Pore Diffusion Coefficient Research Articles

Solid-phase extraction of long-chain fatty acids from aqueous solution

Microbially derived long-chain free fatty acids are useful precursors for biofuel production. However, effective and biocompatible methods for their separation from aqueous solutions do not presently exist. The overall and relative efficacy of several commercially available hydrophobic, anion exchange, and mixed-mode adsorbents for the recovery of laurate, a model 12-carbon saturated fatty acid, was compared according to both equilibrium and kinetic studies. Mixed-mode adsorbents exhibited the greatest adsorption capacity and affinity, with Amberlite IRA-402 able to adsorb up to 430g-laurate/kg. Meanwhile, the anion exchange resin Amberlite IRA-67 adsorbed up to 426g-laurate/kg, while the hydrophobic resin Dowex Optipore L-493 adsorbed a maximum of only 106g-laurate/kg. Polymer gel adsorbents, which display the greatest aqueous swelling, achieved the fastest rates of laurate recovery. Adsorption kinetics were well represented by a pore-diffusion model for all adsorbents. Estimated pore diffusion coefficients were as high as 7.2×10−10m2/s for Amberlite IRA-402.

Modeling the cAMP desorption process from an anion exchange chromatography column

Computational modeling is a useful approach for the characterization, development, and validation of desorption chromatography. Batch and dynamic desorption experimental results are helpful for the selection of an appropriate desorbent and the design of a desorption processes. In this study, we used an aqueous HCl solution ranging from 0.030mol/L to 0.060mol/L to desorb cAMP (adenosine 3′,5′-cyclic monophosphate) from a presaturated anion exchange resin (D-13). Good results were obtained in terms of the desorption rate and cAMP recovery. Subsequently, general rate model (GRM) that incorporated counter-ion flux was used to describe the desorption kinetics of the batch experiments. The superficial rate constant, Kd, of the cAMP/HCl reaction on activated ion exchange sites inside the resin was estimated as 0.130L/(mol/s) using the least squares fitting method, which was then applied for predicting the dynamic desorption processes. The pore diffusion coefficients for Cl− and cAMP were estimated as 1.57×10−9 and 5.71×10−10m2/s, respectively. We verified the applicability of this GRM model to a column desorption process by experimentally investigating the effects of the HCl concentration, flow rate, and column aspect ratio on column desorption. The experimental results could be predicted successfully using the GRM model. The validated GRM may provide an important basis for future scale-up of the cAMP desorption process.

Effects of ligand density and pore size on the adsorption of bovine IgG with DEAE ion‐exchange resins

Immunoglobulin G is an important plasma protein with many applications in therapeutics and diagnostics, which can be purified effectively by ion exchange chromatography. The ligand densities and pore properties of ion-exchange resins have significant effects on the separation behaviors of protein, however, the understandings are quite limited. In this work, with bovine immunoglobulin as the model IgG, the adsorption isotherms and adsorption kinetics were investigated systematically with series of diethylaminoethyl ion-exchange resins with different ligand densities and pore sizes. The Langmuir equation and pore diffusion model were used to fit the experimental data. The influences of ligand density and pore size on the saturated adsorption capacity, the dissociation constant and the effective diffusivity were discussed. The adsorption capacities increased with the increase of ligand density and the decrease of pore size, and an integrative parameter was proposed to describe the combined effects of ligand density and pore size. It was also found that the effective pore diffusion coefficient of the adsorption kinetics was influenced by pore sizes of resins, but was relatively independent on the ligand densities of resins. For a given protein, the ligand density and pore size should be optimized for improving the protein adsorption.

Competitive adsorption of lead and zinc from aqueous solution on activated carbon prepared from Van apple pulp: Study in single- and multi-solute systems

The potential of activated carbon (VAAC) prepared from local agricultural waste, apple pulp, as an alternative low-cost adsorbent was investigated for the removal of lead and zinc from single- and multi metal aqueous solution. VAAC was produced with a reasonable yield, 43% and has remarkable surface area (1067.01m2/g) with a well-developed pore structure. To determine the adsorption process and properties, the effects of various operating parameters, pH of the solutions (2–6), adsorbent dosage (0.01–0.2g), initial concentration of metal ions (25–40mg/L), contact time (3–120min) and temperature (298–308K) were investigated in a batch adsorption technique. The adsorption isotherm data were better fitted by Langmuir model. The pseudo second-order model was found more applicable to describe the kinetic of system in both the single- and multi-solute system. The adsorption capacities of heavy metals decrease in the order of Pb(II) (15.96mg/g)<Pb (Pb+Zn) (13.23mg/g)<Zn(II) (11.72mg/g)<Zn (Pb+Zn) (7.54mg/g) at 298K. Although individual metal ions adsorption decreases in multi-system, the more metal ions are adsorbed (20.77mg/g). The intraparticle diffusion model, external mass transfer coefficient, film and pore diffusion coefficient at different temperatures were also evaluated to investigate the adsorption mechanisms of both systems. The adsorption was mainly controlled film diffusion process at all operating temperatures and concentrations. The thermodynamic parameters indicate that the adsorption process is endothermic, feasible and thermodynamically favored.

Equilibrium, kinetic, and thermodynamic biosorption of Pb(II), Cr(III), and Cd(II) ions by dead anaerobic biomass from synthetic wastewater

Heavy metals are toxic pollutants released into the environment as a result of different industrial activities. Biosorption of heavy metals from aqueous solutions is a new technology for the treatment of industrial wastewater. The aim of the present research is to highlight the basic biosorption theory to heavy metal removal. Heterogeneous cultures mostly dried anaerobic bacteria, yeast (fungi), and protozoa were used as low-cost material to remove metallic cations Pb(II), Cr(III), and Cd(II) from synthetic wastewater. Competitive biosorption of these metals was studied. The main biosorption mechanisms were complexation and physical adsorption onto natural active functional groups. It is observed that biosorption of these metals was a surface process. The main functional groups involved in these processes were hydroxyl (-OH) and carboxylic groups (C=O) with 37, 52, and 31 and 21, 14, and 34 % removal of Pb(II), Cr(III), and Cd(II), respectively. Langmuir was the best model for a single system. While extended Langmuir was the best model for binary and ternary metal systems. The maximum uptake capacities were 54.92, 34.78, and 29.99 mg/g and pore diffusion coefficients were 7.23, 3.15, and 2.76 × 10(-11) m(2)/s for Pb(II), Cr(III), and Cd(II), respectively. Optimum pH was found to be 4. Pseudo-second-order was the best model to predict the kinetic process. Biosorption process was exothermic and physical in nature. Pb(II) offers the strongest component that is able to displace Cr(III) and Cd(II) from their sites, while Cd(II) ions are the weakest adsorbed component.

Stages of evolution of a Toarcian compacted claystone around galleries excavated between 1 and 124 years ago by the study of noble gases dissolved in pore water at the Tournemire Underground Research Laboratory (France)

Abstract The purpose of this work is to study the diffusion properties in an argillaceous formation and how these properties change after the excavation of galleries, over a long period. The Tournemire Underground Research Laboratory (URL) located in Aveyron (France) offers the unique opportunity to investigate different stages of the evolution of the so-called Excavation Damaged Zone (EDZ) over a period of about 124 a. Four horizontal boreholes parallel to the bedding and one vertical borehole were drilled in order to study diffusion transport in the EDZ in both directions in galleries excavated 124, 13, 6, and 1 a ago, respectively. Noble gases dissolved in the pore water of 47 core samples were extracted in order to establish precise depth profiles. Mainly produced in situ by decay of U and Th, radiogenic He accumulates in the pore water of rocks and escapes toward the gallery, allowing a characterization of the diffusive transport in the EDZ and its evolution with time. For the oldest gallery (1882–1888), core mapping reveals an EDZ well developed with fractures up to a depth of 1.8 m. In this zone, all radiogenic He has been lost and at the same time heavy noble gases are trapped in the rock with an enrichment of Xe relative to Kr and of Kr relative to Ar. From 1.8 m, He concentration increases with depth to reach a plateau at about 3.5 m corresponding to a concentration normally found in the unaltered zone. Considering diffusive transport of the radiogenic He to the EDZ, model calculations allowed proposing transport properties in the unfractured and undisturbed zone (UZ) with a pore diffusion coefficient Dp of 1 × 10 −10 m 2 /s deduced from the best-fit curve to experimental data and a mean porosity of 0.1 obtained form petrophysical measurements. The most recent gallery (2008) did not show any evidence of EDZ at depths greater than 7.5 cm. A fracture located around 0.75 m, possibly of tectonic origin, induced large advection and diffusion losses of He on both sides in the next 50 cm. Excesses of Ar, Kr and Xe are found, suggesting diffusion of air from the gallery associated with He losses. The 6-a-old gallery is clearly influenced by fractures of tectonic origin increasing the EDZ thickness of 0.7 m up to a Damaged Zone of 1.8 m. Based on the He concentration profile, the 13-a-old gallery (1996) has a net EDZ of 1.2 m, larger than the 0.7 m deduced from the structural analysis by core mapping, followed by a disturbed zone of up to 3.5 m that could represent an intermediate stage before the development of fractures in the EDZ. The vertical borehole drilled in the same gallery shows a less extensive damaged zone (1.4 m) and allows the determination of a Dp of 3 × 10 −11 m 2 /s taking into account the anisotropy relative to the stratification plane. The rare gas analysis has, therefore, enabled confirmation and better description of the net time-dependent evolution of the EDZ around drifts in the argillaceous Tournemire site: no obvious EDZ for the 1-a gallery (2008), 1.2 m width for the 13-a-old gallery (1996), and 2 m width for the century-old tunnel. The occurrence of a disturbed and unfractured zone (dZ) around the 13-a-old gallery undetected by structural studies and geophysical methods clearly demonstrates the power of radiogenic He in assessing the transport properties around drifts excavated at different ages in compacted clay rocks.

Removal of phenol and lead from synthetic wastewater by adsorption onto granular activated carbon in fixed bed adsorbers: prediction of breakthrough curves

Abstract The adsorption of phenol and lead (II) onto granular activated carbon (GAC) in single and binary system has been studied using fixed bed adsorber. A general rate multi-component model has been utilized to predict the fixed bed breakthrough curves for dual-component system. This model considers both external and internal mass transfer resistances as well as axial dispersion with non-liner multi-component isotherm. The effect of important parameters, such as flow rate, bed height and initial concentration on the behavior of breakthrough curves have been studied. The equilibrium isotherm model parameters such as isotherm model constants, pore diffusion coefficients (D p ) were obtained from batch experiments, while the external mass transfer coefficients and axial dispersion (k f , D z ) were calculated from empirical correlations. The results show that the general rate model was found suitable for describing the adsorption process of the dynamic behavior of the GAC adsorber column.

Mathematical Modeling of Protein Chromatograms

AbstractThe most used mathematical models with a phenomenological basis for simulating chromatographic curves of proteins in size exclusion chromatography, ion exchange chromatography, affinity chromatography, and hydrophobic interaction chromatography are reviewed. The plate model (PM) and the general rate model (GRM) are briefly described, followed by various applications of these models to the different chromatographic strategies. Based on these examples it is concluded that the GRM is the most complete and informative model, despite it needs several parameters that have to be estimated from theoretical correlations nonspecific for proteins. Additionally, values for the effective pore diffusion coefficient are not generally available. Appropriate calibration leads in most cases to predictions that compare favorably with experimental data. The possibility to predict chromatographic curves under different operational conditions similar to those used at industrial scale by applying mathematical models is still a challenge because it could contribute to the reduction of costs involved in suitable purification processes. In addition, new proteins are continually designed and for each case different conditions are needed.

Biosorption of As3+ Ions Using Ternary Microspheres of Chitosan, Yeast, and Gelatin: A Dynamic and Equilibrium Investigation

Ternary biopolymeric microspheres of chitosan, yeast and gelatin were prepared and characterized by FTIR spectral analysis, particle size measurements, and scanning electron micrograph techniques. The prepared microspheres were investigated for static and dynamic studies of adsorption of As+3 ions onto the microspheres surfaces at fixed pH and ionic strength of the aqueous solution.The adsorption data were applied to Langmuir and Freundlich isotherm equations and various static parameters were calculated. The dynamic nature of adsorption was quantified in terms of several kinetic constants such as rate constants for adsorption, Lagergreen rate constant, inter particle diffusion rate constant and pore diffusion coefficient. The influence of various experimental parameters such as solid to liquid ratio, pH, temperature, and chemical composition of biopolymeric microspheres were investigated on the adsorption of arsenic ion and various thermodynamic parameter were also calculated.

The low-density diffusion coefficient of soft-sphere fluids in nanopores: Accurate correlations from exact theory and criteria for applicability of the Knudsen model

Molecular transport in confined spaces is of central importance to many traditional and emerging applications, such as gas separation and storage, catalytic and non-catalytic fluid–solid reactions and nanofluidics. The classical method to model the influence of solid–fluid particles collisions in transport comes from the early works of Knudsen and Smoluchowski, in which van-der-Walls interactions are neglected. While such assumption may be adequate for wide channels or high temperatures, it has been shown to lead to significant overprediction of the low-density diffusion coefficient in narrow pores at low and moderate temperatures, when compared to that obtained through molecular dynamics simulations. However, while molecular dynamics offers a much more accurate route for the calculation of diffusivities, its implementation and use is time-consuming and the Knudsen formulation remains preferred, particularly for interpretation of experimental permeation data. On the other hand, the oscillator model, developed in recent years in this laboratory, provides a straightforward method to estimate the low-density diffusivity, taking into account the dispersive forces exerted by the wall through rigorous statistical–mechanical considerations. The computational demand of the oscillator model is several orders of magnitude lower than that of a typical molecular dynamics run, though much greater than that of the simple Knudsen formulation. In order to facilitate its use, we provide several simple correlations for the fast estimation of the oscillator model-based diffusion coefficient for LJ fluids in simple geometries, as a function of the pore size and the LJ fluid–solid interaction parameters. Moreover, the parameter values for which the Knudsen equation supplies a reasonable estimation of the diffusion coefficient are presented for various degrees of accuracy.

Selective adsorption of 2,6-dichlorophenol by surface imprinted polymers using polyaniline/silica gel composites as functional support: Equilibrium, kinetics, thermodynamics modeling

Based on polyaniline/silica gel composites (PAS) as support and functional monomer, the surface imprinted polymers (MIP–PAS) were synthesized for the selective adsorption of 2,6-dichlorophenol (2,6-DCP) from aquatic environment. The MIP–PAS was characterized by FTIR spectroscopy, scanning electron microscopy, nitrogen adsorption–desorption analysis, particle-size and EDX analysis. The effects of pH, initial analyte concentration, contact time and temperature of medium on the adsorption were studied. Equilibrium data, at various temperatures, can be described well by the Langmuir isotherm model. Kinetic can be described by the pseudo-first-order model, pseudo-second-order model, and by an intraparticle diffusion equation. A diffusion-controlled process as the essential adsorption rate-controlling step was also obtained. Moreover, intraparticle diffusion coefficient (ki) and pore diffusion coefficient (D2) for MIP–PAS elevated with the increased of 2,6-DCP concentration and temperature of medium, while increase in 2,6-DCP concentration was found to reduce film diffusion. Furthermore, the values of film diffusion coefficient (D1) were lower than those of D2, indicating the diffusion process was controlled by film diffusion. Thermodynamics parameters (positive values for delta H° and delta S°, negative values of delta G°) indicated that the process is endothermic and spontaneous. The selectivity of the imprint also demonstrates high affinity for 2,6-DCP over related phenolic compounds and over non-imprinted polymers (NIP).

Effect of Catalyst Diffusion Coefficient on Ethylbenzene Dehydrogenation

The effective diffusion coefficients for a single catalyst pellet were determined by numerical integration of the Johnson-Stewart equation for bimodal and unimodal pore size distributions assuming a transitional diffusion regime. The effectiveness factors of a spherical catalyst pellet were determined at various pore size distribution probability density functions. Using effectiveness factors the production rates were determined. The results showed that the effectiveness factor and production rate are sensitive to catalyst pore size distribution and diffusion coefficient.

Development of a two-dimensional coupled-implicit numerical tool for the optimal design of CDI electrodes

Capacitive deionization, CDI, is a new desalination technology which gained interest recently due to its economic advantages over existing technologies. To develop better electrode materials, this study focused on revealing CDI mechanisms and the most effective parameters. As current experimental techniques have limitations in producing well-defined pore arrangements, a multi-dimensional transient simulation tool was developed based on solving the Nernst–Planck equation with a convection term and Poisson's equation. The equations are solved using a coupled-implicit scheme, which does not require a very short time step due to the convergence problem. The present tool is verified through comparisons with theoretical solutions and other results. The key performance indicator (KPI) was defined as the salt removal rate under a fixed external electrode surface area, which relates to the capital cost of an electrode. The effects of the design parameters on the KPI are studied regarding the electrode gap distance, pore depth, pore diffusion coefficient, pore width, and flow velocity under stagnant water and flowing water conditions. It was found that the pore depth, pore diffusion coefficient and pore width were the most influential parameters on the KPI, while the gap distance and flow velocity had relatively small effects on the KPI.

Removal of Hg(II) from aqueous solutions using a novel impregnated resin containing 1-(2-thiazolylazo)-2-naphthol (TAN)

A novel efficient Hg(II) adsorbent was prepared by impregnating 1-(2-thiazolylazo)-2-naphtol (TAN) onto Amberlite XAD-4 resin beads. Batch sorption experiments were carried out for the removal of Hg(II) from aqueous solutions using the new extractant-impregnated resin, EIR. The influences of various experimental parameters like pH, initial concentration, EIR dosage, contact time and the effect of temperature were evaluated. Optimum conditions for Hg(II) removal were found to be pH range of 5–6, EIR dosage 0.5 g L −1 and equilibrium time 55 min. The equilibrium sorption isotherm was better described by Langmuir sorption isotherm model. The maximum sorption capacity ( q max) of EIR for Hg(II) ions in terms of monolayer sorption was 450.45 mg g −1. Increase of temperature increased the sorption. The obtained negative values of Gibbs free energy (Δ G°) indicated feasible and spontaneous nature of the sorption process at different temperatures. The change of entropy (Δ S°) and enthalpy (Δ H°) were estimated. Results of the kinetic studies showed that the sorption process follows Bangham's kinetic model, and the pore diffusion is the rate-controlling step. The pore diffusion coefficients, D p values, were of the order of 10 −12 m 2 s −1. The new EIR could be successfully recycled for several consecutive cycles without significant loss in its sorption capacity.

Removal of Phenol and Lead from Synthetic Wastewater by Adsorption onto Granular Activated Carbon in Fixed Bed Adsorbers: predication of Break through Curves

The adsorption of phenol and lead (II) onto granular activated carbon (GAC) in single and binary system has been studied using fixed bed adsorber. A general rate multi-component model has been utilized to predict the fixed bed breakthrough curves for dual-component system. This model considers both external and internal mass transfer resistances as well as axial dispersion with non-liner multi-component isotherm. The effect of important parameter, such as flow rate, bed height and initial concentration on the behavior of breakthrough curves have been studied. The equilibrium isotherm Model parameters such as isotherm model constants, pore diffusion coefficients (Dp) were obtained from batch experiments, while the external mass transfer coefficients and axial dispersion (kf, Dz) were calculated from empirical correlations. The results shows that the general rate model was found suitable for describing the adsorption process of the dynamic behavior of the GAC adsorber column.

Influence of the structure of mesoporous adsorbents on transport properties

The transport of caffeine through columns filled with mesoporous silica was studied by liquid chromatography. The mass transfer parameters were measured by modelling the band broadening of the chromatograms. The experimental height equivalent to a theoretical plate (HETP) data were analysed using the general rate model (GRM) in order to determine the effective diffusion coefficient of caffeine in porous particles. Samples are characterized by gas adsorption for pore size determination, whereas the topological tortuosity of the porous particles was determined by electrical measurements. The effective pore diffusion coefficient through porous particles was modelled with a good accuracy by taking into account that both porosity and tortuosity depend on the ratio between the size of the molecule probe and the pore size. This model has been used to estimate the contribution of the surface diffusion coefficients of caffeine which appears to be small for this system.

Numerical Model for Chloride Penetration into Saturated Concrete

Chloride-induced corrosion is the most important durability issue in a reinforced-concrete structure. In this paper, the multispecies model was used to describe the chloride transport in saturated concrete. The model was solved by using the finite-difference method by inputting parameters such as porosity, density, chemical composition of pore solution, diffusion coefficient, and chloride-binding isotherm. A depth-dependent diffusion coefficient, instead of a fixed diffusion coefficient, was used in this model. The chloride-binding isotherm was directly obtained from the diffusion test. Finally, the numerical simulation results were validated with experimental results. It was found that the numerical simulation results were in good agreement with the experimental results.

Study to investigate the importance of mass transfer of naproxen sodium onto activated carbon

In the present study, the adsorption of naproxen sodium onto activated carbons (BK4, obtained from white polymeric waste and SK4, obtained from black polymeric waste) was investigated by calculating the parameters of pH, contact time, the concentration of naproxen sodium and the temperature. The adsorption data of naproxen sodium onto activated carbon follows the Langmuir isotherm model and its kinetic processes were described by various kinetic adsorption models. It was determined that the pseudo-second-order model was the best choice among all the available kinetic models to describe the adsorption behaviour of naproxen sodium onto activated carbon. During the present study, the intraparticle diffusion rate constant, the external mass transfer coefficient and the film and pore diffusion coefficient were evaluated at various temperatures. In addition, the thermodynamic parameters of the adsorption of naproxen sodium onto activated carbon were also calculated.

Biosorption studies of Cu(II) onto Mansonia sawdust: Process design to minimize biosorbent dose and contact time

The aim of this paper is to examine the various operating processes and determine the overall biosorption rate and how each of the processes influences biosorption. The results revealed that external mass transfer, film diffusion and ion exchange were predominant at the initial 5 min of biosorption and their rate constants were measured. The pseudo-second order model rate constants were determined and the relationship between these constants and the biosorption performance such as the approaching equilibrium factor, R w , the rate factor k 2 q e , the biosorption half-life ( t 0.5) and the operating time ( t x ) were determined. The pore and film diffusion coefficients decreased with increasing copper(II) concentration. The values of initial biosorption factor, R i , for the biosorption process showed that for all initial copper(II) concentrations, initial biosorption was faster than intraparticle diffusion. The activation energies, enthalpies, entropies and free energies for each of the operating processes were determined and the results showed that film diffusion had the highest activation energy and may be the overall rate limiting step. Mathematical models for the optimization of multistage process for minimum biosorbent mass and contact time were also developed.

Chemical treated laterite as promising fluoride adsorbent for aqueous system and kinetic modeling

Efficiency of acid–base treated raw laterite (RL) is investigated for removal of fluoride. FTIR, SEM-EDX, and surface area analyzer are used to characterize the treated laterite (TL). The batch adsorption of fluoride is explored using TL under varying process conditions like adsorbent dose, pH of solution, temperature, particle size and contact time. The adsorption isotherm data of fluoride ions on TL are fitted well to both Langmuir and Freundlich models. The temperature dependent maximum Langmuir adsorption capacities of fluoride ion on TL are found to be 36.3, 37.9, and 39.1 mg/g at 288, 305, and 315 K, respectively. A simple shrinking core model is applied to predict the batch adsorption kinetics of fluoride ions onto treated laterite (TL). In the proposed two-resistance model, external mass transfer (K f) and pore diffusion coefficient (D e) are estimated by comparing the simulated concentration profile with the experimental data using a non-linear optimization technique. Estimated values of D e and K f are found to be 4.8 × 10 −10 m 2/s and 8.5 × 10 −4 m/s at 305 K, respectively. The fluoride adsorption in presence of other competitive ions as well as desorption of fluoride ions from spent adsorbent are studied in detail.