Unidimensional Approximation of the Diffuse Electrical Layer in the Inner Volume of Solid Electrolyte Grains in the Absence of Background Ions

In this paper we continue working on our theory of electrical double layers resulting exclusively from dissociation of a solid electrolyte, which we previously proposed as a medium for catalytic interaction between solid cellulose and solid acid catalysts of hydrolysis. Two theoretical unidimensional models of the inner grain volume are considered: an infinitely long cylindrical pore, and a gel electrolyte near a grain outer surface. Despite the model simplicity, the predictions for the cylindrical pore case are in semi-quantitative agreement with literature data on electroosmotic experiments, adequately explaining high proton selectivity of sulfonic membranes, and decline of such selectivity at high background acid concentration. The gel model predicts less concentrated diffuse layer in comparison to electrolytes with impenetrable skeleton (e. g., sulfonated carbons). This suggests limited suitability of gel electrolytes as catalysts if a substrate cannot diffuse into the gel bulk and the reaction is thereby spatially limited to the near-surface region, for example if a substrate is solid like aforementioned cellulose.     

On the viscosity of composite suspensions of aluminum and ammonium perchlorate particles dispersed in hydroxyl terminated polybutadiene--New empirical model

The rheological properties of fuel suspensions with various solid loadings up to close their maximum packing fraction and suspending media having different viscosities are investigated using the rotational viscometer at relatively low shear rates in which suspensions behave as Newtonian fluids. Aluminum (Al) and ammonium perchlorate (AP) particles are major solid components of any solid fuel system which should be distributed uniformly inside a polymeric binder based on hydroxyl terminated polybutadiene (HTPB). The experimental data generated in this investigation indicates that the relative viscosity of the suspensions is independent of viscosity of polymer binder, but in addition to solid content, geometrical aspects of the solid particles affect strongly the relative viscosity of suspensions. Maximum packing fraction of filler is found to be suitable quantitative measure of filler characteristics such as size, size distribution, shape and structure. Consequently, it is revealed that the relative viscosity of fuel suspension is a unique function of reduced volume fraction (Phi). Based on analogy of viscosity enhancement of reactive resin with cure conversion and suspension with filler content, an empirical model with two adjustable parameters originated from resin gelation model is suggested. According to this model and experimental results obtained in this investigation, a generalized model is proposed to describe the relative viscosity as a function of solid content in which the adjustable parameters are found to be general constants. The generalized model which is expressed as mu(r) = (1-Phi)(0.3 Phi-2) is found to be quite accurate to predict the experimental data. Furthermore, the applicability and accuracy of the generalized model are evaluated using the viscosity data of some suspension systems reported in the literature.     

Extended Poisson–Nernst–Planck modeling of membrane blockage via insoluble reaction products

A generalized time-dependent mathematical model is developed for a diffusion–migration–reaction system incorporating a pore blockage effect due to generation of insoluble precipitates in a porous membrane. The system behavior is investigated via direct numerical solution of an extended, highly non-linear equation set based on the classical Poisson–Nernst–Planck equations for ion transport. In order to treat the buildup of solid reaction products in the membrane, this novel formulation incorporates both a reaction term and a space- and time-dependent diffusivity expression based on a simple precipitation model. The model is demonstrated for a generalized case and then extended to cover the well-known reaction of silver and chloride ions to form insoluble AgCl. Time-dependent concentration profiles of all ions in the membrane are obtained and the effects of precipitate buildup in the pore space are investigated. The role of counterions in the transient behavior of the system is also clarified.     

Structural and Transport Properties of Alumina Porous Membranes from Process-Based and Statistical Reconstruction Techniques

We study the structural and transport properties of two model porous membranes made by compaction of spherical monosize gamma-alumina particles. A ballistic deposition process of spherical particles has been employed as a process-based representation method for accurately simulating the pore structure of the membranes. Comparison between the computed and experimental permeability values obtained in the Knudsen regime shows very good agreement for both membranes and indicates that sufficient representation of the original pore structure is achieved with the random sphere packs. In a further step, a medium with the same porosity and autocorrelation function as the sphere pack has been stochastically reconstructed. Comparison between the structural properties of the random sphere pack system (process-based model) and the stochastically reconstructed medium (statistical model) shows nearly identical correlation functions and pore chord length distributions but widely different mass chord length distributions. This is reflected to a significant difference in the prediction of a dynamic property like the Knudsen permeability by a factor of about 4. The results suggest that matching of the porosity and the two-point correlation function alone is not always adequate when pursuing an accurate representation of the structure of a porous material. In such cases, higher order statistical properties of the material contained in the chord length distribution of both pore and solid phase should be satisfied as well. It is also found that proper account of the formation process in the reconstruction of a porous material (process-based model) leads to representations of its structure more accurate than those of statistical reconstruction models. Copyright 2000 Academic Press.     

A generalized kinetic model for heterogeneous gas-solid reactions

We present a generalized kinetic model for gas-solid heterogeneous reactions taking place at the interface between two phases. The model studies the reaction kinetics by taking into account the reactions at the interface, as well as the transport process within the product layer. The standard unreacted shrinking core model relies on the assumption of quasi-static diffusion that results in a steady-state concentration profile of gas reactant in the product layer. By relaxing this assumption and resolving the entire problem, general solutions can be obtained for reaction kinetics, including the reaction front velocity and the conversion (volume fraction of reacted solid). The unreacted shrinking core model is shown to be accurate and in agreement with the generalized model for slow reaction (or fast diffusion), low concentration of gas reactant, and small solid size. Otherwise, a generalized kinetic model should be used.     

Structural Models of Dense Gels

The structural models of gels typically reported concentrate either on the solid space or the pore space of the system. The models described in this paper present a connection between grain and pore spaces, applicable to dense gels with uniform particulate microstructure. The gel structure is depicted as a hierarchy at several levels by means of models built up using the Monte-Carlo technique, on the basis of random close packing (RCP) premises. The pore volume distributions are calculated from the largest sphere radius inscribed within the interstices. These distributions are compared to the pore volume distributions of various RCP classic models and to the pore volume distributions of a series of xerogels measured by means of the Brunauer-Emmett-Teller method. Data on the pore volumes associated with different hierarchical levels (e.g., micro-, meso-, or macropores), the local density of the i-th aggregation level and packing of the successive levels are obtained.     

Diffusion in hierarchical mesoporous materials: applicability and generalization of the fast-exchange diffusion model

Transport properties of cyclohexane confined to a silica material with an ordered, bimodal pore structure have been studied by means of pulsed field gradient nuclear magnetic resonance. A particular organization of the well-defined pore structure, composed of a collection of spatially ordered, spherical mesopores interconnected via narrow worm-like pores, allowed for a quantitative analysis of the diffusion process in a medium with spatially ordered distribution of the fluid density for a broad range of the gas-liquid equilibria. The measured diffusion data were interpreted in terms of effective diffusivities, which were determined within a microscopic model considering long-range molecular trajectories constructed by assembling the alternating pieces of displacement in the two constituting pore spaces. It has further been found that for the system under study, in particular, and for mesoporous materials with multiple porosities, in general, this generalized model simplifies to the conventional fast-exchange model used in the literature. Thus, not only was justification of the applicability of the fast-exchange model to a diversity of mesoporous materials provided, but the diffusion parameters entering the fast-exchange model were also exactly defined. The equation resulting in this way was found to nicely reproduce the experimentally determined diffusivities, establishing a methodology for targeted fine-tuning of transport properties of fluids in hierarchical materials with multiple porosities.     

Kinetic models comparison for steam gasification of different nature fuel chars

The reactivity in steam of five different types of solid fuels (two coals, two types of biomass and a petcoke) has been studied. The fuel chars were obtained by pyrolysis in a fixed-bed reactor at a temperature of 1373 K for 30 min. The gasification tests were carried out by thermogravimetric analysis (TG) at different temperatures and steam concentrations. The reactivity study was conducted in the kinetically controlled regime and three representative gas-solid models, volumetric model (VM), grain model (GM) and random pore model (RPM), were applied in order to describe the reactive behaviour of the chars during steam gasification. The kinetic parameters of these models were derived and the ability of the models to predict conversion and char reactivity during gasification was assessed. The best model for describing the behaviour of the samples was the RPM. The effect of the partial pressure of steam in gasification was studied, and the reaction order with respect to steam was determined. The reactivity of the chars was compared by means of a reactivity index. Biomass exhibited a higher reactivity than coals and petcoke. However, significant differences in reactivity were observed between the two types of biomass used, which could be due to catalytic effects.     

Influence of surface morphology on D2 desorption kinetics from amorphous solid water

The influence of surface morphology/porosity on the desorption kinetics of weakly bound species was investigated by depositing D2 on amorphous solid water (ASW) films grown by low temperature vapor deposition under various conditions and with differing thermal histories. A broad distribution of binding energies of the D2 monolayer on nonporous and porous ASW was measured experimentally and correlated by theoretical calculations to differences in the degree of coordination of the adsorbed H2 (D2) to H2O molecules in the ASW depending on the nature of the adsorption site, i.e., surface valleys vs surface peaks in a nanoscale rough film surface. For porous films, the effect of porosity on the desorption kinetics was observed to be a reduction in the desorption rate with film thickness and a change in peak shape. This can be partly explained by fast diffusion into the ASW pore structure via a simple one-dimensional diffusion model and by a change in binding energy statistics with increasing total effective surface area. Furthermore, the D2 desorption kinetics on thermally annealed ASW films were investigated. The main effect was seen to be a reduction in porosity and in the number of highly coordinated binding sites with anneal temperature due to ASW restructuring and pore collapse. These results contribute to the understanding of desorption from porous materials and to the development of correct models for desorption from and catalytic processes on dust grain surfaces in the interstellar medium.     

Stochastic theory of size exclusion chromatography by the characteristic function approach

A general stochastic theory of size exclusion chromatography (SEC) able to account for size dependence on both pore ingress and egress processes, moving zone dispersion and pore size distribution, was developed. The relationship between stochastic-chromatographic and batch equilibrium conditions are discussed and the fundamental role of the 'ergodic' hypothesis in establishing a link between them is emphasized. SEC models are solved by means of the characteristic function method and chromatographic parameters like plate height, peak skewness and excess are derived. The peak shapes are obtained by numerical inversion of the characteristic function under the most general conditions of the exploited models. Separate size effects on pore ingress and pore egress processes are investigated and their effects on both retention selectivity and efficiency are clearly shown. The peak splitting phenomenon and peak tailing due to incomplete sample sorption near to the exclusion limit is discussed. An SEC model for columns with two types of pores is discussed and several effects on retention selectivity and efficiency coming from pore size differences and their relative abundance are singled out. The relevance of moving zone dispersion on separation is investigated. The present approach proves to be general and able to account for more complex SEC conditions such as continuous pore size distributions and mixed retention mechanism.     

Quantitative information on pore size distribution from the tangents of comparison plots

The comparison plot obtained from the nitrogen adsorption data has a similar shape to that of the curve of accumulating pore volume of a solid. The intrinsic nature of this relation is discussed. It is known that the derivatives of the accumulating pore volume with respect to the pore size are the pore size distribution (PSD) of the solid. Thus, the tangent curve of the comparison plot can display, at least qualitatively, the PSD of a solid, over a wide range of pore sizes (from approximately 1 to 50 nm) because the comparison plot is applicable to both micropores and mesopores. Quantitative pore structure information can be derived from the comparison plots by establishing a relationship between the t value and the pore size from the samples with uniform pore structure and known pore sizes, such as MCM-41 and alumina pillared clay samples. A calculation procedure to derive quantitative PSD from the comparison plots is suggested, giving reasonable results. This study proposes concise and reliable methods based on the comparison plots to derive information on pore structure in porous solids.     

钛酸锌脱硫剂硫化过程的动力学分析

利用固定床反应器对钛酸锌高温煤气脱硫剂硫化过程的动力学进行了研究,考察了硫化反应温度、H2S体积分数对脱硫反应过程的影响。结果表明,脱硫剂具有良好的脱硫反应活性,在400 ℃～600 ℃,脱硫剂的硫化反应速率随着硫化反应温度的升高、反应器入口H2S 体积分数的增大而增大。在实验数据的基础上,利用等效粒子模型对其反应动力学进行了分析,发现该脱硫剂的硫化反应主要受固体内扩散控制,固体内扩散活化能为 61.4 kJ/mol,相应的频率因子为 4.4×105 m2/min。硫化反应后脱硫剂比表面积、孔体积显著减小,脱硫剂表面有颗粒聚集物存在,进一步验证了该脱硫剂的硫化反应主要是通过产物层的体相扩散控制的。     

Heat transfer through fibrous assemblies by fractal method

Fractal theory has been proved effective to characterize the complex pore structure. In this article, the fractal method is utilized to study the structure property of fibrous assemblies. The box dimension parameter is applied to characterize the pore structure of fibrous assemblies by analyzing the electronic scanning microscope images of the fibrous assemblies. Furthermore, a fractal model for predicting effective heat conductivity is established. Experiment is conducted to verify the model, and good agreement is found between the experimental and theoretical results. The fractal model is also compared with the previous models for predicating heat conductivity, and the former is proved to be more accurate.     

Effect of the pore geometry in the characterization of the pore size distribution of activated carbons

In this work, the characterization of Activated Carbons (AC) by using the independent pore models is discussed, with special emphasis on the issue of how the assumed pore geometry can affect the resulting Pore Size Distribution (rPSD) and on the problem of the unicity of the PSD when different probe molecules are used in adsorption experiments. A theoretical test was performed using virtual solids based in the so-called Mixed Geometry Model (MGM) (Azevedo et al. 2010). The MGM uses a kernel of adsorption isotherms generated by GCMC for different pore sizes and two pore geometries: slit and triangular. The adsorption isotherms of a virtual MGM solid were fitted with both the traditional Slit Geometry Model (SGM) and the Mixed Geometry Model (MGM). It is demonstrated that, by assuming a different pore geometry model from that of the real sample, different PSDs may be obtained by fitting adsorption isotherms of different probe gases. Finally, experimental results are shown which both point toward the MGM as an acceptable extension of the SGM and confirm that the MGM is a closer representation of the actual porous structure of most activated carbons.     

Importance of molecular shape in the adsorption of nitrogen,carbon dioxide and methane on surfaces and in confined spaces

The importance of shape in the adsorption of nitrogen, carbon dioxide and methane (common molecular probes for solid characterization) on surfaces and in confined spaces is investigated for its effects on the adsorption capacity and isosteric heat. We study the possibility of using an equivalent pseudo-sphere model to describe the potential energy of interaction of these molecular probes. On a flat open surface, we find that the equivalent pseudo-sphere model describes adsorption of these species sufficiently well. However, in the confined space of pores, especially pores that accommodate three layers or less, the pseudo-sphere model describes the adsorption badly because of the geometrical constraint on the molecular packing. It is recommended that to study adsorption properly in small pores, potential models that correctly describe molecular shape should be used. In characterization, pseudo-sphere models are commonly used to generate the kernels (local isotherms) for the determination of pore size distribution which can lead to misleading results. We illustrate this with an example to show that the wrong pore size distribution results if pseudo-sphere kernels are used.     

Frequency-Dependent Streaming Potentials

An experimental apparatus and data acquisition system was constructed to measure the streaming potential coupling coefficients as a function of frequency. The purpose of the experiments was to measure, for the first time, the real and imaginary portion of streaming potentials. In addition, the measured frequency range was extended beyond any previous measurements. Frequency-dependent streaming potential experiments were conducted on one glass capillary and two porous glass filters. The sample pore diameters ranged from 1 mm to 34 μm. Two frequency-dependent models (Packard and Pride) were compared to the data. Both Pride's and Packard's models have a good fit to the experimental data in the low- and intermediate-frequency regime. In the high-frequency regime, the data fit the theory after being corrected for capacitance effects of the experimental setup. Pride's generalized model appears to have the ability to more accurately estimate pore sizes in the porous medium samples. Packard's model has one unknown model parameter while Pride's model has four unknown model parameters, two of which can be independently determined experimentally. Pride's additional parameters may allow for a determination of permeability. Copyright 2001 Academic Press.     

Numerical studies of hydrate dissociation and gas production behavior in porous media during depressurization process

In this study,a numerical model is developed to investigate the hydrate dissociation and gas production in porous media by depressurization.A series of simulation runs are conducted to study the impacts of permeability characteristics,including permeability reduction exponent,absolute permeability,hydrate accumulation habits and hydrate saturation,sand average grain size and irreducible water saturation.The effects of the distribution of hydrate in porous media are examined by adapting conceptual models of hydrate accumulation habits into simulations to govern the evolution of permeability with hydrate decomposition,which is also compared with the conventional reservoir permeability model,i.e.Corey model.The simulations show that the hydrate dissociation rate increases with the decrease of permeability reduction exponent,hydrate saturation and the sand average grain size.Compared with the conceptual models of hydrate accumulation habits,our simulations indicate that Corey model overpredicts the gas production and the performance of hydrate coating models is superior to that of hydrate filling models in gas production,which behavior does follow by the order of capillary coating>pore coating>pore filling>capillary filling.From the analysis of t1/2,some interesting results are suggested as follows:(1) there is a "switch" value(the"switch"absolute permeability) for laboratory-scale hydrate dissociation in porous media,the absolute permeability has almost no influence on the gas production behavior when the permeability exceeds the "switch" value.In this study,the "switch" value of absolute permeability can be estimated to be between 10 and 50 md.(2) An optimum value of initial effective water saturation Sw,e exists where hydrate dissociation rate reaches the maximum and the optimum value largely coincides with the value of irreducible water saturation S wr,e.For the case of Sw,Swr,e,there are different control mechanisms dominating the process of hydrate dissociation and gas production.