Coupled diffusion of water and ethanol in a polyimide membrane

In this work, the sorplion and steady state permeation of water‐ethanol mixture in an aromatic polyimidc membrane was investigated with the objective of revealing the coupling cherts of water and ethanol in their course of diffusion. The solubility of the watcr‐ethanol mixture in the membrane was determined by means of swelling‐distillation techniques. The sorption behavior was interpreted in terms of the thermodynamic equilibrium equations. The Maxwell‐Stefan mass transfer model was employed as a framework for modeling diffusion. Model equations derived therefrom enable us to cplculate coupled fluxes of water and ethanol from the experimental data. The coupling effects in the diffusion of water and ethanol were revealed by comparing the calculated coupled flux with non‐coupling flux, which was calculated by integration of the Fickian first law using independent diffusion coefficients. Furthermore, the implication of the sole adjustable parameter included in the derived model equations was discussed.     

Two‐dimensional model of methane thermal decomposition reactors with radiative heat transfer and carbon particle growth

A two‐dimensional model of methane thermal decomposition reactors is developed which accounts for coupled radiative heat and polydisperse carbon particle nucleation, growth, and transport. The model uses the Navier–Stokes equations for the fluid dynamics, the radiative transfer equation for methane and particle species radiation absorption, the advection–diffusion equation for gas and particle species transport, and a sectional method for particle species nucleation, heterogenous growth, and coagulation. The model is applied to a tubular laminar flow reactor. The simulation results indicate the development of a reaction boundary layer inside the reactor, which results in significant variation of the local particle size distribution across the reactor. © 2011 American Institute of Chemical Engineers AIChE J, 58: 2545–2556, 2012     

Mass transfer in continuous mixtures with Maxwell–Stefan diffusion using the adaptive characterization method

The adaptive pseudocomponent characterization method for continuous mixtures was extended to mass transfer problems using the Maxwell–Stefan diffusion model. It is based on the direct quadrature method of moments (DQMoM), using a quadrature rule to discretize the molar fraction distribution of the continuous mixture. The solution method was applied to two one-dimensional mass transfer problems: the transient diffusion in a Loschmidt tube and the steady-state diffusion in a thin film. In the latter, it was showed that the DQMoM equations reduce to an equivalent problem with a fixed characterization and solution methods for linearized theory problems can be employed. For these two problems, the proposed method was verified against the discrete component model (DCM), whose implementation was also verified against existing solutions. Results showed that the adaptive method with five pseudocomponents predicts the mixture properties with maximum relative deviation smaller than 1% when compared to the DCM with 57 components.     

Conjugate heat and mass transfer model for predicting thin-layer drying uniformity in a compact,crossflow dehydrator

Abstract

A conjugate heat and mass transfer model was implemented into a commercial CFD code to analyze the convective drying of corn. The Navier–Stokes equations for drying air flow were coupled to diffusion equations for heat and moisture transport in a corn kernel during drying. Model formulation and implementation in the commercial software is discussed. Validation simulations were conducted to compare numerical results to experimental, thin-layer drying data. The model was then used to analyze drying performance for a compact, crossflow dehydrator. At low inlet air temperatures, the drying rate in the compact dehydrator matched the thin-layer drying rate. At higher temperatures, heat losses through the external walls resulted in temperature and moisture variations across the dehydrator.     

DRYING GRANULAR POROUS MEDIA - THEORY AND EXPERIMENT

From a general theory of drying granular porous media, we have constructed a simplified theory that consists of a set of coupled, volume-averaged transport equations for the temperature and the saturation. The theory incorporates the liquid and vapor phase continuity equations, combines the liquid, solid and vapor phase thermal energy equations into a single temperature equation and makes use of Darcy's law for the liquid phase to account for moisture transport owing to capillary action. By purely qualitative reasoning, one can show that combined heat and mass transfer theories of drying cannot provide a complete theoretical explanation of drying phenomena and a detailed comparison between theory and experiment supports this point of view. Speculation concerning the logical course of subsequent theoretical studies is provided.     

Multicomponent mass diffusion in porous pellets: Effects of flux models on the pellet level and impacts on the reactor level. Application to methanol synthesis

A heterogeneous model has been derived for a fixed packed‐bed reactor producing methanol. Several closures for the intra‐particle mass diffusion fluxes; Maxwell–Stefan, Wilke, dusty gas and Wilke–Bosanquet, have been compared on the level of the catalyst pellet and the impacts of the different particle flux closures on the reactor performance are investigated. A preparatory study of the transport phenomena on the pellet level is recommended prior to any large‐scale reactor simulation to determine what are the rate determining transport mechanisms. Hence, if Knudsen diffusion is apparent on the level of the pellet, a combined bulk and Knudsen diffusion model should naturally be used in the reactor simulations as well, because Knudsen diffusion can influence significantly on the reactor conversion. Minor differences are observed between the diffusion flux models on both pellet and reactor level. Hence, for the reactor operation conditions applied in this study, the Wilke model is a good approximation to the rigorous Maxwell–Stefan model, and similarly, the Wilke–Bosanquet model is an appropriate model to use in replacement for the dusty gas model. Moreover, variable pressure and viscous flow can be neglected in the pellet model, as the effect of these contributions are not visible at neither pellet or reactor level. © 2011 Canadian Society for Chemical Engineering     

Mathematical Modelling of Cation Contamination in a Proton‐exchange Membrane

Transport phenomena in an ion‐exchange membrane containing both H⁺ and K⁺ are described using multicomponent diffusion equations (Stefan–Maxwell). A model is developed for transport through a Nafion 112 membrane in a hydrogen‐pump setup. The model results are analysed to quantify the impact of cation contamination on cell potential. It is shown that limiting current densities can result due to a decrease in proton concentration caused by the build‐up of contaminant ions. An average cation concentration of 30 to 40% is required for appreciable effects to be noticed under typical steady‐state operating conditions.     

Mixed convection heat transfer enhancement through latent heat transport in vertical parallel plate channel flows

A detailed numerical study has been performed to examine the heat transfer enhancement through latent heat transport, in conjunction with the evaporation of a liquid film, in laminar mixed convection channel flows. Results for Nusselt numbers are presented for the air–water and air–ethanol systems under various conditions. Considerable augmentation in heat transfer due to the exchange of latent heat during the evaporation process was clearly demonstrated. The results show that the heat transfer is dominated by the transport of latent heat exchange.     

Model based operation of emulsion polymerization reactors with evaporative cooling: Application to vinyl acetate homopolymerization

This work aims at maximizing the productivity of emulsion homopolymerization processes. A dynamic model of emulsion polymerization processes is extended by the inclusion of vaporization from the liquid phases in the reactor to the gaseous phase. The multi-component gas–liquid mass transfer phenomenon is described by the Maxwell–Stefan diffusion equations, which are solved by a special algorithm. A novel operation strategy is developed for running a reactor optimally with respect to batch time. This strategy is applied first to an industrial scale reactor, which is run without using evaporative cooling. Then, based on the extended model, controlled vaporization is included by which additional heat is removed from the reaction system. This makes it possible to extend the restrictions imposed by the limited heat removal of the cooling jacket considerably. Simulation results are presented for the homopolymerization of vinyl acetate in an industrial scale reactor operated in semi-batch mode. The results show that a significant amount of heat can be removed by evaporative cooling thus leading to higher productivity.     

The continuum mechanical theory of multicomponent diffusion in fluid mixtures

The continuum mechanical approach for deriving the generalized equations of multicomponent diffusion in fluids is described here in detail, which is based on application of the principle of linear momentum balance to a species in a mixture, resulting in the complete set of diffusion driving forces. When combined with the usual constitutive equations including the continuum friction treatment of diffusion, the result is a very complete and clear exposition of multicomponent diffusion that unifies previous work and includes all of the various possible driving forces as well as the generalized Maxwell–Stefan form of the constitutive equations, with reciprocal diffusion coefficients resulting from Newton’s third law applied to individual molecular encounters. This intuitively appealing and rigorous approach, first proposed over 50 years ago, has been virtually ignored in the chemical engineering literature, although it has a considerable following in the mechanical engineering literature, where the focus, naturally, has been physical properties of multiphase fluid and solid mixtures. The described approach has the advantages of transparency over the conventional approach of non-equilibrium thermodynamics and of simplicity over those based on statistical mechanical or kinetic theory of gases or liquids. We provide the general derivation along with some new results in order to call attention of chemical engineers to this comprehensive, attractive, and accessible theory of multicomponent diffusion in fluids.     

大面积瓷质砖坯体干燥过程的二维传热传质研究

引用建立于Whitaker的体积平均方程和Darcy定律基础上的多孔介质内部热质传递的等效耦合扩散模型 ,寻出一组关于液体饱和度、温度和气相压力的新支配方程 ,应用该方程组对瓷质砖坯体二维干燥过程进行了数值分析。并将传统干燥器与新型干燥器的模拟数据进行比较 ,以期获得某些定性或定量的结论 ,从而用以指导实际生产过程。     

Performance Optimization of a Brick Dryer Using Porous Simulation Approach

In the present study, an innovative method for an accurate simulation and design of a chamber dryer used in the brick/ceramic industry has been proposed. A thorough investigation of currently used dryers is conducted and optimization criteria are detected and discussed. Three-dimensional modeling of the chamber dryer has been performed. In the second step, from the result of 3D modeling, the critical values for heat transfer coefficient are obtained. The governing equations for a two-dimensional brick as a porous solid are derived by combining conservation laws and Fourier's law for heat conduction and Darcy's and Fick's laws for mass diffusion in porous material. The set of partial differential equations governing heat and mass transport in a single brick together with the respective temperature and humidity boundary conditions have been solved numerically based on finite difference method. Finally, an efficient scheme for the air circulation devices, inlet air temperature and humidity, burner characteristics, flow rates, and drying process control have been proposed for a typical industrial-scale brick dryer.     

瓷质砖湿坯对流干燥过程的传热传质研究

引用建立于Whitaker的体积平均方程和Darcy定律基础止的多孔介质内部热质传递的等效耦合扩散模型，寻出一组关于液体饱和度、温度和气相压力的新支配方程，应用该方程组对瓷质砖坯体干燥过程进行了数值分析和实验测定。在平均含湿饱和度的变化方面，数值解与实验结果十分吻合。还改变影响坯体干燥过程的一些因素进行计算机模拟计算，通过改变这些因素的大小来考察计算结果，以期获得某些定性或定量的结论，从而用以指导实际生产过程。     

Krypton‐xenon separation properties of SAPO‐34 zeolite materials and membranes

Separation of the radioisotope ⁸⁵Kr from ¹³⁶Xe is an important target during used nuclear fuel recycling. We report a detailed study on the Kr and Xe adsorption, diffusion, and membrane permeation properties of the silicoaluminophosphate zeolite SAPO‐34. Adsorption and diffusion measurements on SAPO‐34 crystals indicate their potential for use in Kr‐Xe separation membranes, but also highlight competing effects of adsorption and diffusion selectivity. SAPO‐34 membranes are synthesized on α?alumina disk and tubular substrates via steam assisted conversion seeding and hydrothermal growth, and are characterized in detail. Membrane transport measurements reveal that SAPO‐34 membranes can separate Kr from Xe by molecular sieving, with Kr permeabilities around 50 Barrer and mixture selectivity of 25–30 for Kr at ambient or slight sub‐ambient conditions. The membrane transport characteristics are modeled by the Maxwell‐Stefan equations, whose predictions are in very good agreement with experiment and confirm the minimal competing effects of adsorption and diffusion. © 2016 American Institute of Chemical Engineers AIChE J, 63: 761–769, 2017     

Mass transfer simulation on pervaporation dehydration of ethanol through hollow fiber NaA zeolite membranes

A multi‐layer series‐resistance mass transfer model was developed to simulate mass transfer behaviors of water/ethanol mixture through hollow fiber NaA zeolite membranes. The mass transfer through zeolite layer was described by Maxwell‐Stefan mechanism based on adsorption and diffusion parameters obtained from molecular simulation. The mass transfer through asymmetric hollow fiber support was described by dusty gas model involving Knudsen diffusion and viscous flow. It was found that the sponge‐like layer of support besides of zeolite layer made an important contribution to overall membrane transfer resistance while the finger‐like layer had less effect. When permeate pressure shifted from 0.2 to 7.5 kPa, the mass transfer resistance contribution of sponge‐like layer varied from 27.1 to 17.8%. Effects of microstructure parameters of support on mass transfer through membrane were investigated extensively. Large pore size and thin thickness for sponge‐like layer of support were beneficial to improve water permeation flux. © 2016 American Institute of Chemical Engineers AIChE J, 62: 2468–2478, 2016     

Transport phenomena in electrolyte solutions: Nonequilibrium thermodynamics and statistical mechanics

The theory of transport phenomena in multicomponent electrolyte solutions is presented here through the integration of continuum mechanics, electromagnetism, and nonequilibrium thermodynamics. The governing equations of irreversible thermodynamics, including balance laws, Maxwell's equations, internal entropy production, and linear laws relating the thermodynamic forces and fluxes, are derived. Green–Kubo relations for the transport coefficients connecting electrochemical potential gradients and diffusive fluxes are obtained in terms of the flux–flux time correlations. The relationship between the derived transport coefficients and those of the Stefan–Maxwell and infinitely dilute frameworks are presented, and the connection between the transport matrix and experimentally measurable quantities is described. To exemplify the application of the derived Green–Kubo relations in molecular simulations, the matrix of transport coefficients for lithium and chloride ions in dimethyl sulfoxide is computed using classical molecular dynamics and compared with experimental measurements.     

Applicability of the linearized theory of the Maxwell–Stefan equations

The present article aims for a better understanding of the applicability of the linearized theory of the Maxwell–Stefan equations for multi‐component diffusion. An analysis of the theory's accuracy is performed with respect to the classical two‐bulb diffusion experiments by Duncan and Toor, from which the results are transferred to more general scenarios. It is shown that for an accurate linearized theory it is essential to have a quasi‐stationary and quasi‐one‐dimensional flux, and also a so‐called reference point. Two examples illustrating the theory's failure in case of unmet prerequisites are presented: a three‐bulb configuration and a two‐dimensional diffusion case. For the first setup the linearized theory results in negative concentrations, for the second it requires influxes at openings that are actually outlets. © 2016 American Institute of Chemical Engineers AIChE J, 62: 2929–2946, 2016