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The influence of parameters of the dry-jet wet spinning process was studied on properties of porous polysulfone hollow fiber membranes. The air gap distance, the dope extrusion pressure, bore fluid pressure and temperature were chosen as the studied parameters. Their effect on the geometric and morphological properties of membranes was investigated. The optimal parameters were revealed for the formation of polysulfone hollow fiber membranes, promising for use as porous supports of composite membranes. High gas permeability were achieved with pore sizes providing the Knudsen flow regime: carbon dioxide permeability P/l(CO2) = 48.3 m3 m–2 h–1 atm–1, and values of ideal selectivity α = 2.63 and 0.87 for He/CO2 and CO2/N2 gas pairs, respectively.

We have developed two-membrane air fresheners for continuous non-energized air freshener perfume delivery with significantly superior delivery consistency over a conventional membrane air freshener. In this study, a model perfume is used to investigate the conventional air freshener as functions of temperature and air velocity. The release rate of the conventional air freshener varies greatly from its initial use to its end-of-life under a fixed ambient condition. In order to regulate the evaporation rates of the volatile compounds, the new air freshener consisting of an inner membrane and an outer membrane. The outer membrane is used as the regulation membrane to create a vapor reservoir between the inner wet membrane and the outer membrane so that the vapor generated from the inner membrane can be regulated. Comparing the conventional air freshener to the new air freshener, the outer membrane impregnated with polyethylene glycol (PEG) shows significantly better consistency of perfume delivery rates under different air velocities and temperatures. In addition, a model has been employed to predict the perfume release from the conventional air freshener. The perfume release from the newly developed air fresheners is regulated by vapor transport through the outer membrane which may be predicted through the Knudsen flow or solution diffusion model.

Methane flow in coal is associated with the content of both organic matter (OM) and inorganic matter (IOM). Coal matrix contains nanopores ranging in size from a few to hundreds of nanometers, which leads to a non-Darcy effect where the measured permeability of a gas (apparent permeability) is higher than that of a liquid (intrinsic permeability). In this study, a generalized Lattice Boltzmann model (GLBM) is employed for gas flow through the reconstructed coal matrix consisting of OM, IOM, and fractures. The apparent permeability model is proposed to calculate the total flow flux accounting for multiple transport mechanisms including viscous flow, slip flow, transitional flow, and the Knudsen diffusion. The impact of effective pore radius and gas surface diffusion on permeability in the gas adsorption-desorption process is also considered in the model. What’s more, the weighting factors are adopted to adjust the contribution of the viscous flow and the Knudsen flow. The effect of total organic/inorganic content and the development of fractures on the apparent permeability of the reconstructed coal matrix is also studied. It is found that the apparent permeability is extremely low when a fracture is nonexistent, and varies almost linearly with the total organic/inorganic content. A fracture plays a significant role in determining apparent permeability and the velocity distribution of the coal matrix.

Condensate banking is the most challenging engineering problem in the development of gas-condensate reservoirs where the condensate accumulation can dramatically reduce the gas permeability resulting in impairment of wells productivity. An accurate assessment of condensate banking effect is important to predict well productivity and to diagnose well performance. Traditionally, Darcy law, combined with relative permeability models, has been used for modelling condensate banking effect in conventional reservoirs. This approach is also widely adopted in reservoir engineering commercial tools. However, for shale gas-condensate reservoirs, the gas flow deviates from Darcy flow to Knudsen flow due to the very small pore size in shale matrix (3–300 nm), compared to conventional reservoirs (10–200 μm). This gas flow is highly dependent on pore size distribution and reservoir pressure. In this paper, the effect of condensate saturation on Knudsen flow in shale matrix kerogen is investigated using a 3D pore network with a random pore size distribution. The Knudsen flow is incorporated at the pore level and gas permeability is evaluated for the whole network. In addition, the pore distribution effect in terms of log-normal mean and standard deviation is investigated. The concept of relative permeability in Darcy flow is extended to Knudsen flow by defining a new parameter called relative correction factor ξ r e l to evaluate the effect of condensate banking on Knudsen flow. This parameter can be employed directly in reservoir engineering tools. Simulation results showed that the relative correction factor is not only dependent on condensate saturation but also on pressure. This is due to the impact of pressure on the contribution of pore size ranges into the gas flow. In addition, results showed the effect of the pore size distribution where the standard deviation controls mainly the behaviour of Knudsen flow under condensate saturation. Disregarding this effect can lead to an overestimation of Knudsen flow contribution in well production under condensate banking effect.

In this study, macroporous a - alumina supports were prepared by using vacuum assisted filtration of α-Al 2 O 3 suspensions with different particle size . The average particle sizes of the powders are 400 and 200 nm. The prepared supports had smooth and uniform surface microstructure and well suited for the fabrication of thin continuous membrane. The microstructure consists of a random close packing of 200 nm particles led to improved surface uniformity and roughness. ZnO spheres were prepared by homogeneous precipitation and added to the colloidal suspension to modify the support structure and increase the support flux. Structural parameters such as pore diameter and tortuosity of the prepared macroporous supports were estimated by using He, N 2 , CO 2 permeance measurements. Slight pressure dependence in the permeance values indicated the contribution of viscous flow to the Knudsen flow. The s upports prepared by alumina powder with a larger particle size exhibited He permeance of three times higher than that of prepared with a smaller particle size. The addition of ZnO resulted in the increase in He permeance value significantly for the support prepared by 400 nm particles in size. He permeance was in a range of 8.5-8.7x10 -6 mol/(m 2 sPa) which is very close to the desired value of 1x10 -5 mol/(m 2 sPa).

Gas sorption and non-Darcy flow are two important issues for shale gas reservoirs. The sorption consists of dissolution and adsorption. Dissolved gas and adsorbed gas are different. The former is dissolved in the shale matrix, while the latter is concentrated near the solid walls of pores. In this paper, the Langmuir equation is used to describe adsorption and Henry’s law is used to describe dissolution. The K coefficient in Henry’s law of 0.052 mmol/(MPa g TOC) is obtained by matching experimental data. The amount of dissolved gas increases linearly when pressure increases. Using only the Langmuir equation without considering dissolution can lead to a significant underestimation of the amount of sorbed gas in shales. For non-Darcy gas flow, the apparent permeability model for free gas is established by combining slip flow and Knudsen flow. For adsorbed gas, the surface diffusion effect is also considered in this model. The surface diffusion coefficient is suggested to be of the same scale as the gas self-diffusion coefficient, and the corresponding effective permeability is derived. When $$\frac{1}{p}$$ increases, $$\frac{{k_{\text{app}} }}{{k_{\text{D}} }}$$ increases, but the relationship is not linear as the Klinkenberg effect suggests. The effect of adsorption on the gas flow is significant in nanopores ( $$r \le 2\;{\text{nm}}$$ ). Adsorption increases apparent permeability in shales at low pressures and decreases it at high pressures.

RATIONALE Knudsen effusion mass spectrometry (KEMS) shows improved performance with the “restricted collimation” method of Chatillon and colleagues, which consists of two apertures between the Knudsen cell orifice and the ionizer. These apertures define the shape and position of the molecular beam independently of the sample and effusion orifice and as a result reduces background and improves sampling from the Knudsen cell. Modeling of the molecular beam in restricted collimation allows optimization of the apertures’ diameters and spacing. METHODS Knudsen flow is easily simulated with a Monte Carlo method. In this study a Visual Basic for Excel (VBA) code is developed to simulate the molecular beam originating from a vaporizing condensed phase in a Knudsen cell and passing through the cell orifice and the two apertures. RESULTS The code is able to calculate the transmission coefficient through the cell orifice, through the cell orifice and the first aperture, and through the cell orifice and first and second apertures. Also calculated are the angular distributions of the effusate density emerging from the cell and average number of collisions with the orifice walls. CONCLUSION This code allows the geometry (aperture spacing and diameters) of the sampling system to be optimized for maximum transmission. The calculated effusate distributions and low average number of orifice wall collisions illustrated the advantages of restricted collimation. Calculated transmission factors are also compared to literature values calculated via the analytical method of Chatillon and colleagues.

In filament-free magnetrons which are activated by electron emission from field-radiating cathodes its necessary level is provided by adsorption of active metal barium coming from the main palladium-barium cathode. The developed pressed palladium-barium cathode allows to change barium evaporation speed due to change of its porosity and hence barium Knudsen flow. It will lead to emission level control of field radiating cathodes.

Platinum gamma-alumina (Pt/γ-Al2O3) impregnated membrane was prepared through the evaporative-crystallization deposition method for volatile organic compounds (VOCs) conversion to carbon dioxide (CO2) and water (H2O). The catalytic oxidation of VOCs (propane, n-butane and propylene), fed alone with oxygen were obtained after characterization (SEM-EDXA observation, BET measurement, permeability assessment). VOC conversion of 95%, 52% and 82% for propane, n-butane and propylene was achieved at 378 °C, 245 °C and 420 °C respectively, by varying the reaction temperature using the contactor flow-through catalytic membrane reactor operating in the Knudsen flow regime. The BET surface area and the pore diameter of the 3.52 wt% Pt membrane are 0.426 m2/g and 3.70 nm respectively. The results are comparable with the literature.

The potential impact of nitrogen and ammonia exposure on hydrogen permeance through thin palladium membranes (1.3 µm to 4.1 µm thick) fabricated by electroless plating was studied. Additionally, a robust approach is introduced to quantify the pressure exponent which accounts for contributions to Knudsen flow through defects present in very thin membranes. In sharp contrast to previously published results, no flux inhibition was observed due to nitrogen or ammonia exposure. Studies included 24 h exposures to both pure gases and equimolar hydrogen/nitrogen or hydrogen/ammonia mixtures at trans-membrane pressures ranging up to 1.0 MPa and temperatures of 598 K to 773 K. One membrane did exhibit significant flux inhibition after helium exposure, but this was attributed to changes in surface microstructure associated with hydrogen departing the lattice. This apparent hydrogen flux inhibition behavior was permanently eliminated by air exposure which roughens the surface, and it is suggested that this surface structure mechanism is a more probable explanation for flux inhibition than adsorption of nitrogen–based species.

A tubular commercially available alumina support was coated using the dip coating technique. The objective is to prepare silica and Pt impregnated membranes. Scanning electron microscopy (SEM), energy diffraction X-ray analysis (EDXA), nitrogen adsorption–desorption at 77 K and gas permeation measurements were employed for membrane characterization. The permeation of H 2 , He and N 2 revealed that the membranes are crack-free. H 2 /N 2 selectivity for the silica membrane obtained the highest value of 2.93 at 0.9 barg and 25 °C. On the other hand, H 2 /He selectivity of 1.96 at 1.6 barg and 300 °C for the Pt membrane was obtained and found to be higher than the theoretical Knudsen selectivity. While the silica membrane realised on the thin film coating to enhance the selectivity to hydrogen, the Pt impregnated membrane on the other hand enhance hydrogen transport through an activated surface diffusion in addition to Knudsen flow.

As pore size of gas shale ranges widely, various flow types including viscous flow, slip flow and Knudsen flow could coexist during shale gas production. Currently, different models have to be applied to describe the gas transport behaviours in different flow regions and the selection of the models is highly dependent on the flow classification criteria. This also brings difficulty in selecting proper gas flow models near the flow region boundaries, which again depends on the flow classification criteria. To address this problem, this study proposes a unified method to describe the gas flow in the whole spectrum of flow regions by transforming all the gas transport equations for different flow types into a general form. The modelling results by the unified method are comparable with that by the previous models, but less input parameters are required for the unified method. Since the unified method provides a continuous permeability kea for all flow regions, it avoids discontinuity at the boundary of different flow regions caused by using piecewise flow models. The method is able to depict the gas permeability evolution with reservoir pressure change and is applied to interpret the literature permeability data and to predict the permeability variation among all the flow regions with different gas pressures and pore sizes. The results illustrate that the flow types may change within a specific pore (especially for small pores) during the pressure depletion in shale gas production and different gas transport mechanisms may coexist for some shales with typical bimodal pore size distribution under a specific gas pressure condition. This work provides a unified way to analyse gas flow behaviours and gas permeability variation in different regions and can be readily applied to the reservoir simulation models to predict the gas production behaviour especially the long term gas production behaviour.

The flow of a gas through a bilayer porous membrane with a surface chemical reaction in one of its layers is considered. The reaction (catalytic) layer is assumed to be finely dispersed and characterized by a Knudsen flow regime. The flow regime in the coarsely dispersed support layer is assumed to be hydrodynamic. The asymmetry of membrane catalytic properties, i.e., the dependence of the reacting gas conversion on the orientation of the membrane with respect to the flow, has been studied. The conversion in the reversible and irreversible reactions at the same reagent flow rate is shown to strongly depend on the orientation of the membrane with the possible inversion of the asymmetry effect during the reversible reaction upon a change in the system parameters.

Since the shale gas production data predicted by traditional simulators is far below that of field test, reservoir volume parameters are often modified to meet the fitting demands. Most pressure transient models of reservoir, merely based on Darcy flow in the matrix and natural fractures, neglect the comprehensive influences of viscous flow, slip flow, transition flow and Knudsen flow, etc. In this paper, two gas apparent permeability models considering multiple migration mechanisms are established through theoretical derivation and fitting. The models are applicable to various flow states and will help to simplify percolation models of matrix and fracture system. To achieve a better understanding of the migration mechanisms of shale matrix, the effects of compressed gas in the matrix pores, adsorbed gas on the pore wall and the diffused gas from kerogen on transient pressure should all be taken into account. Based on the newly established gas apparent permeability models, a pseudo-triple-medium transient percolation mathematical model of multi-fractured horizontal well affected by multiple migration mechanisms is presented with the consideration of dissolved gas diffusion in kerogen and adsorbed gas desorption on matrix surface in the shale gas reservoir. Source function idea combined with Laplace transform, linear approximation and δ generalized function is used to get the point source solution of the mathematical model. By discretizing the artificial fractures, the pressure transient response of multi-fractured horizontal well in Laplace space is obtained on the basis of point source solution. Then pressure transient response type curves are plotted by computer programming, and pressure influence factors are also analyzed. Besides, isothermal adsorption experiment data of shale cores indicates that the organic carbon content (TOC) has obvious correlation with the adsorption coefficient defined in this paper, which gives a clue to link up the exploitation research with geological study, playing a guiding role in analyzing pressure response of the shale gas reservoir.

The interaction of propionic and butyric acids on ice and HNO3-doped ice were studied between 195 and 212 K and low concentrations, using a Knudsen flow reactor coupled with a quadrupole mass spectrometer. The initial uptake coefficients (γ0) of propionic and butyric acids on ice as a function of temperature are given by the expressions: γ0(T) = (7.30 ± 1.0) × 10(-10) exp[(3216 ± 478)/T] and γ0(T) = (6.36 ± 0.76) × 10(-11) exp[(3810 ± 434)/T], respectively; the quoted error limits are at 95% level of confidence. Similarly, γ0 of propionic acid on 1.96 wt % (A) and 7.69 wt % (B) HNO3-doped ice with temperature are given as γ(0,A)(T) = (2.89 ± 0.26) × 10(-8) exp[(2517 ± 266)/T] and γ(0,B)(T) = (2.77 ± 0.29) × 10(-7) exp[(2126 ± 206)/T], respectively. The results show that γ0 of C1 to C4 n-carboxylic acids on ice increase with the alkyl-group length, due to lateral interactions between alkyl-groups that favor a more perpendicular orientation and well packing of H-bonded monomers on ice. The high uptakes (>10(15) molecules cm(-2)) and long recovery signals indicate efficient growth of random multilayers above the first monolayer driven by significant van der Waals interactions. The heterogeneous loss of both acids on ice and HNO3-doped ice particles in dense cirrus clouds is estimated to take a few minutes, signifying rapid local heterogeneous removal by dense cirrus clouds.

We present sensitivity analysis of gas transport problems related to experimental setups that are routinely used for determination of effective transport parameters of macroporous solids. The relevance of large total pressure variations to reliable estimation of the effective transport parameters is emphasized in two experimental setups, particularly quasistationary permeation and classical Wicke–Kallenbach cells. It is shown that variations of other system parameters, such as temperature, number of gases or inlet flow rates cannot resemble the efficiency of total pressure changes in estimating the parameters. For the classical Wicke–Kallenbach cell and binary mixtures, it was found that there are narrow intervals of outlet mole fractions in which the related boundary-value problem exhibits the maximum sensitivity to modifications of the transport parameters, i.e. there are the optimal conditions for regression analysis. The rule of adjusting the optimal conditions is simple: the outlet mole fractions, which can easily be controlled by setting the inlet flow rates, must be close to the middle of their admissible intervals. Pore network modelling supported these results and helped us reveal a source of systematic deviations between the effective transport parameters obtained either from permeation experiments or from diffusion experiments. Specifically, the overall network flow rate resulting from non-linear functional relationships between fluxes and driving forces on the pore scale and from the law of mass conservation in network nodes does not exactly conform to the similar flow rate based on the effective parameters if the total pressure span is large. Consequently, biased values of the effective transport parameters counterbalance the deficiency of the associated models.

The standard (p° = 0.1 MPa) molar enthalpy of combustion, Δ c H m ° , of two crystalline compounds, 5,6-dihydro-5-methyluracil and 5,6-dihydro-6-methyluracil, were determined, at T = 298.15 K, using a static bomb combustion calorimeter. The vapor pressures as a function of the temperature were measured for those compounds, by the Knudsen effusion technique, and the standard molar enthalpies of sublimation at the mean temperature of the vapor pressure measurements were derived from the Clausius–Clapeyron equation, and corrected to T = 298.15 K using an estimated value for Δ cr g C p ,m ° . These values were used to derive the standard molar enthalpies of formation of the two compounds studied, in the condensed and gaseous phases. Some considerations about the relative stability of the two isomers were made and compared with similar compounds.

A two-dimensional comprehensive model was developed to predict the transport of water in the nanoporous membrane contactors. The considered membrane distillation device was a counter-current flat-sheet membrane contactor for production of pure water from saline water. The developed model formulates the fundamental transport equations of heat, mass, and momentum in the membrane contactor. The computational fluid dynamics techniques were applied for numerical simulation of model equations. The simulation results were compared with experimental data obtained from literature and showed great agreement with the measured values. A combination of the Knudsen flow and Poiseuille flow was used in the model for estimation of diffusion inside the membrane pores and increased the accuracy of the model. Simulation results revealed that, in the regions adjacent to the membrane wall, the temperature difference is significant. This could be attributed to the fact that a temperature boundary layer is formed near the membr...

The gas permeability of α-alumina, yttria-stabilized zirconia (YSZ), and silicon carbide porous ceramics toward H2, CO2, and H2–CO2 mixtures were investigated at room temperature. The permeation of H2 and CO2 single gases occurred above a critical pressure gradient, which was smaller for H2 gas than for CO2 gas. When the Knudsen number (λ/r ratio, λ: molecular mean free path, r: pore radius) of a single gas was larger than unity, Knudsen flow became the dominant gas transportation process. The H2 fraction for the mixed gas of (20%–80%) H2–(80%–20%) CO2 through porous Al2O3, YSZ, and SiC approached unity with decreasing pressure gradient. The high fraction of H2 gas was closely related to the difference in the critical pressure gradient values of H2 and CO2 single gas, the inlet mixed gas composition, and the gas flow mechanism of the mixed gas. Moisture in the atmosphere adsorbed easily on the porous ceramics and affected the critical pressure gradient, leading to the increased selectivity of H2 gas.

Platinum-alumina (Pt/γ-Al2O3) membrane was prepared using evaporative-crystallization deposition method for volatile organic compounds (VOCs) destruction. SEM-EDXA observation, BET measurement, permeability assessment and the catalytic oxidation of propane, n-butane and propylene representing VOC was obtained. Remarkable propane conversion of VOC with Pt catalyst was achieved at moderate temperature. The temperature at which the catalytic combustion takes place for the VOC is lower than the one obtained from the literature for the same VOC on Pt/γ-Al2O3 catalysts. The conversion was achieved by varying the reaction temperature using flow-through catalytic membrane reactor operating in the Knudsen flow regime.

Study of rarefied gas flow in converging and diverging cross sections is crucial to the development of micro-nozzles and micro-thrusters. In other practical cases too, a microchannel may not always be straight and may include diverging and converging sections in the flow path. In this context, isothermal rarefied gas flow in microchannels of longitudinally varying cross section is studied experimentally in this work. The primary objective is to investigate the existence of Knudsen minimum in microchannels of varying cross sections. The effect of geometrical cross section and fluid properties on the Knudsen minimum are also investigated by performing experiments on three divergence angles (4 degrees, 8 degrees, and 12 degrees) and three different gases (argon, nitrogen, and oxygen) to prove the robustness of the result. The Knudsen minimum, which is one of the characteristic features of rarefied flows, is experimentally observed for the first time in a microchannel of varying cross section. The position of the Knudsen minimum (at Kn approximate to 1) is seen to depend only weakly on the divergence angle and fluid properties. (C) 2016 AIP Publishing LLC.

The general theory of slip flow established in the late 1960s is revisited. For a long time, the complete set of data of the slip and jump coefficients up to the second order of the small Knudsen number have been available only for the Bhatnagar-Gross-Krook model. The present paper provides the complete set of data of those coefficients for a hard-sphere gas on the diffuse reflection boundary. The data are obtained by using the general identities that have been deduced from recently developed symmetry arguments. A few simple application examples are also presented., "28th International Symposium on Rarefied Gas Dynamics 2012"; Conference date: 9–13 July 2012; Location: Zaragoza, Spain

A gas separator that can induce a large variation of mole fraction by a small temperature difference in a single membrane is proposed. The separator makes use of two effects: The first effect is the thermal transpiration through microchannels in the membrane; the second is the accumulation of the effect of micro-channels in the counter flow of gas mixture that flows around the membrane. The numerical results show that small gas separation effects of numerous micro-channels are accumulated to induce a large variation of the mole fraction along the membrane. The numerical calculation is carried out by the direct simulation Monte Carlo (DSMC) method and a fluid model based on the mass conservation which is shown to be able to simulate the DSMC result. The performance of the device is investigated for several temperature differences between the two sides of the membrane. The relation to the membrane gas separation by Knudsen diffusion is also discussed., "28th International Symposium on Rarefied Gas Dynamics 2012"; Conference date: 9–13 July 2012; Location: Zaragoza, Spain

Time lag method is a widely used technique in constant volume systems for the determination of the diffusion and permeability coefficients of gasses in membrane. This technique relies on the assumption that there is no resistance to gas transport downstream from the membrane, which very often might not be the case. To recover the permeability and diffusion coefficients, it is necessary to accurately model the position-dependent resistance effects. The resistance to gas accumulation was modeled in a generalized multi-tank receiver of a constant volume system, by solving Fick's 2nd law of diffusion, which served as a governing partial differential equation, in each tube of the receiver. The diffusion coefficient appearing in each partial differential equation was evaluated using the empirical model of Knudsen, which allowed investigating the effect of transition from Knudsen to the slip flow regime on membrane characterization. The validity of the developed model was verified by comparison of the reconciled membrane properties from the data obtained in a high resistance receiver with the experimental membrane properties determined in a specially designed low resistance receiver.

The question of applicability of Knudsen's equation to dilute adsorbable gas flow in mesoporous media was the subject of a recent debate between Ruthven et al. (2009) , Ruthven (2010) and Bhatia and Nicholson (2010, 2011) . Here, we present a critique of the said debate and introduce new information of critical importance, which has nevertheless been disregarded by both sides thereof. It is pointed out that von Smolukowski's derivation leaves no doubt that Knudsen's equation is meant to apply to the limiting case of zero gas adsorption. In practice, this limit may be expected to be approached at high temperature/low gas adsorbability but the crux of the matter is (i) choice of the right transport parameter (in this case the “reduced permeability”) to provide a useful criterion of approach to the Knudsen limit and (ii) thorough study of the course followed by the said parameter in its approach to the said limit. In this light, we begin our review of the aforesaid new information with conventional surface flow theory, which can deal satisfactorily with higher and moderate, but not with the case of weak, adsorption (because the reduced permeability does not converge smoothly to the Knudsen limit). Even so, we show that it can provide a good answer to a significant question raised in the aforesaid debate. We continue with the more advanced (but still analytical) surface flow approach of Nicholson and Petropoulos (1973) , which has provided a plausible physical mechanism for the experimentally observed passage of the reduced permeability through a minimum with rising temperature, in the weak adsorption region. It is shown here that the said experimental data constitute the first observations (including the “fine structure”) of what we have called “apparent or quasiKnudsen” (to avoid confusion with proper Knudsen) flow behavior, which is the central theme of the debate in question. We then pass onto a discussion on the confirmation of the above interpretation of quasiKnudsen-flow “fine structure”, as well as the identification of conditions favorable to the appearance of such flow in practice, afforded by the results of ab initio evaluation of dilute adsorbable gas flow, under suitable adsorption potentials, in model pores (and model pore networks) by and Petropoulos (1981, 1985) and Petropoulos and Petrou (1991) .

In this study the flow-through catalytic membrane reactor (FTCMR) concept is applied in the thermal oxidation of a chemical warfare simulant, namely dimethyl methylphosphonate (DMMP), in air. Preliminary experiments under different DMMP feed concentrations and reactor temperatures (373–573 K) have demonstrated the potential advantage of the FTCMR concept in the catalytic oxidation of DMMP. Complete destruction of various concentrations of DMMP in air was achieved at lower temperatures, with the FTCMR showing superior performance when compared to a wall-coated, plug-flow reactor (monolith) containing the same amount of catalytic metal. A mathematical model has also been developed in order to provide a better understanding of the fundamental transport phenomena underpinning the FTCMR operation. The model makes use of the Dusty-Gas formulation of transport, and incorporates continuum and Knudsen diffusion, as well as viscous flow as the mechanisms for gas transport through the porous membrane. The model is used for identifying the advantages of the FTCMR concept in comparison with the wall-coated catalytic monolith, and also for investigating some of the limitations, which may exist in applying this concept for the complete oxidation of chemical warfare simulants. The results of the model support the superiority of the FTCMR concept over the more conventional plug-flow monolith reactor.

This paper addresses diffusion of air within a cellular metal. A Knudsen diffusion simulation is performed on both simplified model structures and, for the first time, computed tomography data of real materials. In the first part, the three deflection models (mirror reflection, random deflection and random cosine deflection) are compared. It is found that the Knudsen diffusivities of the model structures exhibit different values for each deflection model. The second part is a Knudsen diffusion simulation on computed tomography data of M-Pore® aluminium foam from which an estimate of its Knudsen diffusivity is obtained. Four sub-geometries of the same specimen are converted into voxel calculation models. All calculations show high Knudsen diffusivities with average values of 1.99 m 2 /s (random cosine deflection) and 2.09 m 2 /s (random deflection). Plots of the Knudsen diffusivity versus porosity show an increase of diffusivity with porosity.

The Knudsen model of diffusion in small pores, originally verified in macropores, is widely applied at the mesopore scale with adsorption effects neglected, largely based on linearity of the T / M correlation. Here, we show that this approach is misleading, and that the correlation masks inconsistencies arising from neglect of van der Waals forces in the Knudsen model. We examine the tortuosity for diffusion of light gases in nanoporous carbons using the Oscillator model of low pressure transport developed in the first author’s laboratory, which incorporates van der Waals interactions. Pore network effects are considered through a hybrid correlated random walk-effective medium theory approach. It is shown that in the presence of a pore size distribution the apparent tortuosity is not a porous medium property alone, but depends also on the temperature and on the diffusing molecule, because of the temperature and the gas-dependent short circuiting effects associated with pores that have high conductance. This short circuiting effect leads to a complex and rich variety of behaviour with respect to pore size, temperature and diffusing gas, which is consistent with experimental evidence, but is absent when the Knudsen model is used with adsorption effects neglected. It is shown that when effects of adsorption on equilibrium and transport are overlooked the commonly used correlation of diffusivity with T / M is deceptive, as the product of the adsorption equilibrium constant and diffusivity (or pore conductance) also approximately scales linearly with the Knudsen diffusivity (i.e. with T / M ). Such behaviour is found for diffusion in mesoporous carbons and silica as well as in silicon. Consequently, claims of validity of the Knudsen model based on such a correlation may be misconceived.

Does pore-size distribution need to be considered to accurately model vapor transport in membrane distillation (MD)? This paper addresses that question from a theoretical perspective. Although some previous work has discussed pore-size distribution in MD, there has yet to be a comprehensive, general analysis of its effects on MD and its various configurations. In this work, a numerical model is used to calculate the flux through all pore sizes to estimate the effect of pore-size distribution on MD flux. The modeling shows that the error in the calculated flux incurred by neglecting pore-size distribution is largest for a microfiltration process, where viscous flow dominates, somewhat smaller for vacuum MD, where Knudsen flow dominates, smaller still for direct-contact MD, where molecular diffusion usually dominates, and smallest for air-gap MD, where the air gap dominates the overall mass transfer resistance. Considering a membrane with a mean pore size of at least 100 nm and a geometric standard deviation of the pore size of 1.2, the error is: 9% for vacuum MD, 3.5% for direct-contact MD, and less than 1% for air-gap MD.

For the first time, the mass transport phenomenon in pervaporation of the ethanol/water system via PVDF asymmetric hollow fiber membranes has been demonstrated through the pore-flow model and a newly modified pore-flow model has been proposed. The modified pore-flow model differs from the pore-flow model by factoring in the contribution of Knudsen flow to vapor transport, which was ignored by the pore-flow model. The correlation of transport parameters to membrane pore size is explored and it is found that the pore size expansion (including the change of membrane surface morphology) is strongly dependent on the solvent in contact. The modified pore-flow model shows a better prediction for the permeate composition than the pore-flow model and both models exhibit an excellent prediction of total permeate mass flux. The significance of Knudsen flow contribution in vapor-phase transport as stated in the modified pore-flow model is discussed from the experimental and theoretical aspects.

The resistance to gas accumulation in constant volume systems has been evaluated by means of a position-depended time lag. The greater the absolute value of the time lag, the greater the error in membrane diffusivity determined using the constant volume system. The time lag, and thus the error in the diffusion coefficient, depends on the position within the receiver of a constant volume system, and regardless of the actual configuration of the receiver, there is always at least one zero time lag position within the receiver. In this paper we have developed an analytical model that allows assessment of the position-dependent time lag in any configuration of the receiver, including multi-tank receivers commonly used in membrane testing laboratories. The model allows optimization of the position of the pressure transducer(s) in the existing receivers, as well as, to understand the effect of important design parameters such as the diameter of tubes, the length of tubes forming direct connection between a membrane cell and the accumulation tank(s), the distribution of the volume between the tanks, and the position of tanks relative to each other and to the membrane cell. The model was verified experimentally using an existing two-tank receiver equipped with three pressure transducers.

The existing assessment of thermodynamic and phase equilibrium data in the Ag–Pd system was revised on the basis of calorimetric data for liquid Ag–Pd alloys published recently in the literature and on new determination of liquidus and solidus temperatures and activity data for Ag in liquid phase, using differential scanning calorimetry (DSC) coupled with Knudsen cell mass spectrometry (KC/MS). A substantially narrower liquid/fcc two-phase field in phase diagram as well as new non-ideal activity data were revealed.

This article describes the derivation of the efficiency for the Knudsen pump for two cases. First, by neglecting the thermal losses to calculate the maximum efficiency, and second, by including the thermal losses along the length of the channel. The Knudsen pump is a thermally driven pump with no moving parts and which functions on the principle of thermal transpiration. Diffusion is the main mode of mass transport, as opposed to bulk fluid motion. The pump functions when the gases are in a rarefied state. The efficiency without thermal losses is shown to asymptotically approach the value of the ideal gas constant divided by the specific heat capacity, while the efficiency with thermal losses is given for rectangular and circular cross sections and is shown to be independent of length.

A two-dimensional mathematical model was theoretically developed to predict the temperature polarization profile of direct contact membrane distillation (DCMD) processes. A concurrent flat-plate device was designed to verify the theoretical prediction of pure water productivity on saline water desalination. The numerical results from the temperature polarization profile were obtained using the finite difference technique to reduce the two-dimensional partial differential equations into an ordinary differential equations system. The resultant simultaneous linear equations system was solved with the fourth-order Runge-Kutta method. The results show theoretical prediction agreement with the measured values from the experimental runs. A combination of the Knudsen flow and Poiseuille flow models in the present mathematical formulation for membrane coefficient estimation was used to establish theoretical agreement. The influence of the inlet saline water temperature and volumetric flow rate on the pure water productivity as well as the hydraulic dissipated energy are also delineated.

A computational and experimental study has been performed for the investigation of fully developed rarefied gas flows through channels of circular, orthogonal, triangular, and trapezoidal cross sections. The theoretical-computational approach is based on the solution of the Bhatnagar-Gross-Krook kinetic equation subject to Maxwell diffuse-specular boundary conditions by the discrete velocity method. The experimental work has been performed at the vacuum facility “TRANSFLOW,” at Forschungszentrum Karlsruhe and it is based on measuring, for assigned flow rates, the corresponding pressure differences. The computed and measured mass flow rates and conductance are in all cases in very good agreement. In addition, in order to obtain some insight in the flow characteristics, the reference Knudsen, Reynolds, and Mach numbers characterizing the flow at each experimental run have been estimated. Also, the pressure distribution along the channel for several typical cases is presented. Both computational and experimental results cover the whole range of the Knudsen number.

The results of a detailed study of the permeation of several light gases through unmodified and modified mesoporous silica membranes are reported. The base membranes which were synthesized by dip-coating multiple layers of a templated silica onto a macroporous alumina support showed relatively high permeances with evidence of both support resistance and a contribution from viscous flow, in addition to Knudsen diffusion, through the active layer. The behavior of the modified membranes, which were prepared by silanation of the original membranes with octadecyldimethylchlorosilane, was more interesting. Permeances were lower and there was no evidence of support resistance or viscous flow. Permeation through the active layer appeared to occur by a “Knudsen-like” process. Permeance and permeance ratios measured in both single component and binary systems showed the characteristic inverse dependence on the square root of the molecular weight (or the molecular weight ratio) but the temperature dependence was much stronger than expected for classical Knudsen flow. The behavior of CO 2 was somewhat anomalous yielding permeances that were about 25% larger than those for propane which has the same molecular weight.

Single gas permeation experiments results using neon, argon, nitrogen and methane are reported. From gas permeation experiments the characteristic parameters of the Knudsen and Poiseuille transport mechanisms were determined by means of an equation derived from the "Dusty-Gas" model. The experiments were performed at different temperatures from 303.15 to 323.15K, in order to study the temperature influence on those parameters. For PVDF and PCTE membranes the influence of the temperature on K, and B. parameters was not significant. Gas influence was also investigated for both types of membrane, a slight tendency of K, to decrease with increase in molar mass and a very slight tendency of B. to increase with increase in molar mass, although these trends were not fulfilled by neon gas.

The Knudsen compressor, based on the rarefied flow phenomenon of thermal creep (or thermal transpiration), is an unconventional nano/micro/mesoscale gas pump or compressor with no moving parts. Recent experimental studies of single micro/mesoscale stages have indicated that, at low pressures (les 100 Pa), stage performance was decreased in qualitatively somewhat understood and quantitatively not-well-understood ways. The investigation reported in this paper was undertaken to establish a detailed picture of the thermally driven flow's behavior for a range of representative Knudsen compressor stage configurations and flow conditions. The objectives of the study were to identify, quantify, and ultimately understand the sources of negative impacts on the performance of single stages using the direct simulation Monte Carlo technique. The findings suggest that once the Knudsen number in the cooling region is less than 0.1, the maximum pressure gain from a single stage of a Knudsen compressor can be carried forward to the next stage with relatively minor performance losses. Simultaneously, for Knudsen numbers below 0.1, the working gas' temperature can be reduced to within a few percent of its initial temperature entering the stage. What was found relates to a necessary characteristic of successful Knudsen compressors, with the same occurrences being anticipated for thermal-creep-driven gas transport channels in other nano/microscale devices.

The changes in the eluted reactant's response curves from a pulse reactor operated in Knudsen flow [e.g. a temporal-analysis-of-products (TAP) reactor] as a function of the pulse size was interpreted as due to varying fractional coverages of the catalyst surface. These were used with the reactor modeling of the response curves to determine the active site concentration on a catalyst powder. The technique uses a transient pulse to bring about significant site coverage, and is an improvement on the present use of gas–surface concentration equilibrium because it is able to selectively determine just the active site concentration and not the entire exposed surface atom concentration.

In this paper, the vapour transport of PbBr2 under vacuum during vacuum distillation refining and its condensation on the wall of the vessel were described. The macro- and micro morphologies of PbBr2 crystals grown in the vessel (glass tube) were studied. The crystal shape changed dramatically depending on the positions of condensation in the vessel, i.e., the crystal shape varied from an isometric polyhedron to columnar crystals with facets, and to a massive crystal without facets with a rise in the wall temperature. These results were interpreted in terms of the concentration gradient of the molecules in the vessel, surface roughening and/or surface melting of the crystals. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

The thermodynamic activity of antimony was determined for nickel-antimony alloys in the composition range between 20 and 52 at% Sb by means of a Knudsen Effusion Mass Spectrometric (KEMS) method. The experimental data in the homogeneity range of the hexagonal {gamma}-NiSb phase (B8-type) were compared with the literature data obtained by a different method. For the activity values in the nonstoichiometric compound Ni{sub 3}Sb (D0{sub 3}-type), a statistical-thermodynamic model was applied which uses the energies of formation of the six different types of point defects, obtained from ab initio calculations, as parameters. According to these formation energies, the most prominent point defects in nonstoichiometric Ni3Sb are nickel vacancies. It was found that the inclusion of a full volume relaxation in the ab initio calculations improves the fit of the theoretical curve considerably.

The interaction of NO3 free radical and N2O5 with laboratory flame soot was investigated in a Knudsen flow reactor at T = 298 K equipped with beam-sampling mass spectrometry and in situ REMPI detection of NO2 and NO. Decane (C10H22) has been used as a fuel in a co-flow device for the generation of gray and black soot from a rich and a lean diffusion flame, respectively. The gas-phase reaction products of NO3 reacting with gray soot were NO, N2O5, HONO, and HNO3 with HONO being absent on black soot. The major loss of NO3 is adsorption on gray and black soot at yields of 65 and 59%, respectively, and the main gas-phase reaction product is N2O5 owing to heterogeneous recombination of NO3 with NO2 and NO according to NO3 + {C} --NO + products. HONO was quantitatively accounted for by the interaction of NO2 with gray soot in agreement with previous work. Product N2O5 was generated through heterogeneous recombination of NO3 with excess NO2, and the small quantity of HNO3 was explained by heterogeneous hydrolysis of N2O5. The reaction products of N2O5 on both types of soot were equimolar amounts of NO and NO2, which suggest the reaction N2O5 + {C} --N2O3(ads) + products with N2O3(ads) decomposing into NO + NO2. The initial and steady-state uptake coefficients gamma 0 and gamma ss of both NO3 and N2O5 based on the geometric surface area continuously increase with decreasing concentration at a concentration threshold for both types of soot. gamma ss of NO3 extrapolated to [NO3] --0 is independent of the type of soot and is 0.33 +/- 0.06 whereas gamma ss for [N2O5] --0 is (2.7 +/- 1.0) x 10(-2) and (5.2 +/- 0.2) x 10(-2) for gray and black soot, respectively. Above the concentration threshold of both NO3 and N2O5, gamma ss is independent of concentration with gamma ss(NO3) = 5.0 x 10(-2) and gamma ss(N2O5) = 5.0 x 10(-3). The inverse concentration dependence of gamma below the concentration threshold reveals a complex reaction mechanism for both NO3 and N2O5. The atmospheric significance of these results is briefly discussed.

Flow in shale nanopores may be vastly different from that in the conventional permeable media. In large pores and fractures, flow is governed by viscosity and pressure-driven. Convection describes the process. Pores in some shale media are in nanometer range. At this scale, continuum flow mechanism may not apply. Knudsen diffusion and hydrodynamic expressions such as the Hagen-Poiseuille equation and their modifications have been used to compute flow in nanopores. Both approaches may have drawbacks and can significantly underestimate molecular flux in nanopores. In this work, we use the dual control volume-grand canonical molecular dynamics simulations to investigate methane flow in carbon nanopores at low and high pressure conditions. Our simulations reveal that methane flow in a slit pore width of 1–4 nm can be more than one order of magnitude greater than that from Knudsen diffusion at low pressure and the Hagen-Poiseuille equation at high pressure. Knudsen diffusion and Hagen-Poiseuille equations do not account for surface adsorption and mobility of the adsorbed molecules, and inhomogeneous fluid density distributions. Mobility of molecules in the adsorbed layers significantly increases molecular flux. Molecular velocity profiles in nanopores deviate significantly from the Navier-Stokes hydrodynamic predictions. Our molecular simulation results are in agreement with the enhanced flow measurements in carbon nanotubes.

This study examines hydrogen (H2) transport and separation factors for various gases on mesoporous membrane for unmodified and dip-coated silica membrane. Single gas permeation of H2, N2, CH4, Ar and CO2 were determined at permeation temperature of 298–373 K and feed gauge pressure of 0.1 to 0.9 barg. H2 permaetion rose from 3.3 to about 6.4 l/min at 0.9 bar. H2 selectivity over N2, CH4, Ar and CO2 for the dip-coated silica membrane at 298 K and 0.9 bar was 2.93, 2.18, 3.51 and 3.61 respectively. Observation of the permeation of these membranes revealed that the transport of gases is governed by a combination of activated transport and knudsen flow.

A nano filter showing the Knudsen flow was demonstrated by a modification of a membrane constructed from rice husk silica. The membrane was prepared by pressing and sintering micron sized rice husk silica with 4 nm pores. The membrane showed a permeability of 5.2 × 10−8 mol m−1 sec−1 Pa−1 for H2 and ratios of gas permeability 2.1 and 3.2 for k(H2)/k(CH4) and k(H2)/k(CO2), respectively. When the membrane was treated by filtration of ∼100 nm sized rice husk silica particles, the permeability decreased to 4.9 × 10−8 mol m−1 sec−1 Pa−1 and the ratios increased to 2.2 and 3.4. In the case of the membrane after treatments with the dispersion and chemical deposition of tetraethylorthosilicate (TEOS), the corresponding permeability and ratios of the membrane were 1.8 × 10−8 mol m−1 sec−1 Pa−1, and 2.9 and 4.5, respectively. From the change of the ratio of gas permeability for the membrane with modifications, it is suggested that ∼100 nm sized rice husk silica particles pack the large pores among the micron sized rice husk silica particles while the chemical deposition of tetraethylorthosilicate (TEOS) reveals the gas flow through 4 nm pores in the rice husk silica by blocking large pores.

Constant volume systems are commonly used for the determination of the diffusion, permeability and solubility coefficients of gases in porous and nonporous media. In this paper we present important considerations for the design of an outflow receiver of a constant volume system to minimize the possible resistance to gas transport downstream from the tested medium. The receiver considered in this paper consists of main tube, a tank, and a tube connecting the main tube with the tank. The resistance of the receiver is quantified using the concepts of the asymptotic solution and the time lag by assuming that gas accumulation in the receiver occurs in the Knudsen flow regime. The effects of the volume of the tank, the position at which the tank is connected to the main tube, the length of the connecting tube, as well as, the position of the pressure sensor in the receiver are discussed.

The gas flow through a network of crossing thin micro-machined channels has been successfully modeled and simulated. The crossings are formed by two sets of v-grooves that intersect as two silicon wafers are bonded together. The gas is distributed from inlets via a manifold of channels to the narrow v-grooves. The narrow v-grooves could work as a particle filter. The fluidic model is derived from the Navier–Stokes equation and assumes laminar isothermal flow and incorporates small Knudsen number corrections and Poiseuille number calculations. The simulations use the finite element method. Several elements of the full crossing network model are treated separately before lumping them together: the straight v-grooves, a single crossing in an infinite set and a set of exactly four crossings along the flow path. The introduction of a crossing effectively corresponds to a virtual reduction of the length of the flow path, thereby defining a new effective length. The first and last crossings of each flow path together contribute to a pressure drop equal to that from three ordinary crossings. The derived full network model has been compared to previous experimental results on several differently shaped crossed v-groove networks. Within the experimental errors, the model corresponds to the mass flow and pressure drop measurements. The main error source is the uncertainty in v-groove width which has a profound impact on the fluidic behavior.

Humidification and dehumidification are common processes in air conditioning industry. In this study, a new technique‐the hydrophobic membrane based air humidification and dehumidification are investigated. The effects of membrane characteristics on moisture exchange effectiveness of the system are studied. A two‐dimensional transient model which takes into account the combined mechanisms of Knudsen flow and ordinary diffusion in membrane pores is proposed and validated. Four membranes, 2 hydrophobic treated Nylon and 2 PVDF, are used in the test to validate the model. Then the effects of variations of membrane properties on the system performance and membrane to total resistance ratio, are evaluated. A dimensionless Number of Transfer Units (NTU) can be summarized to govern the moisture exchange performance. Following, a correlation has been obtained to reflect the relations between the moisture exchange effectiveness and the Number of Transfer Units.