Isotherms of Capillary Condensation Influenced by Formation of Adsorption Films

Isotherms of capillary condensation are often used to determine the vapor sorption capacity of porous adsorbents as well as the pore size distribution by radii. In this paper, for calculating the volume of capillary condensate and of adsorption films in a porous body, an approach based on the theory of surface forces is used. Adsorption isotherms and disjoining pressure isotherms of wetting films are presented here in an exponential form discussed earlier. The calculations were made for straight cylindrical capillaries of different radii and slit pores of different width. The mechanisms of capillary condensation differ in cylindrical and slit pores. In cylindrical pores capillary condensation occurs due to capillary instability of curved wetting films on a capillary surface, when film thickness grows. In the case of slit pores, coalescence of wetting films formed on opposite slit surfaces proceeds under the action of attractive dispersion forces. Partial volumes of liquid in the state of both capillary condensate and adsorbed films are calculated dependent on the relative vapor pressure in a surrounding media. Copyright 2000 Academic Press.     

Sensitivity of drainage and imbibition to pore structures as revealed by computer simulation of displacement process

This work concerns the effects of the properties of porous media on two phase fluid displacement at slow rates. These properties include the size frequency distributions, shape and connectivity of pores and throats, the size correlation of directly connected throats and pores and the spatial arrangement of pores and throats in porous media. Computer simulations using 3-dimensional networks of pores and throats were used to determine the effects of these properties on the form of primary and secondary drainage curves, imbibition curves and scanning loops of a capillary pressure diagram.The application of the results is in deriving information about the structure of a porous medium from capillary pressure curves and understanding how predictions about the form of relative permeability curves can be made from capillary pressure curves.The concepts of finite and infinite throat and pore controlled domains are applied during the filling and emptying of a network. These concepts are then combined with considerations of the accessibility of network sites to non-wetting phase or wetting phase sources and sinks to provide information about the amounts and distribution of continuous and discontinuous wetting phase (wp) and non-wetting phase (nwp) at any stage of a displacement. The distribution of fluids Is strictly controlled by the domains. It is shown that recognition of the types, abundance and distribution of domains provides a fundamental basis for understanding boundary effects, differences in tortuosity in porous systems containing two immiscible phases, breakthrough pressures, and saturations, differences in nwp withdrawal efficiency between uncorrelated and correlated pore-throat size models, differences in hysteresis between drainage and imbibition and differences in the shapes of capillary pressure and relative permeability curves for various types of porous structures.     

Concentration dependence of the distribution coefficient for macromolecules in porous media

Partitioning of macromolecules between pore and bulk solutions directly affects both equilibrium and transport processes such as exclusion chromatography and movement of solutes through porous media. Because of interactions between macromolecules and the pore wall, the variation of the macromolecule activity with concentration is different inside the pore than in bulk solution. This difference causes a concentration dependence of the distribution coefficient, as reported in experiments involving exclusion chromatography. In order to explain this effect, we develop a model for a concentration-dependent distribution which explicitly accounts for a coupling between pore–macromolecule and macromolecule–macromolecule interactions. Predictions using this model are reported for the case of rigid spherical macromolecules in both cylindrical and slit pores, including both steric (hard sphere–hard wall) and long-range (screened electrostatic) interactions. An important result is the existence of a general correlation between the first order concentration effect and measurable properties of the macromolecule and porous medium.     

受限狭缝中CO_2-CH_4体系的汽液相平衡性质

受限条件下CO2-CH4体系的相平衡性质对化工工艺过程的设计具有非常重要的意义.采用Gibbs系综Monte Carlo模拟,对220K下CO2-CH4体系在主体相和受限狭缝中的相平衡性质进行了系统地研究.通过主体相模拟与实验结果比较,验证了流体分子势能参数的合理性;通过改变狭缝壁面原子的能量参数,研究了受限环境对CO2-CH4体系汽液相平衡性质的影响.与主体相相比,在硬壁狭缝中,CO2-CH4体系的露点压力增加,泡点压力降低,压力-组成相图变窄,且体系更容易达到超临界状态;在吸引狭缝中,随壁面原子能量参数的增大,CO2-CH4体系的压力-组成相图上移,临界点处CH4的摩尔分数减小,相图变窄.在体系汽液相总组成相同情况下,硬壁狭缝内体系的汽液相密度均比主体相中小;随壁面原子能量参数增大,气相密度变大、液相密度在CH4的摩尔分数较小时变大而当CH4的摩尔分数达到一定值后反而减小.在体系汽液相总组成相同时,受限环境下的汽化热比主体相的汽化热小且随壁面吸引势的增强越来越小;在主体相和硬壁狭缝中体系的汽化热随CH4含量的增加单调减小,而当壁面势能参数较大时汽化热随CH4含量增加先增大后减小.     

Impact of surface forces on wetting of hierarchical surfaces and contact angle hysteresis

The influence of the long-range surface forces on the wetting of multi-scale partially wetted surfaces is discussed. The possibility of partial wetting is stipulated by a specific form of the Derjaguin isotherm. Equilibrium of a liquid meniscus inside a cylindrical capillary is used as a model. The interplay of capillary and disjoining pressures governs the equilibrium of the liquid in the nano- and micrometrically scaled pores constituting the relief of the surface. It is shown that capillaries with a radius smaller than a critical one will be completely filled by water, whereas the larger capillaries will be filled only partially. Thus, small capillaries will show the Wenzel type of wetting behavior, while the same liquid inside the large capillaries will promote the Cassie-Baxter type of wetting. Consideration of disjoining/conjoining pressure allows explaining of the “rose petal effect”, when a high apparent contact angle is accompanied with a high contact angle hysteresis.     

Solvent-dependent permeability in asymmetric ceramic membranes with tortuous or non-tortuous mesopores

Solvent-dependent transport and the role of surface interactions were examined in commercial mesoporous ceramic membranes using permeability and thermoporometry measurements. The membranes chosen were titania (TiO₂) with tortuous interconnected pores (1, 5, and 50 kDa, corresponding to pore diameters of ca. 8.2, 18.3, and 33.2 nm, respectively) and alumina (Al₂O₃) with non-tortuous 20 nm cylindrical pores. A pre-water/solvent/post-water permeability cycle was employed to account for structural differences between membranes and to gauge the effect of residual solvent on water permeability at different temperatures. Our results suggest that in both types of membranes, restricted permeability of 1-butanol and cyclohexane was due to a combination of surface sorption and an increase in disjoining pressure due to solvation forces. Sorption and solvation forces were prevalent as their length scales were on the same order of magnitude as the pore radii. For 1-butanol, chemisorption changed the surfaces from hydrophilic to hydrophobic, and led to a significant decrease in post-water permeability. While Darcy's law could not describe 1-butanol and cyclohexane permeability, it did apply to water and 1,4-dioxane in the 20 nm alumina membranes. Thermoporometry, coupled with permeability, was further used to evaluate surface wetting within the mesopores.     

The rheology of pseudoplastic fluids in porous media using network modeling

This paper considers the rheology of pseudoplastic (shear thinning) fluids in porous media. The central problem studied is the relationship between the viscometric behavior of the polymer solution and its observed behavior in the porous matrix. In the past, a number of macroscopic approaches have been applied, usually based on capillary bundle models of the porous medium. These simplified models have been used along with constitutive equations describing the fluid behavior (usually of power law type) to establish semiempirical macroscopic equations describing the flow of non-Newtonian fluids in porous media. This procedure has been reasonably successful in correlating experimental results on the flow of polymer solutions through both consolidated and unconsolidated porous materials. However, it does not allow an interpretation of polymer flow in porous media in terms of the flows on a microscopic scale; nor does it allow us to predict changes in macroscopic behavior resulting from variations at a microscopic level in the characteristics of the porous medium such as pore size distribution. In this work, we use a network approach to the modeling of non-Newtonian rheology, in order to understand some of the more detailed features of polymjer flow in porous media. This approach provides a mathematical bridge between the behavior of the non-Newtonian fluid in a single capillary and the macroscopic behavior as deduced from the pressure drop-flow rate relation across the whole network model. It demonstrates the importance of flow redistribution within the elements of the capillary network as the overall pressure gradient varies. As an example of a pseudoplastic fluid in a porous medium, we consider the flow of xanthan biopolymer. This polymer is important as a displacing fluid viscosifier in enhanced oil recovery applications and, for that reason, a considerable amount of experimental data has been published on the flow of xanthan solutions in various porous media.     

Maximum disjoining pressure in protein stabilized concentrated oil-in-water emulsions

A model for the prediction of the equilibrium profile of film thickness and continuous phase liquid holdup profile in a concentrated oil-in-water (O/W) emulsion is proposed. This model is employed to infer the maximum disjoining pressure in a concentrated corn oil-in-water emulsion stabilized by bovine serum albumin (BSA) from the experimental measurements of different proportions of oil, polyhedral O/W foam, and aqueous layers at different centrifugal accelerations. The inferred maximum disjoining pressures were found to be higher at higher concentrations of BSA, lower ionic strengths as well as at pH values farther away from pI. The predicted variations of disjoining pressure with film thickness for a concentrated O/W emulsion stabilized by BSA exhibited two maxima due to steric and electrostatic interactions, respectively. The experimental maximum disjoining pressures for toluene-in-water emulsion stabilized by BSA were found to be about two to three times the predicted maxima due to steric interactions but were two to three orders of magnitude higher than the maxima due to electrostatic interactions, thus indicating that steric interaction is the dominant stabilizing mechanism. The discrepancy between the experimental and predicted maximum disjoining pressures is believed to be mainly due to lack of information with regard to the thickness of the adsorbed protein layer at the oil—water interface.     

Mass transfer in frozen porous bodies

The theory of moisture transport in frozen porous bodies under the action of temperature gradient along unfreezing communications represented by water in thin pores and in interlayers between the pore surface and the ice was elaborated. It was shown that most of the flow in the pores filled with water is directed toward a cold side and can be calculated using the disjoining pressure isotherms of unfreezing interlayers. To obtain isotherms, we used the data of previous measurements of the thickness of unfreezing interlayers in micron-sized quartz capillaries as a function of pressure and temperature. The viscosity of unfreezing interlayers in quartz capillaries was estimated based on the measurements of the displacement velocity of ice columns in the quartz capillaries. Calculated flow rates of unfreezing moisture were consistent with the experimental data for the model porous bodies and frozen grounds.Translated from Kolloidnyi Zhurnal, Vol. 66, No. 6, 2004, pp. 835–839.Original Russian Text Copyright © 2004 by Churaev.     

Review on penetration and transport phenomena in porous media during slot die coating

A distinctive field in the coatings industry is coating of porous media, which has broad applications including paper, textiles, electronics, filtration, and energy sectors. Fluid penetration is an important issue during direct coating of a liquid bead on porous media, which is driven by the pressure from an external flow field and the surface tension in the porous media. Generally, during the coating process, some level of penetration is desirable to obtain specific material properties, but inadequate or excessive penetration is detrimental. To help control the level of penetration, understanding relationships between operating parameters and penetration are highly desirable. In this article, the current state of academic research on modeling penetration in porous media during common coating processes, especially the slot die coating process, is reviewed. Specifically, the challenges, basic ideas, advantages, and disadvantages of macroscale, microscale, and pore-network models on penetration in porous media are discussed. This article concludes with some recommendations for future work. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017 , 55, 1669–1680     

Electrohydrodynamic transport of non‐symmetric electrolyte through porous wall of a microtube

Transport of salt through the wall of porous microtube is relevant in various physiological microcirculation systems. Transport phenomena based modeling of such system is undertaken in the present study considering a combined driving force consisting of pressure gradient and external electric field. Transport of salt is modeled in two domains, in the flow conduit and in the pores of porous wall of the microtube. The solute transport in the microtube is presented by convective‐diffusive mass balance and it is solved using integral method under the framework of boundary layer analysis. The wall of the microtube is considered to be consisting of series of straight parallel cylindrical pores with charged inner surface. The solute transport through the pores is considered to be composed of diffusive, convective and electric potential gradient governed by Nernst‐Planck equation. Transport in the microtube and pores is coupled through the osmotic pressure model for the solvent and Donnan equilibrium distribution for the solute. The simulated results agree remarkably well with the experimental data conducted by in‐house experimental set up. The charge density of the porous wall is estimated through the minimization of errors involved between the experimental and simulated data for different operating conditions.     

Capillary condensation as a morphological transition

The process of capillary condensation/evaporation in cylindrical pores is considered within the idea of symmetry breaking. Capillary condensation/evaporation is treated as a morphological transition between the wetting film configurations of different symmetry. We considered two models: (i) the classical Laplace theory of capillarity and (ii) the Derjaguin model which takes into account the surface forces expressed in terms of the disjoining pressure. Following the idea of Everett and Haynes, the problem of condensation/evaporation is considered as a transition from bumps/undulations to lenses. Using the method of phase portraits, we discuss the mathematical mechanisms of this transition hidden in the Laplace and Derjaguin equations. Analyzing the energetic barriers of the bump and lens formation, it is shown that the bump formation is a prerogative of capillary condensation: for the vapor-liquid transition in a pore, the bump plays the same role as the spherical nucleus in a bulk fluid. We show also that the Derjaguin model admits a variety of interfacial configurations responsible for film patterning at specific conditions.     

Pore formation in polyimide irradiated by high-energy ions and the properties of the obtained membranes

The optimum conditions are determined for etching latent Kr tracks in sodium hypochlorite solution to prepare polyimide track membranes (PI-TMs) with cylindrical pores and the electrosurface properties of the membranes are investigated. The stability of the porous structure of PI-TMs is studied at elevated temperatures (up to 250°C) in aggressive media (pH 1–12). It is shown that the porous structure of PI-TMs is characterized by enhanced chemical and thermal stability.     

Penetration into three-dimensional complex porous structures

The short-term uptake of a fluid by porous media is important in a number of processes, such as in coating and printing operations. We present a new model to predict short-term absorption into real pore geometries taking into account fluid properties, surface forces, and the complex pore geometry. Two assumptions are made to reduce the complexity of the situation: (1) the flow resistance between pores can be estimated from pore geometry or air permeability measurements, and (2) the volume of fluid in the constrictions between pores is small. Pores can be connected in any manner and can be in any arrangement. The absorption rates predicted by the model are compared to experimental values obtained with coating layers of plastic, kaolin, and calcium carbonate pigments. These coatings are characterized in terms of void fraction, pore size, contact angle, and permeability. The comparison is good for water and inks when the air permeability of the porous layer is used to determine the average resistance to flow in the sample. These resistance values are close to the values obtained from pore geometries estimated from particle packing simulations.     

Capillary condensation in a geometrically and a chemically heterogeneous pore: a molecular simulation study

A computer simulation study has been carried out, using an extended Gibbs ensemble Monte Carlo technique, to examine the influence of so-called geometric and chemical disorder on the thermodynamic behavior of simple fluids confined in porous media. The technique allows the equilibrium coexistence of gas and liquid phases to be calculated in a single run. The phase diagram of Lennard-Jones fluid has been calculated in a perfectly cylindrical pore as a reference. Some disorder is then introduced in the porous material, first by spatially modifying the external potential of the initially cylindrical pore, to imitate the geometric disorder of a more realistic pore (undulation, constrictions, etc.) and second by modulating the amplitude of the same initially cylindrical potential to reproduce the energetic disorder of realistic pores due to chemical variations along it. It is shown that the chemical disorder has a much stronger effect on the phase diagram of the confined fluid. The complete adsorption/desorption isotherms are also calculated to help in understanding the large effects of chemical disorder.     

Wetting kinetics of films containing nonadsorbing polymers

Kinetics of wetting by a polymer solution have been studied theoretically for a film pinned to a slot. The fluid mechanical equations have been solved using a numerical scheme. The role of polymers appears in the disjoining pressure in the model. The spreading kinetics are observed to follow a power law: a power of 14 is observed at short times due to the Laplace pressure, and 12 at large times under the Hamaker part of the disjoining pressure at very large times and with no equilibration. It is argued and demonstrated that techniques which have low resolutions such as microscopy will measure quite different kinetics: at short times a power of 14 as for wetting liquids and then a sudden equilibration as reported in these experiments. It is also argued on the basis of steric exclusion, and quantified in the disjoining pressure, that the behavior returns to that of wetting liquids when the polymer molecular weight becomes very high, as also observed in the experiments. Examples of how these features can find practical applications, and hence, the importance of use of polymers as additives are given.     

Two-fluid model for the simultaneous flow of colloids and fluids in porous media

To describe the velocities of particles such as ions, protein molecules and colloids dispersed or dissolved in a fluid, it is important to also describe the forces acting on the fluid, including pressure gradients and friction of the fluid with the particles and with the porous media through which the fluid flows. To account for this problem, the use of a two-fluid model is described, familiar in the field of fluid mechanics, extended to include osmotic effects. We show how familiar relationships follow in various situations and give examples of combined fluid/particle transport in neutral and charged membranes driven by a combination of electrostatic, diffusional and pressure forces. The analysis shows how the same modeling framework can be generally used both for multidimensional electrokinetic flow through macroscopic channels and around macroscopic objects, as well as for mean-field modeling of transport through porous media such as gels and membranes.