed fluid and porous layers: Influence of the interfacial jump boundary condition

Macroscopic modeling of momentum transport at a fluid-porous interface has been improved by the derivation of a stress jump boundary condition related to the spatial variations of the effective properties of the porous medium at the interfacial region. This Communication concerns the influence of this jump condition on the onset of thermal natural convection in fluid/porous stratified layers. A linear stability analysis shows that, for small depth ratio, the effective jump coefficient strongly influences the bimodal marginal stability curves. At large wave numbers, the “fluid mode” (the convective flow is confined in the fluid layer) is found to be more unstable while the porous mode, corresponding to small wave numbers, remains unchanged. The influence of the thickness and the dimensionless permeability of the porous layer is also presented.

The transverse permeability of disordered fiber arrays: a statistical correlation in terms of the mean nearest interfiber spacing

In the porous media literature, unidirectional fibrous systems are broadly categorized as ordered or disordered. The former class, easily tractable for analysis purposes but limited in its relation to reality, involves square, hexagonal and various staggered arrays. The latter class involves everything else. While the dimensionless hydraulic permeability of ordered fibrous media is known to be a deterministic function of their porosity ϕ, the parameters affecting the permeability of disordered fiber arrays are not very well understood. The objective of this study is to computationally investigate flow across many unidirectional arrays of randomly placed fibers and derive a correlation between K and some measure of their microstructure. In the process, we explain the wide scatter in permeability values observed computationally as well as experimentally. This task is achieved using a parallel implementation of the Boundary Element Method (BEM). Over 600 simulations are carried out in two-dimensional geometries consisting of 576 fiber cross-sections placed within a square unit cell by a Monte Carlo procedure. The porosity varies from 0.45 to 0.90. The computed permeabilities are compared with earlier theoretical results and experimental data. Analysis of the computational results reveals that the permeability of disordered arrays with ϕ < 0.7 is reduced as the non-uniformity of the fiber distribution increases. This reduction can be substantial at low porosities. The key finding of this study is a direct correlation between K and the mean nearest inter-fiber spacing \(\bar{\delta}_{1}\), the latter depending on the microstructure of the fibrous medium.

Stability of Natural Convection in Superposed Fluid and Porous Layers Using Integral Transforms

A stability analysis of thermal natural convection in superposed fluid and porous layers is carried out. The two-layer system is described using a one-domain formulation, and the eigenvalue problem resulting from the stability analysis is solved using the generalized integral transform technique (GITT). The numerical results confirm that the onset of convection can have a bimodal nature depending on the depth ratio. The influence of the dimensionless permeability and thermal diffusivity ratio are investigated.

Disposition of Formononetin via Enteric Recycling: Metabolism and Excretion in Mouse Intestinal Perfusion and Caco-2 Cell Models

The purpose of this study was to determine the absorption and metabolism of formononetin using the mouse intestinal perfusion model, mouse intestinal homogenate, and the Caco-2 cell culture model. In the perfusion model where upper and lower small intestine were perfused simultaneously, absorption of formononetin was rapid and dimensionless effective permeabilities of formononetin (2.53-2.90) were similar to those for rats. Moreover, the amounts of sulfates excreted in mouse intestine (8-11 nmol/30 min/10 cm) were significantly higher than those for rats whereas the amounts of glucuronides excreted (7-10 nmol/30 min/10 cm) were comparable. Small amounts of formononetin glucuronide but not sulfate were found in mouse bile, but the total amounts were 120 times less than those for rats. Multidrug-resistance-related protein (MRP) inhibitors (leukotriene C(4) plus MK-571, C(26)H(26)ClN(2)O(3)S(2)) significantly decreased the excretion of glucuronide and sulfate in mouse intestine (52-74% for glucuronide, 13-26% for sulfate) and in Caco-2 cells (92% for glucuronide, 37% for sulfate). They also inhibited formation of conjugates in intestinal homogenate (approximately 60% for glucuronide, approximately 30% for sulfate) and Caco-2 cell lysate (approximately 92% for glucuronide, approximately 37% for sulfate). Organic anion transporter (OAT) inhibitors (estrone sulfate plus dihydroepiandrosterone sulfate) did not significantly change the excretion of formononetin conjugates in either model, even though they significantly decreased the formation of both. In conclusion, our study showed that formononetin has similar absorption in rat and mouse intestine, but metabolism was species-dependent. The mouse perfusion model may have an advantage over the rat intestinal perfusion model for flavonoid disposition studies in that both sulfates and glucuronides are excreted, as shown in humans.

The effect of channel-to-channel gas crossover on the pressure and temperature distribution in PEM fuel cell flow plates

The air flow in a simplified model of the flow plate and adjacent diffusion layer of a PEM fuel cell has been numerically studied. The flow plate has been assumed to have serpentine flow channels with a square cross-section. It has been assumed that the flow in the porous diffusion layer can be modelled by using Darcy’s law. It has also been assumed that there is a uniform rate of heat generation at the base of this diffusion layer. The three-dimensional flow and temperature distribution in the flow plate-diffusion layer combination has been numerically studied by writing the governing equations in dimensionless form and solving the resultant equations using a commercial software package. As a result of the pressure drop along the flow channel, there can be crossover of air through the porous diffusion layer from one part of the channel to another. The conditions under which this crossover becomes important and the effect this crossover on the pressure distribution in the channel and the temperature distribution in the flow plate has been examined in this study. Attention has been given to flow plates having a single serpentine channel. Various numbers of flow passes through the plates have been considered these flow passes leading to what are effectively a series of parallel serpentine channels in the plate. The effects of Reynolds number, relative flow plate material thermal conductivity, dimensionless permeability of the diffusion layer and of flow channel geometry on the channel flow and the plate temperature distribution have been numerically examined and related to air crossover.

Quantitative description of foam drainage: transitions with surface mobility.

We have performed forced drainage experiments on aqueous foams of bubble diameters D varying from 0.18 to 8 mm, and made with different surfactant and protein solutions (providing different surface viscoelastic properties). Changing bubble size or surface properties allows to evolve between two drainage regimes, the respective dimensionless permeabilities also varying with these parameters. We show that the bubble size and surface properties can be incorporated into a single surface mobility parameter that controls the transition between the two drainage regimes. The permeability measurements indicate how do the hydrodynamic resistances of the foam channels and nodes depend on surface mobility. Taking advantage of the large range of experimental conditions, leading to a variation of the mobility parameter over more than 3 decades, a simple and consistent description of both the drainage regimes and the transition in between them is obtained. For the smallest bubbles (D < 0.5 mm) anomalous behaviors are observed and discussed.

Advective flow in a sludge floc.

The interior of sludge floc is highly heterogeneous, while the large pores in the floc control the advective flow. This work for the first time numerically details fluid flow and mass transfer processes in pores of activated sludge floc. The dimensionless permeabilities and mass dispersion coefficients were contoured against pore size ratio and the floc Reynolds number. With a pore size less than 20% of the floc size, the commonly adopted homogeneous model overestimates the floc permeability, and pore velocity is less than 2% of the bulk velocity. This is particularly true for flocs with low porosity. Although the convective flux is low, the dispersive mass transfer rate can be much higher than the diffusional rate, attributable to the strong Taylor dispersion effect. The three-dimensional pore structures in waste activated-sludge floc were identified using confocal laser scanning microscope (CLSM) images. Large pores were used to numerically estimate the permeability and dispersion coefficient for these pores. The permeability and the dispersion coefficient of the tortuous pores can be one order of magnitude lower than those for the equivalent straight pores. Besides the dispersion effect, the pore tortuosity appeared as the most important geometrical factor retarding the advective flow in the sludge pores. In addition, the small side pores connected to the large pore had only a mild effect on the flow process, and can be neglected in analysis.

On the motion of a sphere in a Stokes flow parallel to a Brinkman half-space

A three-dimensional analysis is presented of the Stokes flow, adjacent to a Brinkman half-space, that is induced or altered by the presence of a sphere in the flow field that (a) translates uniformly without rotating, (b) rotates uniformly without translating, or (c) is fixed in a shear flow that is uniform in the far field. The linear superposition of these three flow regimes is also considered for the special case of the free motion of a neutrally buoyant sphere. Exact solutions to the momentum equations are obtained in terms of infinite series expansions in the Stokes-flow region and in terms of integral transforms in the Brinkman medium. Attention is focused on the approach to the asymptotic limit as the ratio of Newtonian- to Darcy-drag forces vanishes. From the leading-order asymptotic approximations, implicit recursion relations are derived to determine the coefficients in the series solutions such that those solutions exactly satisfy the boundary and interfacial conditions as well as the continuity equations in both the Stokes-flow and Brinkman regions. For each of the three flow regimes considered, results are presented in terms of the drag force on the sphere and torque about the sphere centre as a function of the dimensionless separation distance between the sphere and the interfacial plane for several small values of the dimensionless hydraulic permeability of the Brinkman medium. Finally, the free motion of a neutrally buoyant sphere is found by requiring that the net hydrodynamic drag force and torque acting on the sphere vanish. Results for this case are presented in terms of the dimensionless translational and rotational speeds of the sphere as a function of the dimensionless separation distance for several small values of the dimensionless hydraulic permeability. The work is motivated by its potential application as an analytical tool in the study of near-wall microfluldics in the vicinity of the glycocalyx surface layer on vascular endothelium and in microelectromechanical systems devices where charged macromolecules may become adsorbed to microchannel walls.

LATTICE-BOLTZMANN SIMULATIONS OF FLOW THROUGH NAFION POLYMER MEMBRANES

Simulations of flow through three-dimensional porous structures of NAFION polymer membranes are performed with a Lattice-Boltzmann method (LBM) for incompressible fluid. Geometry data of NAFION are constructed from a result of a dissipative particle dynamics simulation for three values of the water content, 10%, 20%, and 30%, and are used as the geometry input for the LBM. Permeability of the porous structure is extracted from results of the LBM simulation using Darcy's low. The permeability K is shown to be expressed as K = L2 × Ktpl with a characteristic length L and the dimensionless permeability Ktpl depending only on the topological structure of the porous media. Dependence of Ktpl is examined on the pressure gradient, the fluid viscosity, and the resolution of the computational grid.

An Explicit Physics-Based Model for the Transverse Permeability of Multi-Material Dual Porosity Fibrous Media

A simple, explicit model for the transverse permeability of porous media comprised of alternating layers of tows of varying permeability has been proposed. The development of the model is based on results of numerical simulations as well as an earlier developed analytical model for the permeability of such systems (Markicevic and Papathanasiou, 2003). Based on the above, as well as on physical arguments regarding the flow across such dual porosity media, we formulate an explicit model in terms of dimensionless permeabilities. Extensive validation of the model is carried out through numerical simulations using the CFD package FIDAP. A good agreement between the permeabilities predicted by the simple explicit model and those calculated numerically is found. From this model, the form of a master curve for the permeability of such system has been deduced.

Intestinal Metabolism and Absorption of Cholecystokinin Analogs in Rats

Intestinal metabolism and poor permeability were known to be major barriers for oral absorption of large peptide drugs. Dimensionless wall permeability values of C-terminal octa- and tetra-peptides cholecystokinin analogs (CCK8 and CCK4) were estimated and found out to be greater than 1, suggesting no permeability-limited absorption for CCK analogs. Thus, a strategy employing enzyme inhibitors and a specific delivery site to improve the absorption was developed and tested with CCK8, followed by identification of metabolites of the analogs and their participating enzymes in rabbit brush-border membrane vesicles. Thiorphan and amastatin, a specific enzyme inhibitor for enkephalinase and aminopeptidase, respectively, in pH 4 buffer solution were coadministered with CCK8 to the ileum in fistulated rats. The absolute bioavailability (F) of CCK8 was 5.4% and increased to 19% in the presence of the enzyme inhibitors, while the F values following oral administration were close to zero. These results indicate that peptide oral delivery is possible.

Hydrodynamic lubrication of porous journal bearings using a modified Brinkman-extended Darcy model

A numerical solution for the hydrodynamic lubrication of finite porous journal bearings considering the flexibility of the liner is introduced. The Brinkman-extended Darcy equations and the Stokes' equations are utilized to model the flow in the porous region and fluid film region, respectively. A stress jump boundary condition at the porous media/fluid film interface and effects of viscous shear are included into the lubrication analysis. Elrod's cavitation algorithm, which automatically predicts film rupture and reformation in the bearing, is implemented in the solution scheme. The present analysis predictions for pressure distributions, load carrying capacity, and friction factor are in good agreement with three different sets of experimental results available in the literature. Furthermore, the effects of dimensionless permeability parameter, and stress jump parameter on performance parameters such as load carrying capacity, side leakage, friction factor, and attitude angle, are presented and discussed.

Coupled ice–till deformation near subglacial channels and cavities

AbstractPrevious models of ice–till deformation near subglacial channels or cavities neglect the fact that the motions of the two materials are coupled, and thus the interface between ice and till may not remain stationary. Here, we analyze in succession two models which address the effect of such coupling via specification of appropriate continuity conditions for stress and velocity across the interface. The modelled scenario is that of a shallow channel–cavity, with its long axis parallel to the principal ice-flow direction, overlying actively deforming till sediments. By applying asymptotic techniques, we investigate how the pattern and velocity of the creep flow depend generally on the ratio between the ice and till viscosities, and on the deforming-till thickness. A more sophisticated, non-linear rheology for till sediments is then introduced. It reveals that the two-way interaction between water percolation and deformation in the till will enhance the localization of sediment flow near the channel margins. The length scale over which transition of effective stress in the till takes place — from its relatively high, far-field value to the low, channel value — is found to depend critically on a dimensionless permeability parameter (Λ). In any case, coupled deformation causes sediment (and ice) flow towards the channel, subsidence of the ice–till interface just outside the channel, and extension of the area over which the ice is in contact with till. Apart from having direct implications for subglacial sediment transport, these results indicate that coupled deformation can contribute significantly to the spatial evolution of stress distribution under a glacier, and thus its incorporation into future sliding and drainage theories for a soft bed should be considered essential.