Hindered diffusion of oligosaccharides in high strength poly(ethylene glycol)/poly(acrylic acid) interpenetrating network hydrogels: Hydrodynamic vs. obstruction models

Diffusion coefficients of small oligosaccharides within high strength poly(ethylene glycol)/poly(acrylic acid) interpenetrating network (PEG/PAA IPN) hydrogels were measured by diffusion through hydrogel slabs. The ability of hindered diffusion models previously presented in the literature to fit the experimental data is examined. A model based solely on effects due to hydrodynamics is compared to a model based solely on solute obstruction. To examine the effect of polymer volume fraction on the observed diffusion coefficients, the equilibrium volume fraction of polymer in PEG/PAA IPNs was systematically varied by changing the initial PEG polymer concentration in hydrogel precursor solutions from 20 to 50 wt./wt.%. To examine the effect of solute radius on the observed diffusion coefficients, solute radii were varied from 3.3 to 5.1 Å by measuring diffusion coefficients of glucose, a monosaccharide; maltose, a disaccharide; and maltotriose, a trisaccharide. Both the hydrodynamic and obstruction models rely on scaling relationships to predict diffusion coefficients. The proper scaling relationship for each of the hindered diffusion models is evaluated based on fits to experimental data. The scaling relationship employed is found to have a greater significance for the hydrodynamic model than the obstruction model. Regardless of the scaling relationship employed, the obstruction model provides a better fit to our experimental data than the hydrodynamic model.     

Modelling of microporous diffusion of n-paraffins in zeolite 5A

Sorptive liquid-phase diffusion of two n-paraffins, C₁₀H₂₂ and C₁₁H₂₄, dissolved in isooctane, onto micropore of 5A zeolite was studied to assess multicomponent diffusion and competitive effects. Diffusion coefficients for adsorbing components are determined from experimental batch reactor data. The experimental data indicate that diffusion through the microporous zeolite crystals is the primary diffusional resistance. A mathematical model of the rate of adsorption of a solute from a liquid by micropore adsorbent in a batch system was developed. The equation describing the mass transport by diffusion in a micropore adsorbent has been solved in order to obtain theoretical uptake curves for systems when the adsorption equilibrium isotherm is the favourable and nonlinear one. A computer simulation of the microporous diffusion is performed by use of the ISIM-Interactive Simulation Language. The effect of main term and cross-term coefficients of micropore diffusion for the system considered is investigated.     

沸石催化剂内液相交互扩散系数的测定

采用简单实用的试验方法研究了苯和异丙苯在沸石内的交互扩散情况,通过测定不同时间点的扩散质的浓度,利用适宜的数学模型和最小二乘法关联出两种体系中各扩散质在沸石催化剂内的交互扩散系数。可以为苯烷基化反应的工业模拟提供重要的基础数据。     

采用泰勒分散法测量蜡分子扩散系数

蜡分子扩散系数是蜡沉积预测模型中非常重要的物性参数。为测量蜡分子（高碳数正构烷烃）在液相体系中的分子扩散系数,建立了基于泰勒分散法的扩散系数测量装置,并对装置操作注意事项进行了详细探讨。采用该装置测量了丙酮水溶液、n-C₆+n-C₇溶液以及甲醇水溶液中溶质在溶剂中的分子扩散系数,以文献值对测量值进行校验,验证了装置的可靠性。分别以n-C₁₈、n-C₂₀、n-C₂₂、n-C₂₄、n-C₂₆为溶质,以n-C₇为溶剂,在不同温度、浓度下测量蜡分子在液相体系中的分子扩散系数,并将实验测量值与Hayduck-Minhas关系式计算值进行比较。结果表明：蜡分子扩散系数随温度升高而线性增大,随溶液中蜡分子摩尔分数的增大而以指数形式减小;在相同条件下,高碳数正构烷烃的分子扩散系数低于低碳数正构烷烃的分子扩散系数。采用Hayduck-Minhas关系式的计算结果比实验测量结果平均小50%,应用于蜡沉积预测时,将低估蜡分子扩散质量流。     

Hydrodynamic dispersion of reactive solute in a Hagen-Poiseuille flow of a layered liquid

An analysis of the solute dispersion in the liquid flowing through a pipe by means of Aris-Barton's ⒈method of moments',under the joint effect of some finite yield stress and irreversible absorption into the wall is presented in this paper.The liquid is considered as a three-layer liquid where the center region is Casson liquid surrounded by Newtonian liquid layer.A significant change from previous modelling exercises in the study of hydrodynamic dispersion,different molecular diffusivity has been considered for the different region yet to be constant.For all time period,finite difference implicit scheme has been adopted to solve the integral moment equation arising from the unsteady convective diffusion equation.The purpose of the study is to find the dependency of solute transport coefficients on absorption parameter,yield stress,viscosity ratio,peripheral layer variation and in addition with various diffusivity coefficients in different liquid layers.This kind of study may be useful for understanding the dispersion process in the blood flow analysis.     

Estimation of diffusion coefficient for solute–polymer systems

Diffusion coefficients are needed for the analysis of many mass transfer problems involving polymers. Since the diffusivity for such systems are strong functions of temperature and concentration, the analysis of these problems is greatly facilitated if predictive methods are available for the determination of the required diffusion coefficient. Because of the limitations of the theoretical approaches for estimating diffusivity, empirical correlation of solute–polymer diffusion coefficient data with physical properties of the solute were investigated. Chemical permeation measurements were made for several organic liquids through three elastomers (polychoroprene, butyl and nitrile rubber) at five different temperatures, ranging from 25 to 65°C. The collected diffusivities were correlated with liquid kinematic viscosity. Diffusivities (at different temperatures) depend mainly on the kinematic viscosity of solutes. The results also indicate a close relation between the variation of diffusivity and viscosity with temperature.     

Mass Tansfer Characteristics of a Microchannel Device of Split‐Flow Type

A solute was transferred from an aqueous solution to deionized water in a microchannel device with a rectangular channel of 200 μm × 200 μm. The two liquid layers flowed in parallel within the rectangular channel. After making contact in the channel, the layers were split into two streams through a knife‐edge. The amount of solute transferred was determined by analyzing liquid samples taken from the outlet. Thus, conventional analytical instruments were readily available for obtaining the total concentration. Mass tansfer characteristics were examined through the measurement of diffusion coefficients for several solutes. Although the two liquids were carefully supplied at the same velocity, equal flow splitting was difficult to obtain. The unequal splitting led to scattering of the observed solute concentrations at a fixed supply flow rate. This could be a serious drawback as a mass tansfer device; however, a method was proposed to choose an appropriate value for equal splitting. The ratio of effluent flow rate of one liquid to another was changed intentionally. The solute concentration in the receiving liquid for the flow rate ratio of unity corresponds to the data for equal flow splitting. On the basis of the solute concentrations defined, the diffusion of benzoic acid was successfully analyzed using a conventional penetration model with a correction parameter. Furthermore, diffusion coefficients for sucrose and glycine were determined using the basic equation obtained with benzoic acid. The observed values compared fairly well with reported ones. The correction parameter expresses characteristics of the microchannel device; however, the physical picture is still unclear.     

Ternary diffusion formulation for diffusiophoresis

A ternary diffusion formulation for diffusiophoresis, the migration of a particle in a solute gradient, is suggested. The formulation, derived from irr contributions in the D₁₂ “cross-term” diffusivity. The ternary diffusion formulation allows both measurement of the magnitude of diffusioph transport situation. Measured coefficients of diffusiophoresis agree reasonably well with previous electrohydrodynamic theories.     

Measurement of the diffusion coefficient of a model food dye (malvidin 3,5-diglucoside) in a high pressure CO2+methanol system by the chromatographic peak-broadening technique

The accurate determination of the diffusion coefficients of solutes in supercritical solvents is a prerequisite for the modeling and design of extraction processes. At present, reported data on the diffusion of polar solutes in the system CO₂+methanol at high pressure is scarce. In the work described here, malvidin 3,5-diglucoside was chosen as a representative example of anthocyanin compounds (natural food dyes). The diffusion coefficient of this compound was determined using a chromatographic peak-broadening technique. The effect of the amount of methanol in the solvent has been analyzed and the results show that a decrease in the diffusion coefficient occurs as the amount of methanol increases. This behavior has been attributed to the formation of solute–methanol clusters. Finally, the results obtained have also been correlated with temperature, solvent density and viscosity, with the best fit found in the correlation with density.     

Cosolvent effects on the diffusions of 1,3-dichlorobenzene, l-carvone, geraniol and 3-fluorophenol in supercritical carbon dioxide

In order to get an insight into solute-cosolvent interactions and to predict the cosolvent effects on diffusions, several cosolvents and solutes with different size, hydrogen-bond donor (HBD) acidity, and hydrogen-bond acceptor (HBA) basicity were chosen, and the molecular diffusion coefficients of the solutes in pure and modified supercritical carbon dioxide were measured by the Taylor-Aris chromatographic peak broadening method. Cosolvent effect parameter, which is defined as the ratio of diffusion coefficient with and without cosolvent, respectively, is introduced to quantitatively compare the strength of different types of interaction between solute and cosolvent, especially hydrogen bonding. For cosolvent without hydrogen-bond ability, the cosolvent effect parameter decreases with the increase of molecular volume and weight of the solutes, in that the strength of dispersion force with cosolvent increases with their size. For cosolvent with only HBA basicity, the solute with higher HBD acidity has smaller cosolvent effect parameter, due to the fact that the strength of hydrogen-bond interaction between the solute and cosolvent only depends on and increases with the HBD acidity of the solute. For amphiprotic cosolvent, the solute with higher HBD acidity has smaller cosolvent effect parameter, it can be inferred from which that HBD acidity rather than HBA basicity of the solute makes a major contribution to the hydrogen-bond interaction between solute and cosolvent. These results are consistent with the interpretation by the Kamlet-Taft solvatochromic parameters (HBD acidity and HBA basicity). Moreover, a nonlinear decrease in diffusion coefficient with the increase of cosolvent concentration is observed, which is typical of the behavior of the system with strong interaction.     

High flux,single solute mass transfer in spherical rigid drops

High flux (i.e. high solute concentrations) mass transfer in spherical, rigid drops has been studied for the case of a single transferring solute. Model equations have been solved for the cases of (a) infinite and (b) finite continuous phase mass-transfer coefficients—or constant, and variable, interface compositions.The partial differential equations were solved to illustrate the influences of high solute concentrations and the continuous phase mass-transfer coefficients. In fact, the model diffusion equation resulting from a differential solute balance remains unchanged from the well-known low flux equation. It is only at the boundary, where the convective flux contribution must be taken into account, as it increases the total flux into (or out of) the drop as solute concentrations increase. Extraction efficiencies were also calculated. These proved relatively insensitive to the concentration level because the solute convective flux contribution simply increases the drop size. The diffusive flux into the drop interior changes little with the concentration level, so resulting in the small differences in the extraction efficiencies.     

Magnetic resonance imaging to measure concentration profiles of solutes diffusing in stagnant beds of cellulosic fibers

The evolution of the concentration profiles of an adsorbing solute diffusing in a stagnant bed of cellulosic fibers is measured using magnetic resonance imaging. Effective diffusivities are calculated by matching concentration profiles with a numerical model of one‐dimensional Fickian diffusion. The measured values of the effective diffusion coefficients are interpreted using a model that accounts for the porosity, tortuosity, and adsorption equilibrium constant. The effective diffusivities in fiber beds are significantly lower than the bulk diffusivity of the solute and highly dependent on fiber type. The diffusivity is lower for the fiber type that exhibited stronger adsorption properties. The influence of concentration, adsorption, and other fiber characteristics on diffusion rates and rates of reaction is discussed. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

Diffusion coefficient measurements in consolidated clay by RBS micro-scale profiling

The determination of radionuclide diffusion coefficients is necessary for performance assessment of clay formations as a geological barrier for deep geological repositories for high-level radioactive waste.Diffusion coefficients of elements that are retained by the clay and have short diffusion lengths are quite difficult to measure over reasonable time spans, by conventional techniques.This paper presents a novel application of the Rutherford Backscattering Spectrometry (RBS) technique to determine solute diffusion coefficients in consolidated clays. The RBS technique was selected because it allows the measurement of concentration profiles at short range distances (μm).The proposed methodology was tested on the Opalinus clay (OPA) from the Swiss Jura, where the Mont Terri underground laboratory is located. The diffusion of four elements with different adsorption behaviors onto the clay was analyzed: Eu and U as adsorbing elements, Sr as low adsorbing, and Re as a non-adsorbing element with anionic behavior.Apparent diffusion coefficients (D_a) could be experimentally determined for Re, Eu and U after a few days of diffusion time, while for Sr it was only possible to estimate a lower limit for the diffusion coefficient. The uncertainties of the proposed methodology are discussed on the basis of sensitivity studies.     

Detailed Mathematical Analysis of Solute Transport in Armfield's Liquid Diffusion Apparatus

A solute's diffusivity is a key property in the design and analysis of mass transfer systems. A simple method to determine such coefficients in aqueous media is Armfield's diffusion apparatus, in which reservoir (donor) and bath (receiver) compartments are separated by a honeycomb array of liquid‐filled cylindrical pores. The solute of interest, i.e., NaCl, diffuses from the reservoir and pores into the bath. The electrical conductivity of the bath solution, which is proportional to the NaCl molarity, is tracked as a function of time at constant temperature. A comprehensive mathematical model is presented which combines simultaneous solute transport in the three compartments, allowing estimation of the aqueous NaCl diffusivity from experimental data. The model improves existing theoretical analyses of such data and can be adapted to study other challenging systems.     

Diffusion behaviour of the lead—acetate system

Variations in polarographic diffusion current constants for the lead—acetate system at constant ionic strength are shown to correlate with published equilibrium data. There is evidence that different types of solute—solute and solute—solvent interactions can be detected and distinguished by means of diffusion parameters.     

Kinetic analysis of phenol adsorption from aqueous systems

The kinetic adsorption of mixtures of phenolic compounds onto a polymeric adsorbent from aqueous solutions was studied. Experimental data for single‐component solutions were obtained and fitted to a parallel diffusion model. Effective diffusion coefficients were related to liquid‐phase diffusion and surface diffusion. The effect of solute concentration and salinity on these parameters was also analysed. Van Laar's equation is proposed to evaluate the influence of concentration on diffusion. The adsorption kinetics for phenol and pcresol mixtures at different initial concentration ratios were determined and correctly adjusted to the mentioned kinetic model. Results confirm that adsorption from multicomponent aqueous solutions is a surface diffusion‐controlled process.     

Correlations for prediction of diffusion in liquids

Based on an extensive experimental data collection (about 1925 points), empirical correlations for the estimation of binary liquid diffusion coefficients have been developed. The new correlations for organic mixtures and for aqueous solutions (including dissolved gases) require only well known and simple parameters like the viscosity of the solvent and the molar volumes of solute and solvent at the normal boiling point. They are shown to predict the limiting diffusion coefficients with the same or sometimes better accuracy than established correlations which make use of additional parameters. The concentration dependence of the mutual diffusion coefficients can be estimated from the knowledge of the two limiting diffusion coefficients and thermodynamic data. Established equations are investigated and classified for different groups of systems e.g. nonpolar + nonpolar, nonpolar + polar and polar + polar liquid mixtures.     

EFFECT OF INTERPHASE MASS TRANSFER ON UNSTEADY CONVECTIVE DIFFUSION:PART I, PLANE-POISEUELLE FLOW OF A POWER-LAW FLUID IN A CHANNEL

The paper presents an all-time analysis of unsteady convective diffusion of solute undergoing an irreversible first-order chemical reaction at the bounding walls of a parallel-plate channel. The heterogeneous chemical reaction significantly influences the convective and diffusive coefficients. A new coefficient arises exclusively due to the incorporation of wall reaction. The effects of wall-catalysed reaction and power-law index 'N' on dispersion are investigated against the background of the no-reaction problem. The analytical result on dispersion of solute with wall catalysed reaction at long times is compared with the analytical solution when.reaction is absent. The Taylor [1 ] and Ans [2] regimes of dispersion for the present problem are obtained as limiting cases from the study. The graphical results of the study serve as a jury on any numerical study that might be undertaken considering non-asymptotic all-time analysis.     

THEORETICAL ANALYSIS OF THE DIFFUSION PROCESS INSIDE PROLATE SPHEROIDAL SOLIDS

ABSTRACT

A numerical solution of the diffusion equation to describe solute transport inside ellipsoids, assuming a constant difiusion coefficient and a corrective boundary condition, is presented. The difiusion equation in a prolate spheroidal coordinate system was used for a hidimensional case. The finite volume method was employed to discretize the basic equation, utilizing a uniform grid size. The equation was solved irteratively using the Gauss-Seidel method. The effect of Biot number and the aspect ratio of the body on diffusion rate and concentration during the process is presented. Plots are presented for Biot numbers from 0.05 to infinity and aspect ratios of 1.1, 2.0 and 5.0. To investigate the effect of the aspect ratio, different results changing the aspect ratio for Bi= 1.0 are shown. The results show that the model is consistent and it may be used to solve other cases such as those that include cylinder and sphere geometry, and/ or those with variable diffusion coefficients with small modifications.     

ARRESTED-FLOW CHROMATOGRAPHIC MEASUREMENT OF GASEOUS DIFFUSION COEFFICIENTS

Diffusion coefficients for He—(CH₄, C₂H₆, C₃H₈, and n-C₄H₁₀) mixtures of gases at 23°C and 100°C, and at 2.1 atm were measured using an arrested-flow chromatographic method after Knox and McLaren (1963). By this procedure the flow of a band of solute gas in a carrier gas (He) is stopped when the band reaches the midregion of the column. The band spreads by diffusion during the period of arrested flow, and is then eluted by resuming the flow. The band variance at the column exit varies with the time of arrested flow such that the slope is proportional to the diffusion coefficient. The method appears to be an accurate and accessible method to measure binary diffusion coefficients.