Mathematical Simulation of Gas Transfer through a Bilayer Membrane with Account for Adsorption Kinetics

Mathematical simulation has been employed to study the permeability of a bilayer membrane taking into account finite rates of adsorption on the external surfaces of the membrane and internal diffusion in it. Analytical expressions are derived for transmembrane gas flux and permeability of the membrane. It has been revealed that the permeability may depend on the direction of gas flux (asymmetry effect). It has been shown that the asymmetry effect arises at different values of the parameters of the isotherms of gas sorption in membrane layers at a finite gas pressure. The main characteristics that govern the degree of asymmetry have been determined and analyzed. The rate of adsorption has been found to substantially influence the magnitude of the asymmetry effect in the bilayer membrane. It has been found that a two-layer membrane can function as a diffusion "diode", if adsorption is the limiting stage of gas transfer.     

On the separation factor of binary gaseous mixtures in two-layer nanoporous membranes

The separation factor is calculated for a binary gaseous mixture in two-layer membranes composed of nano- and microporous layers. The transfer in nanosized pores is described with regard to the diffusion in an adsorption layer. The mutual influence of components when they pass through the fine-pore layer is taken into account. The dependence of the diffusion coefficients in the adsorption layer on the degree of surface coverage is taken into account. It is shown that the mutual influence of the components on the transfer in the adsorption layer substantially affects the separation factor and its dependence on process parameters. The problem concerning the asymmetry of the separation factor at different membrane orientations with respect to the flow is discussed.     

Mass transfer,adsorption and reaction in slurry reactors

The performance of three-phase isothermal slurry reactors with continuous gas flow and batch liquid may be affected by gas-bubble-to-liquid and liquid-to-catalyst-particle mass transfer, intraparticle diffusion in the pores of the particles, and adsorption and surface reaction. In dynamic operation, e.g. by introducing a pulse of reactant in the gas feed, the rates of adsorption and surface reaction are not necessarily equal. Equations for a first-order reaction are developed for the zeroth and first moments, in both the effluent gas and the batch liquid, in terms of the separate rate constants for adsorption and surface reaction and the other pertinent rate and equilibrium constants. The results show that under some operating conditions it should be possible to evaluate, from experimentally determined moments, the separate values of the adsorption and reaction rate constants. This would eliminate the assumption that one of the steps is rate controlling.Dynamic adsorption and reaction data are apparently unavailable at present to apply in the derived equations. However, for the special case of adsorption in the absence of reaction, for which experimental data are available, the predicted moments agree with the experimental values.     

Asymmetric transmembrane transfer caused by a difference in adsorption characteristics at interfaces

A surface adsorption mechanism is proposed for the effect of asymmetric diffusion permeability of a modified membrane. A model is developed to describe diffusion transfer through the modified membrane with regard to the finiteness of the rate of adsorption on external membrane surfaces. Expressions are derived for diffusion fluxes as functions of transfer direction, and asymmetry coefficient is calculated for the diffusion permeability of the membrane. It is shown that the difference in the kinetic properties of the external surfaces of the membrane, which results from the modification of one of the surfaces, may induce the effect of asymmetric diffusion permeability.     

Experimental analysis of the reaction layer structure in a gas diffusion electrode

The micro-structure of the reaction layer and the performance of a PTFE-bonded gas diffusion electrode having different PTFE contents have been studied experimentally using electrochemical techniques and a mercury pore sizer. A more practical image of the structure has resulted in comparison with any of the models postulated previously. Maximum performance was obtained at 30% PTFE content for oxygen reduction with ca. 75% utilization of platinum clusters, where an activation process is controlling the performance. The reaction layer consists of two distinctive pore distributions with a boundary of ca. 0.1 μm. The smaller pore (primary pore) was assigned to the space in-between the primary particles in their agglomerate and the larger one (secondary pore) to that in-between the agglomerates. Platinum clusters of ca. 80% were located in the primary pores and most of the PTFE was in the secondary pores. On the basis of the experimental results, a schematic micro-structure for the reaction layer is proposed. It was possible to determine the degree of occupation of each pore by the electrolyte or gas from the experimental results. It was revealed that the primary pore works as a reaction volume while the secondary pore works as main gas channels, e.g. 80% of the former is occupied by electrolyte and 30% of the latter contains gas at the composition of maximum performance. Increased gas channels and high utilization of platinum clusters are essential for a high-performance gas diffusion electrode. They were achieved by dispersing efficiently both the catalysed carbon black and the PTFE.     

Mass transfer in porous systems, flooded in part with water, of gas diffusion and catalytic layers of the cathode of a fuel cell with a solid polymer electrolyte

Mass transfer in porous gas diffusion and catalytic layers of the cathode of a hydrogen-air fuel cell with a solid polymer electrolyte is considered. The transport processes are considered with allowance made for the partial flooding of porous systems of these layers with water, which forms during the fuel cell operation. The consideration also allows for the influence of the diluent gas present when air oxygen is used as the oxidant. The fraction of water-flooded pores is calculated within percolation theory as a function of structural parameters of the porous system. Conditions leading to the beginning of the gas diffusion layer flooding are presented.     

A new method of modification of inorganic membranes with pyrocarbon nano-sized crystallites

Gas-separating membranes were obtained according to an original method of directed modification of ultra filtration membranes having 50 nm pores by means of pyrocarbon nano-sized crystallites (PNCs). For the first time, the size of the pores was reduced not along the entire depth of the selective layer but only at the pore orifice, increasing their productivity by several orders of magnitude. PNC deposition was done at 800 and 650°C using methane and propane as a pyrolyzed gas at 90–100 kPa, respectively. The depth of PNC deposition was determined by scanning electron microscopy and energy dispersive spectrometry. It was demonstrated that at the used pressure, the depth of deposition was 1.5 μm, i.e., PNCs were deposited in the pore orifices. Gas permeability analysis for a membrane with r _pore ～ 0.8 nm allowed us to estimate the Knudsen ratio and surface diffusion. The Knudsen and surface diffusion fluxes were estimated. The advantages and challenges of the proposed approach are discussed; these are mainly related to the thermal stability of the porous structure and the compatibility of the thermal expansion coefficients of the porous substrate and deposited PNCs. An analysis of the obtained results is presented, along with an outline for further studies.     

Fundamentals of electroporative delivery of drugs and genes

Electrooptical and conductometrical relaxation methods have given a new insight in the molecular mechanisms of the electroporative delivery of drug-like dyes and genes (DNA) to cells and tissues. Key findings are: (1) Membrane electroporation (ME) and hence the electroporative transmembrane transport of macromolecules are facilitated by a higher curvature of the membrane as well as by a gradient of the ionic strength across charged membranes, affecting the spontaneous curvature. (2) The degree of pore formation as the primary field response increases continuously without a threshold field strength, whereas secondary phenomena, such as a dramatic increase in the membrane permeability to drug-like dyes and DNA (also called electropermeabilization), indicate threshold field strength ranges. (3) The transfer of DNA by ME requires surface adsorption and surface insertion of the permeant molecule or part of it. The diffusion coefficient for the translocation of DNA (M(r) approximately 3.5 x 10(6)) through the electroporated membrane is Dm = 6.7 x 10(-13) cm2 s-1 and Dm for the drug-like dye Serva Blue G (M(r) approximately 854) is Dm = 2.0 x 10(-12) cm2 s-1. The slow electroporative transport of both DNA and drugs across the electroporated membrane reflects highly interactive (electro-) diffusion, involving many small pores coalesced into large, but transiently occluded pores (DNA). The data on mouse B-cells and yeast cells provide directly the flow and permeability coefficients of Serva blue G and plasmid DNA at different electroporation protocols. The physico-chemical theory of ME and electroporative transport in terms of time-dependent flow coefficients has been developed to such a degree that analytical expressions are available to handle curvature and ionic strength effects on ME and transport. The theory presents further useful tools for the optimization of the ME techniques in biotechnology and medicine, in particular in the new field of electroporative delivery of drugs (electrochemotherapy) and of DNA transfer and gene therapy.     

The nature of permeability anisotropy and catalytic activity

The phenomena of permeability anisotropy and an increase in the rates of catalytic reactions in porous membranes modified with highly dispersed catalytic systems were analyzed. A model of stochastic gas motions was proposed; this model is based on the hypothesis of the specific interaction of molecules with the inner surface of pores resulting in a nonisotropic distribution of molecules over traveling directions. The effects of asymmetric gas transfer in porous and gradient-porous membranes were considered to explain differences in the rates of heterogeneous catalytic reactions in a nanoporous membrane reactor under changes in the direction of supplying a reaction mixture. From the model proposed, it follows that the transversal diffusion of gas molecules is most probable in the porous medium of a ceramic membrane with a pore-size distribution gradient from large to small pores along the flow direction. This diffusion results in an increase in the frequency of molecular collisions with the wall of a microchannel and, correspondingly, in an increase in the contact time. The model proposed explains the intensification of a number of heterogeneous catalytic reactions performed in the porous media of catalytic porous membranes.     

Characterization of microporous membranes for use in membrane contactors

Methods of selecting applicable membranes for use in membrane contactors for flue gas desulfurization are proposed in this paper. The mass transfer mechanism for SO₂ diffusion through gas filled pores is explored by simple measurements in order to identify suitable membrane structures for use in contactors for flue gas cleaning. It is attempted to correlate the experimentally determined membrane mass transfer coefficient to intrinsic physical properties of the membrane by applying theoretical and empirical correlations for the porosity-tortuosity relationship of the porous structure. Thereby limiting fluxes can be predicted with good accuracy from data quoted in the manufactures catalogue.     

Asymmetry of diffusion permeability of bi-layer membranes

To reveal the reason of asymmetry of the diffusion permeability of bi-layer electrodialysis membranes the following problems have been solved using the model of "homogeneous porous membrane": - diffusion of non-electrolyte solutions across a bi-layer membrane; - diffusion of electrolyte solutions across a non-charged bi-layer membrane; - diffusion of electrolyte solutions across a charged single layer membrane; - diffusion of electrolyte solutions across a charged bi-layer membrane. It is shown that the main factor responsible for the asymmetry is the difference between absolute values of densities of fixed charges (or so called "exchange capacities") of different layers of a membrane under investigation. Only in this case the ratio of the thickness of the membrane layers as well as the ratio of ion diffusivities contributes also to the asymmetry of the diffusion permeability. In the present review we survey and generalize our previous investigations and propose a new theory of asymmetry of diffusion permeability of bi-layer membranes. We have deduced explicit algebraic formulas for the degree of asymmetry of diffusion permeability of bi-layer membranes under consideration.     

Adsorption-Desorption Flow of Condensable Vapors through Mesoporous Media: Network Modeling and Percolation Theory

Flow of condensable vapors in mesoporous media is investigated theoretically and experimentally during adsorption and desorption processes. A typical permeability curve of a condensable vapor is strongly enhanced in the capillary condensation region. This is because additional capillary pressure gradients are imposed on the capillary-condensed pores, which act as "good" conductors compared to the noncondensed pores, which are considered "poor" conductors. The percolation scaling properties that hold for a system of "good" and "poor" conductors are confirmed for the cases examined. As the ratio of gas flow/capillary-enhanced flow decreases, the rise of permeability with pressure becomes sharper. The network connectivity has a strong impact on the maximum permeability value and on the width of the scaling law regions. The contribution of surface flow does not affect the permeability in the peak region, but results in a shrinkage of the scaling law regions. During desorption, a marked hysteresis in the permeability curves is found and it is attributed only to thermodynamic hysteresis. The maximum permeability values in this case are higher and shifted to lower relative pressures. Copyright 2000 Academic Press.     

Active layer of the oxygen cathode in a fuel cell with Nafion and platinum: The role played by the diffusion and ohmic restrictions and the selection of the working thickness of the active layer

The basic parameters that characterize the operation of the active layer of a cathode with Nafion are the effective coefficient of the diffusion of oxygen, the effective ionic conductance, and the thickness of the active layer. One of the deficiencies intrinsic to the fuel cells containing Nafion is their extreme sensitivity to the heat and moisture exchange. Nafion demands an optimum degree of humidification. Upon thoroughly draining the active layer of a cathode with Nafion, its effective ionic conductance substantially lowers, and large diffusion restrictions arise following the flooding of pores in the active layer. The goal of this work is to perform a comparison of values of some dimensional characteristics pertaining to the flooded and thoroughly drained active layers of a cathode with similar indicators of an active layer in its optimum (normal) state. It is demonstrated how one should perform the selection of the working thickness of an active layer that would provide for the efficiency of its functioning.     

Mathematical simulation of atomic hydrogen diffusion transfer through a multilayer metal membrane at finite pressures

Diffusion transfer of atomic hydrogen through multilayer metal membranes has been studied within the lattice model of an ideal gas, with the transfer being described by a set of nonlinear algebraic equations. It has been shown that, for multilayer membranes composed of less than four layers, an analytical expression describing a diffusion flux can be derived. Atomic hydrogen transfer through a membrane consisting of a vanadium layer, the surfaces of which are coated with palladium films, has been analyzed in detail. It has been found that the value of the flux may depend on the transfer direction. The effect of diffusion asymmetry arises at finite pressures of hydrogen on the outer membrane surfaces, when its dissolution in metals is described by nonlinear sorption isotherms. The degree of the diffusion asymmetry increases with a rise in hydrogen pressure and depends on the arrangement of the layers composing a membrane.     

Study of intracrystalline diffusion in zeolites 6. Comparison of the results obtained by the method of densitometry of light and the adsorption method

The use of the method of densitometry of light passing through a layer of zeolite crystals permits determining the limiting stage of diffusion during adsorption by zeolites. Diffusion in transport pores and external heat exchange play the basic role in adsorption of benzene by NaX zeolite, while diffusion in crystals is the determining mechanism of transport in adsorption of water by NaA and NaX zeolites. The diffusion coefficients of water in NaX zeolite have an order of magnitude of 10^–17 m²/sec and increase with an increase in the degree of filling. An explanation for the anomalous behavior of the kinetic adsorption curve for brief times of adsorption of water by zeolite is proposed.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 6, pp. 1224–1228, June, 1990.     

Gas separation mechanisms in microporous modified γ-al2o3 membranes

The transport of pure gases and of binary gas mixtures through a microporous composite membrane is discussed. The membrane consists of an alumina support with a mean pore diameter of 160 nm and an alumina top (separation) layer with pores of 2-4 nm. The theory of Knudsen diffusion, laminar flow and surface diffusion is used to describe the transport mechanisms. It appears for the composite membrane that Knudsen diffusion occurs in the toplayer and combined Knudsen diffusion/laminar flow in the support at pressure levels lower than 200 kPa. For the inert gas mixture H₂/N₂ separation factors near 3 could be achieved which is 80% of the theoretical Knudsen separation factor. This value is shown to be the product of the separation factor of the support (1.9) and of the top layer (1.5). The value for the top layer is rather low due to the relatively small pressure drop across this layer. This situation can be improved by using composite membranes consisting of three or more layers resulting in a larger pressure drop across the separation layer.CO₂ surface diffusion occurs on the internal surface of the investigated alumina membranes. At 250-300 K and a pressure of 100 kPa the contribution of surface diffusion flow measured by counterdiffusion is of the same order of magnitude as that resulting from gas diffusion. The adsorption energy amounts —25 kJ/mol and the surface coverage is 20% of a monolayer at 293 K and 100 kPa. The calculated surface diffusion coefficient is estimated to be 2-5 x 10^-9 m²/sec.Modification of the internal pore surface with MgO increases the amount of adsorbed CO₂ by 50-100%.Modifications with finely dispersed silver are performed to achieve O₂ surface diffusion.     

Molecular Simulation of the Adsorption Characteristics of Methane in Pores of Coal with Different Metamorphic Degrees

In order to study differences in the methane adsorption characteristics of coal pores of different metamorphic degrees, 4 nm pore structure models based on three typical coal structure models with different metamorphic degrees were constructed. Based on the molecular mechanics and dynamics theory, the adsorption characteristics of methane in different coal rank pores were simulated by the grand canonical Monte Carlo (GCMC) and molecular dynamics methods. The isothermal adsorption curve, Van der Waals energy, concentration distribution, and diffusion coefficient of methane under different conditions were analyzed and calculated. The results showed that at the same pore size, the adsorption capacity of CH₄ is positively correlated with pressure and metamorphic degree of coal, and the adsorption capacity of CH₄ in high metamorphic coal is more affected by temperature. The relative concentration of CH₄ in high-order coal pores is low, and the relative concentration at higher temperature and pressure conditions is high. The CH₄ diffusion coefficient in high-rank coal is low, corresponding to the strong Van der Waals interaction between CH₄ and coal. The research results are of great significance for further exploration of the interaction mechanism between CH₄ and coal with different metamorphic degrees and can provide theoretical support for the selection of gas extraction parameters.     

苯在酸碱处理多级孔Y分子筛上的吸附及传质行为

利用H_4EDTA-NaOH共处理的方法制备了具有不同孔径分布的多级微-介孔NaY分子筛。运用XRD、N_2吸附、SEM、TEM对其结构进行了表征。采用频率响应(FR)和智能重量分析仪(IGA)技术研究了苯在改性后的多级孔NaY分子筛及微孔NaY分子筛上的吸附和传质性能。结果表明,适当的酸碱处理不会改变分子筛的晶体结构,但可调变NaY分子筛的精细结构;介孔的引入降低了分子在孔道中的扩散阻力,较大的孔径和较好的孔道贯通性有利于扩散和吸附中心的可接近性;对于微孔NaY分子筛,苯在分子筛上的吸附过程为其传质过程的速控步骤,对于酸碱处理的多级孔NaY分子筛,分子筛颗粒中微/介孔内的扩散过程及分子筛微-介孔孔道间的分子交换过程是传质过程的速控步骤。