Critical Pore Radius Research Articles

Permeability of porous media: Role of the critical pore size

AbstractThe knowledge of the permeability of porous media is crucial to understand fluid flow in various natural and artificial materials. Due to the complex nature of pore structure, the pore characteristic (porosity and pore radius) determining the permeability has long been under discussion. Here we determined the critical pore radius, which is the radius of the largest sphere that can freely pass through a porous medium, using the water expulsion method, an experimental technique measuring the pressure at which gas passes through a water‐saturated porous medium. We demonstrate that the critical pore radius correlates well with the permeability for a variety of porous granular media and volcanic products with an extensive range of porosities (0.71%–50%) and permeabilities (10−20–10−10 m2). We also obtained a porosity‐critical pore radius‐permeability relationship that provides a better prediction of the permeability compared with predictions obtained by previous correlations.

A theoretical study of the occurrence state of shale oil based on the pore sizes of mixed Gaussian distribution

The analysis of the occurrence state of crude oil in shale rock is crucial for the formation evaluation of shale oil reservoirs. A method based on Gaussian Mixture Model for estimating the fractions of physically adsorbed, immobile (trapped in the pore space resulting from van der Waals), and free oil while considering both organic and inorganic pores is established. In this work, the critical pore radius for immobile oil is assumed to be equal to the thickness of the adsorption region. A sensitivity analysis of the derived formulae is conducted to demonstrate the following: (a) physically adsorbed and immobile oil in shale rock are primarily distributed within organic pores; (b) the ratio of physically adsorbed or free oil is dominated by the organic porosity ratio; (c) the ratio of immobile oil is dominated by organic parameters, while inorganic factors only possess a minor impact; (d) the ratio of physically adsorbed oil is slightly underestimated using a pure circular pore model; and (e) the fractions of immobile, physically adsorbed and free oil are most likely to exist in the ranges [0, 10%], [20%, 30%], and [65%, 80%], respectively. A sensitivity analysis on the average pore radius demonstrates that the non-negligible, if not substantial, quantities of physically adsorbed and immobile oil in shale rock are very unique. Consequently, the efficient exploitation of immobile oil is probably a new fundamental issue in enhanced shale oil recovery research. Currently, the porosity related to immobile oil can be regarded as “dead porosity” and excluded from measured porosity for more accurate formation evaluation. Finally, comparisons are constructed to illustrate the superiority of the Gaussian Mixture Model in the depiction of the complicated and random porous structure of shale rock. This work can help with the formation evaluation of shale oil reservoirs and will provide insight toward the development of shale resources.

Equation-of-state modeling of confined-fluid phase equilibria in nanopores

Perturbed-chain statistical associating fluid theory (PC-SAFT) is coupled with Young–Laplace equation to investigate and represent fluid-phase equilibria in nanosize pores. The calculated pure-substance properties at capillary condensation (critical temperature, critical pore radius, surface tension, condensed-phase equilibrium pressure, and saturated densities) are found to be consistent with experimental data, theoretical models, and molecular simulation. The information obtained for pure substances can then be applied to predict the phase equilibria of fluid mixtures in porous mediums. The promising results presented in this work establish a strong platform for further development of an effective model toward engineering applications in real settings of confined fluids such as chemical systems encountered in unconventional reservoirs (e.g., shale oil and shale gas).

The effect of surface oxidized modification on the mechanical properties of SiC3D/Al

In this study, the effect of surface oxidized modification on the mechanical properties of silicon carbide 3D/aluminum composites (SiC3D/Al) is explained. The basis of this study may be outlined as follows: the shear force of extrusion testing proves the effect of SiO2 layer thickness from the perspective of interface failure mechanism; and the critical pore radius explains the effect of SiO2 layer distribution from the perspective of a biconnected structure. The compression and flexural tests prove that compressive strength is mainly affected by the average SiO2 layer thickness. Bending strength is affected by the critical pore radius, which is the primary contributor to SiO2 layer thickness of the special structural space and stress concentration. Thus, the structural characteristics of SiC3D/Al affect the SiO2 growth mechanism, as indicated by the aforementioned results.

Paranematic-to-nematic ordering of a binary mixture of rodlike liquid crystals confined in cylindrical nanochannels.

We explore the optical birefringence of the nematic binary mixtures 6CB_{1-x}7CB_{x} (0 ≤ x ≤ 1) embedded into parallel-aligned nanochannels of mesoporous alumina and silica membranes for channel radii of 3.4 ≤ R ≤ 21.0 nm. The results are compared with the bulk behavior and analyzed with a Landau-de Gennes model. Depending on the channel radius the nematic ordering in the cylindrical nanochannels evolves either discontinuously (subcritical regime, nematic ordering field σ<1/2) or continuously (overcritical regime, σ>1/2), but in both cases with a characteristic paranematic precursor behavior. The strength of the ordering field, imposed by the channel walls, and the magnitude of quenched disorder varies linearly with the mole fraction x and scales inversely proportionally with R for channel radii larger than 4 nm. The critical pore radius, R_{c}, separating a continuous from a discontinuous paranematic-to-nematic evolution varies linearly with x and differs negligibly between the silica and alumina membranes. We find no hints of preferred adsorption of one species at the channels walls. By contrast, a linear variation of the nematic-to-paranematic transition point T_{PN} and of the nematic ordering field σ versus x suggests that the binary mixtures of cyanobiphenyls 6CB and 7CB keep their homogeneous bulk stoichiometry also in nanoconfinement, at least for channel diameters larger than ∼7 nm.

Pore Formation in a Membrane Submitted to High Voltages. Influence of the Membrane Vicosity

We present here a new model of pore formation based on physical considerations of membrane energy. The idea is to revisit the pore expansion theory, as described by Weaver, Chizmadzhev et al. [4] in the 90's. We first recover the curvature-driven closure of the pore as obtain by Kroeger et al. [2], thanks to Langevin equation written on the pore area instead of the pore raldius. Then we consider the influence of the membrane viscosity around the region where pores have already appeared. This changes in membrane viscosity have been reported in the experiments of Tsai et al. [3] Around the pore region, the mobility of the lipids is constraint, which makes the membrane viscosity decrease locally. Then, once a critical pore radius is reached, it costs more to enlarge the pore, than to create another pore elsewhere. This has also an influence on the number of pores, which are hardly created in the high viscocity regions. Our model avoids an important drawback of the previsous models: the pore radius and the pore density cannot grow infinitely unlike the model of Krassowska, Neu et al [1]. After the derivation of the equations, we will present numerical simulations that corroborate quantitatively the experimental data obtained by patch-clamp experiments.[1] K. DeBruin et al. Modelling electroporation in a single cell. Biophysical Journal, 77, 1999.[2] Jens H Kroeger, et al.Curvature-driven pore growth in charged membranes during charge-pulse and voltage-clamp experiments. Biophysical journal, 96(3), 2009.[3] J. Tsai, et al. Non-brownian diffusion of membrane molecules in nanopatterned supported lipid bilayers. Nano Letters, 8(2), 2008.[4] J.C. Weaver and Y.A. Chimazdzhev. Theory of electroporation: A review. Bioelectrochemistry and Bioenergetics, 41, 1996.

Microstructural Evolution During Vacuum Sintering of Yttrium Aluminum Garnet Transparent Ceramics: Toward the Origin of Residual Porosity Affecting the Transparency

Controlling residual amount of defects in transparent ceramics is a major challenge for laser applications. This study was focused on microstructural evolution of Nd:YAG ceramics during their reactive solid‐state sintering which was correlated to their optical transmittance. From microstructural observations, the microstructural maps and grain size‐density and grain size‐pore size sintering trajectories of Nd:YAG ceramics were established as a function of silica content. For densities higher than 99.7%, the occurrence of intragranular porosity was correlated to a critical pore radius of 0.16 μm. Silica appears to favor the formation of intragranular porosity which was attributed to the increasing of the grain growth rate compared with the densification one. An analytical model was established by coupling the analytical laws derived from sintering trajectories and the classical theory of light diffusion, allowing to correlate the microstructural features of transparent Nd:YAG ceramics to their optical properties.

Mechanics of membrane bulging during cell-wall disruption in Gram-negative bacteria

The bacterial cell wall is a network of sugar strands crosslinked by peptides that serve as the primary structure for bearing osmotic stress. Despite its importance in cellular survival, the robustness of the cell wall to network defects has been relatively unexplored. Treatment of the gram-negative bacterium Escherichia coli with the antibiotic vancomycin, which disrupts the crosslinking of new material during growth, leads to the development of pronounced bulges and eventually of cell lysis. Here, we model the mechanics of the bulging of the cytoplasmic membrane through pores in the cell wall. We find that the membrane undergoes a transition between a nearly flat state and a spherical bulge at a critical pore radius of ~20 nm. This critical pore size is large compared to the typical distance between neighboring peptides and glycan strands, and hence pore size acts as a constraint on network integrity. We also discuss the general implications of our model to membrane deformations in eukaryotic blebbing and vesiculation in red blood cells.

Vitrification from solution in restricted space: Formation and stabilization of amorphous nifedipine in a nanoporous silica xerogel carrier

Purpose The goal was to find thermodynamic criteria that must be satisfied in order to prevent formation of crystalline state of drugs within a confined space (e.g., nanopores of inorganic solid). Similarly, criteria that lead to stabilization of amorphous drug within such pores were investigated. Methods In the theoretical part, the classical thermodynamics of nucleation is applied to the conditions of a restricted space. The theoretical findings are verified using porous silica as a carrier and nifedipine as a model drug. The amorphicity of the latter is checked using XRD and thermal analysis (DTA, DSC) in combination with BET measurements. Results It is shown that there exists a critical pore radius of a host below which the entrapped substance will solidify in an amorphous form. There also exists a critical pore radius below which the entrapped amorphous solid will not be able to crystallize. Specifically, incorporation of NIF into a silica xerogel with an average pore diameter of about 2.5 nm produces and stabilizes its amorphous form. Conclusion Entrapment of drugs into solid nanoporous carriers could be regarded as a potentially useful and simple method for production and/or stabilization of non-crystalline forms of a wide range of drugs.

A quantitative stress-related model for the evolution of the pore size in porous silicon during high temperature annealing

An original two dimensional model for the simulation of structural pore evolution post-high temperature annealing of porous silicon is proposed. The model treats the pore as a group of vacancies and deals with their diffusion in crystalline materials under mechanical stress. A coupled solution of the mechanical and diffusion field equations is carried out numerically using finite element method. It is found that the pore shape evolution upon annealing at high temperature is essentially dependent on the initial strain created by the pore. The proposed model provides a theoretical basis for the determination of the critical initial pore radius that determines whether the pore will increase or decrease in size upon annealing. Such a critical radius is found to be dependent on the annealing temperature and is calculated for the range 700–1300°C.

Distribution of Carbon Nanotube Sizes from Adsorption Measurements and Computer Simulation

The method for the evaluation of the distribution of carbon nanotube sizes from the static adsorption measurements and computer simulation of nitrogen at 77 K is developed. We obtain the condensation/evaporation pressure as a function of pore size of a cylindrical carbon tube using Gauge Cell Monte Carlo Simulation (Gauge Cell MC). To obtain the analytical form of the relationships mentioned above we use Derjaguin-Broekhoff-deBoer theory. Finally, the pore size distribution (PSD) of the single-walled carbon nanohorns (SWNHs) is determined from a single nitrogen adsorption isotherm measured at 77 K. We neglect the conical part of an isolated SWNH tube and assume a structureless wall of a carbon nanotube. We find that the distribution of SWNH sizes is broad (internal pore radii varied in the range 1.0-3.6 nm with the maximum at 1.3 nm). Our method can be used for the determination of the pore size distribution of the other tubular carbon materials, like, for example, multiwalled or double-walled carbon nanotubes. Besides the applicable aspect of the current work the deep insight into the problem of capillary condensation/evaporation in confined carbon cylindrical geometry is presented. As a result, the critical pore radius in structureless single-walled carbon tubes is determined as being equal to three nitrogen collision diameters. Below that size the adsorption-desorption isotherm is reversible (i.e., supercritical in nature). We show that the classical static adsorption measurements combined with the proper modeling of the capillary condensation/evaporation phenomena is a powerful method that can be applied for the determination of the distribution of nanotube sizes.

Tri-dimensional modelling of cementitious materials permeability from polymodal pore size distribution obtained by mercury intrusion porosimetry tests

An analytical model is developed to predict permeability of cement-based materials. It is based on the geometrical modelling of a porous structure as a tri-dimensional cubic pore network, which contains an association of n types of pores with radii Ri and lengths li. This geometrical configuration gives the model the ability to be applied to all types of pore size distribution. The permeability is expressed in function of porosity, tortuosity, critical pore radius and constrictivity, which depends on pore size distribution. These parameters are obtained from mercury intrusion porosimetry measurements. The predicted permeability values were compared with experimental ones obtained by direct measurements according to Darcy's law. The experimental validation concerns three mortars chosen for their polymodal pore size distribution. Theoretical and experimental results are in the same order of magnitude. However, the model could be improved by a better estimation of the material morphological parameters. This would be possible by using further investigation methods, in addition to mercury intrusion porosimetry tests.

Influence of cholesterol on electroporation of bilayer lipid membranes: chronopotentiometric studies

This paper presents the results of constant-current (chronopotentiometric) measurements of the egg yolk phosphatidylcholine (PC) bilayer membrane without and with cholesterol. The experiments were performed on planar bilayer lipid membrane (BLM) formed by the Mueller–Rudin method. It is demonstrated that the constant-intensity current flow through bilayer membranes generated fluctuating pores in their structure. The presence of cholesterol in the membrane caused an increase in the value of the breakdown potential. It is postulated that greater stability of the bilayer with cholesterol can result from an increased critical pore radius (at which the bilayer would undergo irreversible rupture). This confirms that cholesterol has a stabilizing effect on BLM. Besides, our results suggest that addition of cholesterol causes shift in the distribution of pore conductance towards a smaller value. It is suggested that this can be connected with the phenomenon of domain formation in the membranes containing high concentration of cholesterol. Moreover, it is shown that chronopotentiometry with programmable current intensity is a promising method for observation of the membrane recovery process.

A new model to calculate water permeability of cement-based materials from MIP results

In this article, we have established an analytical model of cement-based material permeability. The permeability is expressed in function of porosity, tortuosity, constrictivity factor and critical pore radius of the material. The modelling is based on the use of a tridimensional cubic pore network. Two types of measurements are carried out on mortars and cement paste: (a) mercury intrusion porosimetry (MIP) measurements so as to determine the model entry parameters which allow calculation of the ‘theoretical’ permeability; (b) direct water permeability measurements by the application of the Darcy's law so as to validate the model. The calculated and measured permeabilities are globally in the same order of magnitude. However, some differences are noted. They can be explained by the complexity of correctly estimating some model entry parameters (e.g. tortuosity). Moreover, the permeability expression established shows that it is more affected by tortuosity and critical pore radius variations than by porosity or constrictivity.

A new model to calculate water permeability of cement-based materials from MIP results

In this article, we have established an analytical model of cement-based material permeability. The permeability is expressed in function of porosity, tortuosity, constrictivity factor and critical pore radius of the material. The modelling is based on the use of a tridimensional cubic pore network. Two types of measurements are carried out on mortars and cement paste: (a) mercury intrusion porosimetry (MIP) measurements so as to determine the model entry parameters which allow calculation of the ‘theoretical’ permeability; (b) direct water permeability measurements by the application of the Darcy's law so as to validate the model. The calculated and measured permeabilities are globally in the same order of magnitude. However, some differences are noted. They can be explained by the complexity of correctly estimating some model entry parameters (e.g. tortuosity). Moreover, the permeability expression established shows that it is more affected by tortuosity and critical pore radius variations than by porosity or constrictivity.

A Hydrophobic Gating Mechanism for Nanopores

Water-filled pores of nanometer dimensions play important roles in chemistry and biology, e.g., as channels through biological membranes. Biological nanopores are frequently gated, i.e., they switch between an open and a closed state. In several ion channel structures the gate is formed by a ring of hydrophobic side chains that do not physically occlude the pore. Here we investigate whether a hydrophobic pore can act as a gate via molecular dynamics simulations of the passage of water through atomistic models of nanopores embedded within a membrane mimetic. Both the geometry of a nanopore and the hydrophilicity vs hydrophobicity of its lining determine whether water enters the channel. For purely hydrophobic pores there is an abrupt transition from a closed state (no water in the pore cavity) to an open state (cavity water at approximately bulk density) once a critical pore radius is exceeded. This critical radius depends on the length of the pore and the radius of the mouth region. Furthermore, a closed hydrophobic nanopore can be opened by adding dipoles to its lining.

Water permeability and chloride ion diffusion in portland cement mortars: Relationship to sand content and critical pore diameter

The pore structure of hydrated cement in mortar and concrete is quite different from that of neat cement paste. The porous transition zones formed at the aggregate-paste interfaces affect the pore size distribution. The effect of the sand content on the development of pore structure, the permeability to water, and the diffusivity of chloride ions was studied on portland cement mortars. Mortars of two water-to-cement ratios and three sand volume fractions were cast together with pastes and tested at degrees of hydration ranging from 45 to 70%. An electrically-accelerated concentration cell test was used to determine the coefficient of chloride ion diffusion while a high pressure permeability cell was employed to assess liquid permeability. The coefficient of chloride ion diffusion varied linearly with the critical pore radius as determined by mercury intrusion porosimetry while permeability was found to follow a power-law relationship vs. this critical radius. The data set provides an opportunity to directly examine the application of the Katz-Thompson relationship to cement-based materials.

A new insight on pore structure and permeability

The flow of water through a porous medium is simulated numerically using a cubic network of cylindrical capillary tubes as the conceptual model of the medium. Poiseuille's law is used to relate the viscous dissipation within the fluid to the pressure gradient driving the flow. The pore size distribution is determined from the capillary pressure function of the medium, and the tubes are randomly arranged within the network. A critical pore radius is identified as the limiting pore size which contributes to the permeability structure of the medium. When only tubes from that part of the pore size distribution above this critical radius are used to form the network, the permeability of the network equals the measured permeability of the medium. This parameter, the critical pore radius, links the permeability to the pore size distribution and gives insight into the topological structure of the medium.

Stochastic model for electric field-induced membrane pores. Electroporation.

Electric impulses (1-20 kV cm-1, 1-5 microseconds) cause transient structural changes in biological membranes and lipid bilayers, leading to apparently reversible pore formation ( electroporation ) with cross-membrane material flow and, if two membranes are in contact, to irreversible membrane fusion ( electrofusion ). The fundamental process operative in electroporation and electrofusion is treated in terms of a periodic lipid block model, a block being a nearest-neighbour pair of lipid molecules in either of two states: (i) the polar head group in the bilayer plane or (ii) facing the centre of a pore (or defect site). The number of blocks in the pore wall is the stochastic variable of the model describing pore size and stability. The Helmholtz free energy function characterizing the transition probabilities of the various pore states contains the surface energies of the pore wall and the planar bilayer and, if an electric field is present, also a dielectric polarization term (dominated by the polarization of the water layer adjacent to the pore wall). Assuming a Poisson process the average number of blocks in a pore wall is given by the solution of a non-linear differential equation. At subcritical electric fields the average pore size is stationary and very small. At supercritical field strengths the pore radius increases and, reaching a critical pore size, the membrane ruptures (dielectric breakdown). If, however, the electric field is switched off, before the critical pore radius is reached, the pore apparently completely reseals to the closed bilayer configuration (reversible electroporation ).

A similar law may govern water freezing in minerals and living organisms

THERE is an interesting similarity between the freezing of water in minerals and in biological tissues. Mazur1,2 observed that many living organisms lose viability at threshold temperatures near −10 °C. After investigating this phenomenon from the point of view of possible mechanisms by which living cells suffer damage on freezing, he concluded that a key step in the freezing process is the penetration of ice into the cell to nucleate the internal water, and that at −10 °C ice can penetrate the membrane, whereas above this temperature, it cannot. This implies that the water in the cell-membrane pores or a portion of them, starts to freeze at about −10 °C. From the Kelvin equation which describes freezing in terms of the ice-water surface tension and the radius of cylindrical capillaries, Mazur deduced that1 “the lower melting point of ice in a capillary can account for the barrier properties of the plasma membrane”. He observed, however, that “there is a large quantitative discrepancy. The evidence suggests that the plasma membrane ceases to be a barrier at approximately −10 °C. On the basis of equation (4), (ref. 1) the critical pore radius at −10 °C is 30 A, whereas the estimated pore size from permeability studies is 3–8 A”. To account for the discrepancy he postulated that the contact angle of water in the membrane pores is not 0 ° but 80 °. This enabled him to find the simple relationship where ΔT is the freezing point depression and a is the pore radius in A, which predicts that water in 5 A pores will freeze at −10 °C and thus agrees with experimental observations on membrane pore sizes.