Fixed-bed ion exchange columns operating under non-equilibrium conditions: Estimation of mass transfer properties via non-equilibrium modeling

The present work describes a new technique for the estimation of particle film mass transfer coefficients, k_f and homogeneous solid diffusivity, D_hs for resins in fixed-bed ion exchange columns under non-linear adsorption isotherm conditions. The experimental set-up is composed of a fixed-bed ion exchange column operating under recycling flow, and a reservoir. The experiments are carried out with custom made para-magnetic composite ion exchange resin filled columns. The single pass non-equilibrium packed-bed adsorption model is adapted to the present recirculation system and the model equations are numerically solved by the implicit schemes of the finite differences technique for predicting the mass transfer parameters. In order to find the k_f values, model predicted reservoir concentration profiles for early-time data are generated, and different k_f values were substituted into the model until the predicted and the experimental reservoir vs. time profiles agree. Once k_f is known, a second version of the model is used by substituting different D_hs values where no time constraint is made. When the model output and the experimental reservoir concentration profiles agree, the corresponding D_hs value is taken as the homogeneous solid diffusion coefficient. The present methodology allows the experimental determination of k_f and D_hs values for fixed-bed ion exchange columns through a simple recirculation system.     

Percutaneous absorption of volatile solvents following transient liquid exposures II. Ethanol

The permeation of neat ethanol through split-thickness cadaver skin was measured in non-occluded Franz cells placed in a fume hood. The test compound spiked with ¹⁴C radiolabel was applied to skin using four doses ranging from 6.33 to 50.6 μL/cm² (5-40 μL over an area of 0.79 cm²). Additional gravimetric experiments were conducted with ethanol and benzene to determine the evaporation mass transfer coefficient. The experimental data were analyzed by non-linear regression analysis using a previously developed diffusion model in order to ascertain the optimal values of two adjustable parameters, the fractional deposition depth (f_dep) and the permeant diffusivity inside the stratum corneum (D_SC). Constant diffusivity and variable diffusivity models were considered. Both models were able to describe the combined observations from absorption data from three of the four applied doses. The best correlation between the experimental data and model predictions was observed with the variable diffusivity model.     

Evaluation of shear-induced particle diffusivity in red cell ghosts suspensions

The shear-induced particle diffusivity in the red blood cell suspensions was evaluated based on the flow model and experimental results in a rectangular flow chamber. The effective diffusivity (D_e) of solute in the particle suspensions is equal to the stationary diffusivity (D_s) of the solute plus the shear-induced particle diffusivity (D_p). The effective diffusivity (D_e) of bovine serum albumin (BSA) in the red blood cell (RBC) ghost suspensions was determined under diffusion-limited conditions using a total internal reflection fluorescence (TIRF) method as a function of suspended RBC ghost volume fractions (0.05-0.7) and shear rates (200-1,000 s,^-1). The stationary diffusivity (D_s) of BSA in RBC ghost suspensions was calculated by Meredith and Tobias model. Therefore the shear-induced particle diffusivity undergoing laminar shear flow can be evaluated. The shear-induced RBC ghost diffusivity was ranged from 0.35xl0^-7 to 21.2xl0^-7 cm²/s and it increased with increasing shear rate. Also the shear-induced RBC ghost diffusivity increased as a particle volume fraction increased as well, up to a particle volume fraction of 0.45. However, for RBC ghost volume fractions above 0.45, the shear-induced particle diffusivity decreased with increasing particle volume fraction. The shear-induced particle diffusivity in RBC ghost suspensions is a function of a particle Peclet number (or shear rate) and particle volume fractions. The dimensionless particle diffusivity (D^ρ/a²γ) was investigated as a function of particle volume fraction and these results are in good agreement with the literature values.     

A generalized model for the measurement of effective diffusion coefficients of heterovalent ions in ion exchangers by the zero-length column method

A generalized theoretical model for the measurement of effective diffusion coefficients of heterovalent ions in ion exchange resins by the zero-length column method was developed. The model included the resistance to mass transfer both in the particle and in the film and described ion fluxes with Nernst-Planck equations. Equilibria were described using a model based on the mass action law. The values of intraparticle diffusivity of Cu²⁺, Cd²⁺, Zn²⁺, and H⁺ on commercial Amberlite IR-120 were obtained by non-linear regression, these values agree fairly well with data reported previously in literature. The following trend was observed: D_Cu>D_Zn>D_Cd.     

Simulation of packed bed reactors using lattice Boltzmann methods

Lattice Boltzmann (LB) methods are used to simulate hydrodynamics, reaction and subsequent mass transfer in a disordered packed bed of catalyst particles at sub-pore length-scales. In contrast to previous studies, a variety of modifications are introduced in the LB method enabling particle Pe numbers up to 10⁸, and hence realistic values of diffusivity, to be accessed. These include decoupling the hydrodynamics from mass transfer and the use of a rest fraction in the LB formulation of mass transfer. In addition the mass transfer simulations are modified to permit spatially varying values of diffusivity, essential to differentiate between intra- and inter-particle diffusivity (D_intra and D_inter, respectively). The simulation method is applied to both a disordered and ordered 2D packing for a range of Pe (15.6-1557.8) and Re (0.16-1.56) numbers, as well as various ratios of D_intra/D_inter (0-1), whilst simulating an esterfication reaction catalyzed by an ion-exchange resin. The value of D_intra is found to have limited effect, whilst reducing Pe number results in a considerable increase in overall conversion. The simulation method is then applied to a 3D lattice for which experimental conversion data is available. This experimental data is straddled by the simulation case of D_intra=0 and D_intra=D_inter, as expected.     

Model for the determination of diffusion coefficients of heterovalent ions in macroporous ion exchange resins by the zero-length column method

A generalized theoretical model for the measurement of effective diffusion coefficients of heterovalent ions in macroporous ion-exchange resins by the zero-length column method was developed. The model includes the resistance to mass transfer both in the particle and in the film and described ion fluxes with Nernst-Planck equations. Equilibrium was described using the Langmuir type empirical equation. The values of intraparticle diffusivity of Cu²⁺, Cd²⁺, Zn²⁺, and H⁺ on commercial Lewatit TP-207 were obtained by non-linear regression, these values agree fairly well with data reported previously in literature. The following trend was observed: D_Cu>D_Zn>D_Cd.     

Determination of adsorption and diffusion parameters in zeolites through a structured approach

Temporal analysis of products (TAP) is a transient pulse-response technique that allows to extract kinetic information from reacting and adsorbing systems. In a previous work (Chem Eng Sci 57(2002) 1835), a detailed-transport model for the Multitrack set-up, a TAP-like system, was developed, which allows studying systems with a low bed resistance. The use of structured beds, having both a low bed resistance and small sorbent particles, is required to determine adsorption and diffusion parameters when strong adsorption and slow diffusion occurs. A method is presented to extend the range of measurable adsorption and diffusion parameters in zeolitic sorbents in the TAP technique by a structured approach. Small zeolite crystals are coated on larger non-porous glass beads. Adsorption and diffusion parameters for n-butane, SF₆ and 3-methylpentane have been determined in MFI-type zeolites. Absolute diffusivity values in the zeolite coating are estimated by using a well-defined silicalite sample as a reference to determine the effective diffusion length in the coating.Two criteria have been derived, one for the characteristic time for transport through the bed, , and one for the ratio of the latter and the characteristic diffusion time in the zeolite crystal, 0.01<α<200t_bed/(1+t_bed), which should be satisfied both to be able to determine values of the zeolite diffusivity.     

Distribution functions for the breakdown of passive films

A deterministic treatment is presented of the statistical nature of the breakdown of passive films on metal surfaces, in which it is assumed that breakdown sites on the surface are normally distributed in terms of the cation vacancy diffusivity (D) or log D. This analysis, which is based on the point defect model for the breakdown of passive films, predicts normal or near-normal distributions in the breakdown voltage, depending upon whether it is log D or D that is normally distributed. The model also yields distribution functions for the induction time that mimic the highly asymmetric form exhibited by experimental data. By using values for D, log D and their associated standard deviations, determined from the distributions in the breakdown voltage, the point defect model is able to account quantitatively for the experimentally observed distributions in the induction time for the breakdown of passive films on Fe-17Cr in 3.5% NaCl solution at 30°C, as reported by Shibata[1].     

Application of √t-type, logarithmic and half-time methods in desorptive measurements of diffusivity in narrow humidity ranges

This paper concerns the use of non-stationary desorptive measurement techniques for defining the mass diffusivity of cement based materials. Three different procedures are presented: √t-type calculation; logarithmic; and half-time procedures. Cement mortars of different water to cement ratios (w / c), equal to 0.50, 0.65 and 0.80 were selected as the model environment for testing the usability of the above-mentioned desorptive techniques. The study was carried out at the temperature (T) of 20 °C within narrow relative humidity (φ) ranges: from φ₁ = 30% to φ₂ = 12%, and 50% → 30%, 75% → 50%, 85% → 75%, 97% → 85%. The results obtained are used to evaluate the conformity of these methods. The conformity is analyzed with regard to each mortar in all the above humidity ranges Δφ. The values of diffusivity D_m, defined by means of the √t-type calculation and the logarithmic procedure, demonstrated rather high conformity, all relative differences between D_m(√t) and D_m(ln) did not exceeded 20%. However, the half-time procedure can be applied for rough estimation of the diffusivity only. That is because deviations between D_m(t_1 / 2) and the values found by means of the two other methods were too large.     

Preparation of zeolite‐incorporated poly(dimethyl siloxane) membranes for the pervaporation separation of isopropyl alcohol/water mixtures

ZSM‐5 zeolite‐incorporated poly(dimethyl siloxane) membranes were prepared, and the molecular dispersion of the zeolite in the membrane matrix was confirmed with scanning electron microscopy. After the swelling of the membranes was studied at 30°C, the membranes were subjected to the pervaporation separation of isopropyl alcohol/water mixtures at 30, 40, and 50°C. The effects of the zeolite loading and feed composition on the pervaporation performances of the membranes were analyzed. Both the permeation flux and selectivity increased simultaneously with increasing zeolite content in the membrane matrix. This was examined on the basis of the enhancement of hydrophobicity, selective adsorption, and the establishment of molecular sieving action. The membrane containing the highest zeolite loading (30 mass %) had the highest separation selectivity (80.84) and flux (6.78 × 10^?2 kg m^?2 h^?1) at 30°C with 5 mass % isopropyl alcohol in the feed. From the temperature dependence of the diffusion and permeation values, the Arrhenius activation parameters were estimated. A pure membrane exhibited higher activation energy values for permeability (E_p) and diffusivity (E_D) than zeolite‐incorporated membranes, and signified that permeation and diffusion required more energy for transport through the pure membrane because of its dense nature. Obviously, the zeolite‐incorporated membranes required less energy because of their molecular sieving action, which was attributed to the presence of straight and sinusoidal channels in the framework of the zeolite. For the zeolite‐incorporated membranes, the activation energy values obtained for isopropyl alcohol permeation were significantly lower than the water permeation values, and this suggested that the zeolite‐incorporated membranes had higher selectivity toward isopropyl alcohol. The E_p and E_D values ranged between 21.81 and 31.12 kJ/mol and between 15.27 and 41.49 kJ/mol, respectively. All the zeolite‐incorporated membranes exhibited positive values of the heat of sorption, and this suggested that the heat of sorption was dominated by Henry's mode of sorption. sorption. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 96: 1377–1387, 2005     

Combined analysis of self-diffusion, conductivity, and viscosity data on room temperature ionic liquids

The self-diffusion coefficient of anions and cations, the ionic conductivity and the viscosity of four room-temperature ionic liquids, 1-ethyl-3-methylimidazolium tetrafluoroborate (EMIBF₄), 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide (EMITFSI), 1-butylpyridinium tetrafluoroborate (BPBF₄), and 1-butylpyridinium bis(trifluoromethylsulfonyl)imide (BPTFSI) were analysed within a comprehensive ionic transport model. The experimental data, covering wide temperature ranges, were taken from the work of Noda et al. [J. Phys. Chem. B, 105, 2001]. To compare the dc conductivity with the self-diffusion coefficients, the former quantity was converted into a charge diffusivity D_σ using the Nernst-Einstein equation. In a similar way, we calculated a viscosity-related diffusivity D_η with the aid of the Stokes-Einstein equation. Taking three mobile species into account, i.e., single cations, single anions and neutral ion pairs, our model yields their individual diffusivities that obey a uniform Vogel-Tammann-Fulcher-like temperature dependence described by common values of the parameters B and T₀. Evaluating simultaneously all experimental data within this model yields the contribution of ion pairs to the self-diffusion coefficient of cations and anions separately. We further obtain the temperature-independent cation transference number and the effective hydrodynamic radius, which are important characteristics of charge and mass transport in these ionic liquids.     

Liquid phase axial mixing in bubble columns operated at high pressures

Liquid phase axial mixing was measured in a 100 mm i.d. bubble column operated in the pressure range of 0.1-0.5 MPa. Water, ethanol and 1-butanol were used as the liquid phase and nitrogen as the gas phase. The temperature and superficial gas velocity were varied in the range of 298-323 K and 0.01-0.21 m/s, respectively. The axial dispersion coefficient increased with an increase in the gas density due to pressure. The temperature had surprisingly a small effect. A CFD model was developed for the prediction of flow pattern in terms of mean velocity and eddy diffusivity profiles. The model was further extended for the prediction of residence time distribution and hence the axial dispersion coefficient (D_L). The predictions of axial dispersion coefficient agree favorably with all the experimental data collected in this work as well as published in the literature. The model was extended for different gas-liquid systems. The predicted values of axial dispersion coefficient were found to agree very well with all the experimental data.     

Axial mixing in laminar pipe flows

A computational model has been developed to simulate the axial dispersion phenomena in laminar pipe flows. Peclet number (Pe=au₀/D_m) and dimensionless time (τ=D_mt/a²) have been covered over a wide range of 1-10⁵ and 10⁻⁸ to 10², respectively. An extensive comparison of predicted mean concentration profiles with the experimental data has been presented. The proposed computational model for concentration profiles was found to give an excellent agreement with the experimental measurements. Further, the results compare well with other analytical and experimental studies. The solution has been shown to be valid at both the short and long times and for all values of the Peclet number.     

CFD simulations of bubble column reactors: 1D, 2D and 3D approach

CFD simulations have been carried out for the predictions of flow pattern in bubble column reactors using 1D, 2D and 3D k-ε models. An attempt has been made to develop a complete correspondence between the operation of a real column and the simulation. Attention has been focused on the cylindrical bubble columns because of their widespread applications in the industry. All the models showed good agreement with the experimental data for axial liquid velocity and the fractional gas hold-up profiles. However, as regards to eddy diffusivity, only the 3D model predictions agree closely with the experimental data.The CFD model has been extended for the estimation of an axial dispersion coefficient (D_L) using 1D, 2D and 3D models. Excellent agreement was found only between the experimental values and the 3D predictions. The 1D and 2D simulations, however, yielded D_L values, which were lower by 25-50%. For this, a mechanistic explanation has been provided.     

Optimizing membrane synthesis parameters via Taguchi method: An approach to prepare high performance mixed-matrix membranes for carbon capture applications

Mixed-matrix membranes (MMMs) comprising polysulfone (PSF) and zeolite 4A (Z4A) were prepared for carbon capture applications. Membranes of varying compositions were fabricated by solution casting technique. Viscous solutions of dissolved ingredients were cast on a clean glass plate followed by evaporation and drying of prepared membrane. Fabricated composite membranes were subjected to morphological, structural, and permeation analyzes. The morphological results showed a uniform dispersal of zeolite nanoparticles with agglomerates formation at higher nanofiller loadings. The structural analysis corroborated the noninteractive behaviour of organic polymer and inorganic zeolite phases. Permeation results suggested that the fabricated membranes were more permeable to CO₂ gas, which can be described by higher diffusivity and structural affinity for CO₂. Taguchi statistical analysis was employed to optimize carbon capture performance of developed hybrid membranes by carefully controlling the membrane casting parameters such as loading levels of functional nanofiller, sonication time, and drying time of casting solution. The statistical investigation of permeation results suggested the sensitivity of casting parameters on membrane performance in the following manner: zeolite loading > sonication time > drying time. The optimized membrane casting parameters obtained from signal-to-noise ratio analysis performed on Minitab led to synthesis of a composite membrane with both high CO₂/N₂ selectivity and CO₂ permeability. The chosen technique also assisted in justifying the dependence of permeation results on various membrane casting parameters, associating it with the morphological results. The technique also facilitated the optimization of the membrane characteristics and is recommended for future study based on membrane separation processes.     

Probing surface structure via time-of-escape analysis of gas in Knudsen regime

Continuing the study begun in [Feres, R., Yablonsky, G., 2004. Knudsen's cosine law and random billiards. Chemical Engineering Science 59, 1541-1556], we consider transport in the Knudsen regime of inert gases through straight channels and investigate how small-scale surface geometry of a macroscopically flat channel affects the diffusion characteristics of the gas. We show that the diffusivity constant contains information about the surface micro-geometry.Our investigation is carried out partly by analytical means and also through numerical simulation of what we call time-of-escape experiment. This is a type of multi-scattering experiment that measures the mean residence time in channels of varying lengths, allowing for an analysis of the transport process at various stages of development.We focus attention on the smoothness constantξ=D/D₀, defined as the ratio of diffusivity for a given micro-geometry, D, and diffusivity D₀ under “ideal roughness,” i.e., under the assumption that the Knudsen cosine law holds at each collision. The dependence of ξ on small-scale surface morphology is investigated using a variety of parametrized families of micro-geometries. We show that ξ can tell the presence of certain geometric features, such as curvature or sharp angles at the microscopic level. For example, for a simple two-dimensional model of atomically smooth surface made of a linear packing of spheres of radius R probed by gas molecules of radius A (Fig. 6), we obtain the approximate relation ξ∝1+A/R, with a proportionality constant of roughly 1.3. (See Section 2 for the range of parameters considered.) This relates to rapid diffusion phenomena recently observed by [Holt, J.K., Park, H.G., Wang, Y., Stadermann, M., Artyukhin, A.B., Grigoropoulos, C.P., Noy, A., Bakajin, O., 2006. Fast mass transport through sub-2-nanometer carbon nanotubes. Science 312, (1034)]. In the classical collision model of Maxwell-Smoluchowski, with no detailed regard of surface geometry, one always has ξ?1, but we observe that ξ can sometimes be less than 1 (Section 2.5). We obtain exact values for the mean number and duration of collisions as function of the micro-geometry (Section 3). This is needed to determine the relative importance of these quantities on diffusivity. We also extend the analysis of the scattering operator of random billiards of [Feres, R., Yablonsky, G., 2004. Knudsen's cosine law and random billiards. Chemical Engineering Science 59, 1541-1556] by giving a general criterion for the validity of Knudsen's cosine law, and describe some of the spectral properties of this operator.     

Correlation aspects of the selective gas permeabilities of polymeric materials and membranes

Although the solubility and diffusivity of each gas in each polymer are temperature- and may be pressure-dependent properties of every system nevertheless regular trends are noted when either many gases are studied in a single polymer or a single gas is studied in many polymers. Several empirical though scientifically based correlations of such data have been proposed which are at best semi-quantitative. In this paper improved correlations are described to correlate data on diffusivities D and the related energies of activation, and solubilities S and related heats of solution of gases in polymers. The procedures rely on determining an effective Lennard-Jones force constant and molecular diameter for each gas, which parameters hold in all polymers above T_g and, with slightly smaller diameters for the multiatomic gases, in all polymers below T_g. Each polymer is characterized by four temperature-dependent parameters, two for diffusivity and two for solubility, which hold with all gases. Rules are given for determining these parameters. It is demonstrated that D is correlated to within ±20% and S to ±30%. The procedure described may be used to predict D and S, and hence permeabilities, in cases where data do not already exist. The values and ratios of the predicted permeabilities are a valuable guide when seeking polymers for separating gas mixtures by membrane processing.