Concentration-dependent Diffusion Research Articles

Self-association of Zn-insulin at neutral pH: Investigation by concentration gradient-static and dynamic light scattering

Equilibrium self-association of Zn-insulin at pH 7.0 was characterized over the range 0.3–5 mg/mL by simultaneous measurement of static and dynamic light scattering. Analysis of static light scattering yielded a concentration-dependent weight-average molecular weight, and analysis of dynamic light scattering yielded a concentration-dependent intensity-average diffusion coefficient. The concentration dependence of both quantities may be accounted for to within experimental precision by a simple model, according to which the basic structural unit of Zn-insulin at concentrations exceeding 0.3 mg/mL is a hexamer H. With increasing total protein concentration, hexameric protomers may self-associate in accordance with an isodesmic scheme in which a protomer may add to any prexisting oligomer H n to form H n + 1 with an invariant stepwise equilibrium association constant.

The Measurement of Polymer Swelling Processes by an Interferometric Method and Evaluation of Diffusion Coefficients

The amorphous polymer film swelling in a liquid solvent below the glass transition temperature was characterized by a few kinetic parameters (especially the mutual diffusion coefficient of swelling and its mean value) obtained by interference of monochromatic light in the wedge arrangement. This interferometric method allows one to determine the concentration field in the swollen surface layer and consequently to compute the concentration-dependent diffusion coefficient. A software system developed at the Department of Physics and Material Engineering at TBU in Zlin has been used for the evaluation of the main kinetic parameters of the swelling process. The software can be used for the on-line analyses of interferograms during the swelling process. The main application outputs are the computation of the concentration profile, the concentration gradient, the mutual diffusion coefficient of the swelling by the solvent and its mean value.

Modelling of diclofenac sodium diffusion from swellable and water-soluble polyethylene oxide matrices

Abstract Objectives The main objective of this study was to develop a mathematical model for the characterization of diclofenac sodium diffusion from polyethylene oxide (PEO) matrices. A model was developed on the basis of the diffusion theory accounting for the characteristics of the polymer: swelling with subsequent dissolution in water. The concentration-dependent diffusion of drug and water was taken into account. Experimental data were analysed using a computer software program as an aid for solving partial differential equations. Methods Six formulations of matrix tablets with different drug-excipient ratios were prepared using low-molecular-weight PEO as a matrix-forming material. For obtaining drug release data, dissolution studies were performed and water uptake by pure PEO matrices was studied as well. Key findings A good agreement of the developed model with experimental results was demonstrated. Some anomalies in drug diffusion were observed and their origin was questioned. Changes in the parameters characterizing the process of diffusion are attributed to glassy-rubbery polymer transitions. Additional interpretation of this phenomenon on the basis of percolation theory is also provided. Conclusions The obtained model has the ability to predict the required characteristics of matrices for desired drug release. The composition of batches with undesirable release properties can be predetermined and avoided in manufacturing.

Influence of the crystal field effect on chemical transport in Earth's mantle: Cr 3+ and Ga 3+ diffusion in periclase

Experiments were performed to determine concentration-dependent diffusion coefficients of Cr 3+ and Ga 3+ in periclase at temperatures of 1563–2273 K. Diffusion profiles measured in the quenched samples are consistent with a theoretical model in which the mobile species is a bound M 3+-vacancy pair, and each profile was fitted to determine the binding energy and diffusion coefficient of the pair. Trivalent chromium-vacancy pairs diffuse more slowly than Ga 3+-vacancy pairs, and with higher migration energy, 237 kJ/mol vs. 190 kJ/mol. Cation vacancies also bind less tightly to Cr 3+ than to Ga 3+, with average binding free energies of −22 and −83 kJ/mol, respectively. At all concentrations and temperatures, Cr 3+ diffuses much more slowly than Ga 3+, by up to two orders of magnitude. The differences between Cr 3+ and Ga 3+ cannot be explained by differences in ionic radius or dipole polarizability, but are consistent with the influence of the crystal field on the partially occupied 3d orbitals of Cr 3+. The crystal field splitting stabilizes Cr 3+ on the octahedral cation site, increasing the energy required for Cr 3+ to exchange positions with an adjacent vacancy. It also makes Cr 3+-vacancy pairs less favorable, with the presence of a nearest-neighbor vacancy disrupting the symmetry of the octahedral site, thus diminishing the crystal field stabilization. Trends in the diffusion of first-row divalent transition metals in periclase can also be explained by the crystal field effect. High-spin to low-spin transitions in Fe 2+, Co 2+ or Mn 2+ would significantly enhance their crystal field stabilization in periclase, and if such spin transitions occur in the deep mantle, they would be expected to slow the diffusivity of these ions significantly, perhaps by several orders of magnitude.

On the Maxwell−Stefan Approach to Diffusion: A General Resolution in the Transient Regime for One-Dimensional Systems

The diffusion process in a multicomponent system can be formulated in a general form by the generalized Maxwell-Stefan equations. This formulation is able to describe the diffusion process in different systems, such as, for instance, bulk diffusion (in the gas, liquid, and solid phase) and diffusion in microporous materials (membranes, zeolites, nanotubes, etc.). The Maxwell-Stefan equations can be solved analytically (only in special cases) or by numerical approaches. Different numerical strategies have been previously presented, but the number of diffusing species is normally restricted, with only few exceptions, to three in bulk diffusion and to two in microporous systems, unless simplifications of the Maxwell-Stefan equations are considered. In the literature, a large effort has been devoted to the derivation of the analytic expression of the elements of the Fick-like diffusion matrix and therefore to the symbolic inversion of a square matrix with dimensions n x n (n being the number of independent components). This step, which can be easily performed for n = 2 and remains reasonable for n = 3, becomes rapidly very complex in problems with a large number of components. This paper addresses the problem of the numerical resolution of the Maxwell-Stefan equations in the transient regime for a one-dimensional system with a generic number of components, avoiding the definition of the analytic expression of the elements of the Fick-like diffusion matrix. To this aim, two approaches have been implemented in a computational code; the first is the simple finite difference second-order accurate in time Crank-Nicolson scheme for which the full mathematical derivation and the relevant final equations are reported. The second is based on the more accurate backward differentiation formulas, BDF, or Gear's method (Shampine, L. F. ; Gear, C. W. SIAM Rev. 1979, 21, 1.), as implemented in the Livermore solver for ordinary differential equations, LSODE (Hindmarsh, A. C. Serial Fortran Solvers for ODE Initial Value Problems, Technical Report; https://computation.llnl.gov/casc/odepack/odepack_ home.html (2006).). Both methods have been applied to a series of specific problems, such as bulk diffusion of acetone and methanol through stagnant air, uptake of two components on a microporous material in a model system, and permeation across a microporous membrane in model systems, both with the aim to validate the method and to add new information to the comprehension of the peculiar behavior of these systems. The approach is validated by comparison with different published results and with analytic expressions for the steady-state concentration profiles or fluxes in particular systems. The possibility to treat a generic number of components (the limitation being essentially the computational power) is also tested, and results are reported on the permeation of a five component mixture through a membrane in a model system. It is worth noticing that the algorithm here reported can be applied also to the Fick formulation of the diffusion problem with concentration-dependent diffusion coefficients.

Simulation of kinetic curves in mass transfer phenomena for a concentration-dependent diffusion coefficient in polymer membranes

Two methods are developed for the determination of the diffusion parameters of a penetrant inside polymer membranes whose diffusivity varies exponentially with its concentration. Two cases are considered in this report depending on the sign of the plasticization coefficient parameter. The method using differential permeation data is based on the correlations between the slope of the reduced permeation flux versus time plot at the inflexion point, and the two key parameters of the concentration-dependent diffusivity laws. For the transient sorption/desorption method, the slope of the penetrant mass uptake versus square-root of time curve leads to the same parameters of the diffusion law via similar correlations. No specific computer software is required for the use of these methods and they are user friendly.

Modelling of diclofenac sodium diffusion from swellable and water-soluble polyethylene oxide matrices

The main objective of this study was to develop a mathematical model for the characterization of diclofenac sodium diffusion from polyethylene oxide (PEO) matrices. A model was developed on the basis of the diffusion theory accounting for the characteristics of the polymer: swelling with subsequent dissolution in water. The concentration-dependent diffusion of drug and water was taken into account. Experimental data were analysed using a computer software program as an aid for solving partial differential equations. Six formulations of matrix tablets with different drug-excipient ratios were prepared using low-molecular-weight PEO as a matrix-forming material. For obtaining drug release data, dissolution studies were performed and water uptake by pure PEO matrices was studied as well. A good agreement of the developed model with experimental results was demonstrated. Some anomalies in drug diffusion were observed and their origin was questioned. Changes in the parameters characterizing the process of diffusion are attributed to glassy-rubbery polymer transitions. Additional interpretation of this phenomenon on the basis of percolation theory is also provided. The obtained model has the ability to predict the required characteristics of matrices for desired drug release. The composition of batches with undesirable release properties can be predetermined and avoided in manufacturing.

Ensemble Measurement of Diffusion: Novel Beauty and Evidence

Recording the evolution of concentration profiles in nanoporous materials opens a new field of diffusion research with particle ensembles. The technique is based on the complementary application of interference microscopy and IR micro-imaging. Combining the virtues of diffusion measurements with solids and fluids, it provides information of unprecedented wealth and visual power on transport phenomena in molecular ensembles. These phenomena include the diverging uptake and release patterns for concentration-dependent diffusivities, the mechanisms of mass transfer at the fluid-solid interface and opposing tendencies in local and global concentration evolution.

Intraparticle Transport and Release of Dextran in Silica Spheres with Cylindrical Mesopores

The transport of oligomeric molecules in silica spheres with cylindrical mesopores has been quantified and related to the structural features of the spherical particles and the interactions at the solid-liquid interface. An emulsion-solvent evaporation method was used to produce silica spheres having cylindrical mesopores with an average pore diameter of 6.5 nm. The transport of dextran molecules (fluorescently tagged) with molecular weights of 3000 and 10,000 g/mol was quantified using confocal laser scanning microscopy (CLSM). The intraparticle concentration profiles in the dextran-containing spheres were flat at all times, suggesting that the release is not isotropic and not limited by diffusion. The release of dextran into the solution is characterized by an initial burst, followed by long-term sustained release. The release follows a logarithmic time dependency, which was rationalized by coupling concentration-dependent effective diffusion constants with adsorption/desorption.

Measurement of the SiCl4 Diffusion Coefficient in a Room-Temperature Ionic Liquid by an Optical Moiré-Pattern Technique

The diffusion coefficient of SiCl4 in trimethyl-n-hexylammonium bis(trifluoromethylsulfonyl)imide was estimated by means of an optical moiré-pattern technique. It revealed that the diffusion coefficient varies with concentration from 0.79 × 10−6 cm2 s−1 at 0.1 mol L−1 to 1.05 × 10−6 cm2 s−1 at 0.4 mol L−1 at 298 K. This technique is superior to any other methods to measure the diffusion coefficient especially in the following point. The conventional electrochemical methods such as chronopotentiometry and chronoamperometry yield just a single effective diffusivity over the similar concentration range. On the other hand, the moiré-pattern method is so powerful that just one experiment is adequate to estimate the concentration-dependent diffusivity because the local diffusivities at the points with different concentrations can be measured at once.

Predicting emission characteristics of volatile organic compounds from wet surface coatings

A mathematical model is developed to describe the emission characteristics of VOCs from homogeneous wet coating materials deposited on impermeable substrates. The model considers mass transfer in the material and in air, boundary layer resistance and the change in the coating thickness with time due to emission of VOC. Key features of the model are incorporation of concentration dependent VOC diffusion coefficients predicted from a physical model and nonlinear equilibrium isotherm at the coating/air interface. The model is applied to predict emission characteristics of MMA from acrylic based surface coatings. In an attempt to investigate the influences of equilibrium isotherm type and diffusion formalism on the predictions, simulations are performed with either constant or concentration dependent diffusivities and linear or nonlinear equilibrium isotherms. The lowest MMA concentration in air is predicted by incorporating the concentration dependent diffusivity and nonlinear equilibrium isotherm. The results suggest that assuming the diffusivity of MMA constant or equilibrium isotherm linear may lead to wrong conclusions about the emission rates from wet coatings. The model is general, fully predictive and can be used to predict emission rates of different VOCs from different coating materials if diffusion and thermodynamic parameters are available.

The Effective Diffusion/Dispersion Coefficient in Vapor Extraction of Heavy Oil

In this study, a new correlation for determination of effective diffusion/dispersion coefficients in the vapor extraction of heavy oil/bitumen (VAPEX) is introduced. This model takes into account the solvent concentration as well as the drainage height and permeability dependency of these coefficients. The concentration dependency in this model stems from the mixture viscosity changes, while the height dependency appears directly in the correlation. The correlation was obtained using the experimental results of the VAPEX experiments that were conducted with physical models of varying sizes and different permeability sand-packs. Estimation of a proper mass transfer coefficient has been a challenging issue for the analytical and numerical simulation of the VAPEX and other similar processes. Incorporating the effect of drainage height on dispersion with a concentration-dependent diffusivity model enables one to estimate the dispersion coefficient values involved in this process.

Impact of Concentration-Dependence of Diffusion Coefficient on VAPEX Drainage Rates

Abstract The VAPEX analytical model is extended to cover situations when diffusion coefficients are dependent on concentration due to the extreme viscosity reduction with solvent dissolution into bitumen. The new analytical model covers such situations along with the cases in which the diffusion coefficient and viscosity relate to each other under the Stokes-Einstein law. In the process, a new concept of the 'average flow fraction of bitumen' in the flowing mixtures is introduced. The modelled result on overall functionality of the drainage rate of bitumen has confirmed the square-root relationships to most of the key reservoir parameters as the previous theories indicate. However, its dependence to the inverse of kinematic viscosity at the interface is closer to linear rather than square-root correlation with the concentration-dependent diffusion coefficient. The theoretical relationships are confirmed by the correlations of the unified bitumen rates to kinematic viscosity at the interface using the existing VAPEX and SAGD experimental data in the literature. This finding indicates that VAPEX process in heavy oils with lower native viscosity can be more effective than originally recognized. Introduction Dunn et al.(1) developed the theoretical model of the gravity drainage process for bitumen recovery known as VAPEX based on the model of the steam-assisted gravity drainage (SAGD) process by Butler et al.(2) This model assumed that the diffusion coefficients of solvent-bitumen systems are constant similar to the case of thermal diffusivity. Thus, the steady-state profiles of solvent concentration ahead of the solvent-bitumen interface is the smooth exponential decay towards an infinite distance. In reality, the diffusion coefficients of both solvent and bitumen are strongly dependent upon compositions due to the extreme viscosity contrasts between the solutes and solvents. As a result, the observed concentration profiles in diffusion experiments exhibit the abrupt front-end profiles(3). The theoretical endeavour here is to understand the impact of the non-exponential concentration profiles on the VAPEX drainage and bitumen rates. Governing Mechanisms The most fundamental mechanism of the process is the gravity drainage caused by the density difference between the liquid-bitumen phase and the injected vapour phase. The drainage flow of the bitumen phase occurs only from viscosity reduction due to the impact of the injected solvent (or heat in the case of SAGD) of the otherwise semi-solid bitumen. Therefore, how the injected solvent penetrates into the bitumen phase in the reservoir is of primary importance to the process. According to Fick's law, a material balance across a differential distance, dx, in this situation can be expressed as a continuity equation for the change of concentration (volume fraction is chosen), C, with time, t, by using the diffusion coefficient, D: Equations (available in full paper)

Reply to the Discussion by K. K. al-Tarawneh, O. Buzzi, K. Krabbenh Oft, and A. V. Lyamin on Experimental Investigations into Concentration-Dependent Chloride Diffusivity in Glass Beads and Fine Sand

Reply to the Discussion by K. K. al-Tarawneh, O. Buzzi, K. Krabbenh Oft, and A. V. Lyamin on Experimental Investigations into Concentration-Dependent Chloride Diffusivity in Glass Beads and Fine Sand

Discussion of the Paper "Experimental Investigation into Concentration-Dependent Chloride Diffusivity in Glass Beads and Fine Sand" by K. Prabhakaran Nair, A. Praveen, and S. Chandrakaran

In this Discussion we shall reflect on various aspects of the recently published paper by Elaiw and Ibrahim (2008). Their paper considers hie onset of convective instabilities of a mixed convection boundary layer induced by the combined presence of a hot horizontal surface in an unbounded porous medium and an externally imposed uniform horizontal forced convective flow. These authors also adopt a power law variation in the surface temperature and allow for the effects of nonuniform porosity caused by inefficient packing of the porous medium near the horizontal surface. The primary aim of the present Discussion is to discuss the theoretical foundations of the analysis of Elaiw and Ibrahim (2008) in order to clarify them unambiguously.

Diffusion in multi-component polymeric systems: Diffusion of non-volatile species in thin films

Polymeric films for high-tech products like LCD-panels, transdermal patches or medical test strips typically consist of a polymer and one or more non-volatile additives. If during the production process a multi-component solution is coated and subsequently dried, the diffusion of solvents and non-volatile species in the polymeric systems plays an important role. Recent experiments revealed that the drying conditions can have a significant influence on the formation of inhomogeneous distribution of the non-volatile components in the final foil and therefore affects desired product properties. The distribution of the non-volatile components in the final film has an important impact on the physical and chemical properties, including mechanical and optical properties, wetting behavior or drug release rates i.e. the product quality of the polymeric system. To be able to describe the diffusion of non-volatile species in a multi-component polymeric system during drying correctly, reliable information about the influence of the solvent concentration on the mobility of the additive are essential. To obtain information about the mobility of the additive in the polymeric solution new experiments were performed and observed by means of Inverse-Micro-Raman-Spectroscopy (IMRS). By fitting simulated concentration profiles to the experimental data, the temperature and concentration dependent diffusion coefficient of the non-volatile additive in the polymer solution was determined. The investigations are part of a bilateral funding of NFG in the US and DFG in Germany. Diffusion of volatile species in multicomponent polymeric systems are investigated by the group of Richard Cairncross.

Drug release into external absorber: Concentration‐dependent diffusivity

AIChE JournalVolume 55, Issue 2 p. 548-553 Fluid Mechanics and Transport Phenomena Drug release into external absorber: Concentration-dependent diffusivity Sung-Hwa Lin, Corresponding Author Sung-Hwa Lin [email protected] Dept. of Chemical Engineering and Materials Engineering, National Ilan University, Yilan 26047, TaiwanDept. of Chemical Engineering and Materials Engineering, National Ilan University, Yilan 26047, TaiwanSearch for more papers by this author Sung-Hwa Lin, Corresponding Author Sung-Hwa Lin [email protected] Dept. of Chemical Engineering and Materials Engineering, National Ilan University, Yilan 26047, TaiwanDept. of Chemical Engineering and Materials Engineering, National Ilan University, Yilan 26047, TaiwanSearch for more papers by this author First published: 23 December 2008 https://doi.org/10.1002/aic.11663Citations: 1Read the full textAboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Citing Literature Volume55, Issue2February 2009Pages 548-553 RelatedInformation

Theoretical analysis and experimental study on SO2 adsorption onto pistachio‐nut‐shell activated carbon

AbstractThe adsorption study of SO2 onto the activated carbon prepared from pistachio‐nut shell was studied theoretically and experimentally. A single‐particle sorption model known as concentration‐dependent surface diffusivity micropore, surface and macropore diffusion control model incorporating micropore, macropore and surface diffusions, together with a nonlinear isotherm at the micropore mouth, has been derived and solved by a finite difference method. The effects of different types of nonlinear isotherms and concentration dependent surface diffusivities have been thoroughly studied. The effects of adsorbate concentration and temperature on adsorption were studied experimentally. Good agreement was found between the model predictions and the experimental results. The value of the tortuosity factor and the extracted diffusion coefficients obtained are consistent with their corresponding values reported. © 2008 American Institute of Chemical Engineers AIChE J 2009

Water barrier properties of polyamide 12/montmorillonite nanocomposite membranes: Structure and volume fraction effects

The water barrier properties of polyamide 12/organo-modified montmorillonite nanocomposites were studied by differential permeation. The water permeability and diffusivity were calculated from permeation kinetics and discussed with respect to the composite compositions. Depending on the clay volume fraction in the 0–5% range and the rotation speed during the composite processing, two different structures were obtained: a partially intercalated structure and a partially exfoliated structure, characterized by a higher level of exfoliation for the higher speed. In agreement with the tortuous path model, the water permeability and the diffusivity decrease with increasing clay volume fraction, ϕ, up to 2.5%, for both structures. However, beyond ϕ = 2.5% for partially intercalated nanocomposites and ϕ = 4% for partially exfoliated nanocomposites, the permeability no longer decreases, but increases. This effect was larger for the partially intercalated structure than for the partially exfoliated structure. The singular variations in the water permeation properties of nanocomposite membranes were interpreted in considering not only the structural properties, including the polymer crystallinity, but also various nanocomposite/permeant interactions, taking into account the plasticization phenomenon, solubility and free volume variations. It was possible to well simulate the permeation data by considering a water concentration dependent diffusion coefficient. Tensile measurements have shown the influence of the preparation conditions of nanocomposite membranes (clay volume fraction and the rotation speed) on the mechanical properties. As for permeation tests, the best performances were obtained with partially exfoliated nanocomposites compared to partially intercalated ones.

Reduced water vapour sorption in cellulose nanocomposites with starch matrix

The effects of microfibrillated cellulose nanofibers from wood on the moisture sorption kinetics (30% RH) of glycerol plasticized and pure high-amylopectin starch films were studied. The presence of a nanofiber network (70 wt% cellulose nanofibers) reduced the moisture uptake to half the value of the pure plasticized starch film. The swelling yielded a moisture concentration-dependent diffusivity. Quite surprisingly, the moisture diffusivity decreased rapidly with increasing nanofiber content and the diffusivity of the neat cellulose network was, in relative terms, very low. It was possible to describe the strong decrease in zero-concentration diffusivity with increasing cellulose nanofiber/matrix ratio, simply by assuming only geometrical blocking using the model due to Aris. The adjusted model parameters suggested a “simplified” composite structure with dense nanofiber layers oriented in the plane of the film. Still, also constraining effects on swelling from the high modulus/hydrogen bonding cellulose network and reduced amylopectin molecular mobility due to strong starch–cellulose molecular interactions were suggested to contribute to the reductions in moisture diffusivity.