Steady-state Diffusion Coefficient Research Articles

Effect of the Various Solvents on the <i>In Vitro</i> Permeability of Vitamin B<sub>12</sub> through Excised Rat Skin

Purpose: To investigate the effect of different solvents on the in vitro skin permeability of vitamin B 12 . Method: Vitamin B 12 (B 12 ) permeability experiments through rat skin pretreated with various solvents namely, propylene glycol, oleoyl macrogol-6-glycerides, propylene glycol monocaprylate and oleic acid, were performed in Franz diffusion cells and compared with hydrated rat skin as control. The permeability parameters evaluated include steady-state flux (J ss) , lag time (T lag ), permeability coefficient (Kp) and diffusion coefficient (D). The solvents’ permeability enhancement mechanisms were investigated by comparing of changes in peak position and their intensities of assymmetric (Asy) and symmetric (Sym) C-H stretching, and C=O stretching absorbance using Fourier transform infrared spectroscopy (FTIR), as well as by comparing mean transition temperature (Tm) and their enthalpies (∆H) using differential scanning calorimetery (DSC). Results: All the solvents significantly decreased diffusion coefficient (p < 0.05), with capryol showing the greatest enhancement ratio (ER D) based on diffusion coefficient followed by labrafil, oleic acid and propylene glycol. Flux enhancement ratio (ER flux ) for all the solvents was < ER D. The solubility of B12 in stratum corneum was the rate-limiting step in partitioning. All solvents with different lipophilic properties decreased drug solubility in the stratum corneum and hence lowered partitioning and flux. FTIR and DSC results showed lipid fluidization and extraction by labrafil and capryol, disruption of lipid structure and fluidization by oleic acid, and interaction with stratum corneum keratin by propylene glycol. Conclusion: Water is a suitable topical vehicle for B 12 as it can increase partitioning and diffusion through rat skin.

Steady-State Diffusion Coefficients for Water in Nafion in the Absence of Inert Gas

Steady-state diffusion coefficients of water in Nafion were determined in the absence of inert gases at 25°C. A large range of water activity was investigated to determine average and differential diffusion coefficients. Flux decreased toward zero as the water activity gradient between water vapor and liquid water approached zero, indicating no Schroeder's paradox. The average diffusion coefficients varied between 1 × 10−6 and 5 × 10−6 cm2/s, with a minimum at 14 moles H2O/mol SO3−. Differential diffusion coefficients ranged between 4 × 10−7 and 2 × 10−5 cm2/s, with a minimum at 14 moles H2O/mol SO3−.

Prediction of Equivalent Steady-State Chloride Diffusion Coefficients

This paper presents an approach for determining the chloride migration rate of hardened concrete by applying fundamental electrochemistry for different cementitious mixtures using the measurements from the chloride-ion penetration test (CIPT) data following ASTM C1202 specifications. The steady-state condition is verified by comparing the numerical values of chloride migration rates during 5, 30, and 360 minutes of testing. Three different theoretical approaches—Nernst-Plank, Nernst-Einstein, and the Zhang-Gjorv method—were applied to obtain the equivalent steady-state diffusion coefficients for different cementitious materials. These results are compared with the diffusion coefficients obtained from Berke’s empirical equation using CIPT data. These methods for the computation of diffusion coefficients include both the joule effect and temperature dependency and eliminate the need for other extended migration tests to obtain the steady-state conditions. Overall, this research presents a reliable method of determining the chloride migration rate for diffusion coefficient prediction.

Modeling Nafion: Water Diffusion and Polymer Relaxation

Transient water sorption was measured using gravisorption at 50 degrees C. The water diffusion coefficient is 3{plus minus}1x(10)^-8 cm2/s, a hundred times smaller than the steady-state diffusion coefficients reported in the literature. A water-diffusion polymer-relaxation model was developed and provides a semiquantitative fit of the experimental data. In this model, the polymer relaxation rate constant is 100,000 s.

Improvement of the chloride ingress resistance of OPC mortars by using spent cracking catalyst

The influence of the incorporation of spent cracking catalyst (FC3R) on the chloride ingress resistance has been evaluated. Thermogravimetric analyses have shown that the pozzolanic reaction of FC3R yields higher contents of hydrated calcium aluminates and silicoaluminates, so chloride binding capacity of mortars was highly improved. Mercury intrusion porosimetry analyses demonstrated that FC3R produces a significant reduction of capillary pore volume. As a result non-steady-state and steady-state chloride diffusion coefficients were reduced, enhancing the chloride ingress resistance of mortars incorporating FC3R. Additionally, the corrosion behaviour of steel embedded in Portland cement mortars partially substituted by spent cracking catalyst (FC3R) under chloride attack has been studied. Results showed that the incorporation of FC3R decreased the corrosion rates of steels and increased chloride thresholds for corrosion. For this reason, FC3R is an interesting pozzolanic material that can be used in reinforced concrete for civil engineering applications exposed to the action of chlorides.

On the Problem of Diffusivity in Heterogeneous Biological Materials with Random Structure

Biological tissues are multicompartmental heterogeneous media composed of cellular and subcellular domains. Randomly walking water molecules may have different diffusion coefficients and densities (concentrations) in different domains, namely within cells and within the outer medium. Results of the proposed effective media scale-averaging iterative scheme are used to explore the effects of a large range of microstructural and compositional parameters on the apparent (effective) diffusion coefficient. A self-consistent modelling framework for predicting the steady-state effective diffusion coefficient is presented; the framework reveals the strong dependence of the apparent diffusion coefficient on the ratio of the microscopic diffusion coefficients of the comprising phases, permeability of the cells, and their volume fractions.

Type Curves for Dry CBM Reservoirs With Equilibrium Desorption

Abstract The purpose of this work is to model the single-phase radial gas flow in coalbed methane including equilibrium sorption phenomena in the coal matrix and Darcy flow in the natural fracture network. Considering a control volume, the gas desorption rate as a function of time and space is incorporated into the radial continuity equation as a source term. Using a Langmuir-type sorption isotherm, the gas desorption rate is determined at any radius of the reservoir. Introducing the definition of pseudo-pressure and pseudo-time, the resulting continuity equation is converted into the linearized diffusivity equation by modification of total gas compressibility. It is shown how the traditional definition of the material balance pseudo-time is modified for dry CBM reservoirs. With the help of these transformations, the traditional (PTA and RTA) type curves can be employed for analysis of production data of dry CBM reservoirs. The model developed here is validated against Fekete's numerical CBM simulator over a wide range of reservoir parameters. In addition, one set of field data from Horseshoe Canyon coals of the Western Canadian Sedimentary Basin is analyzed using the solution procedure presented in this paper. Introduction Coalbed methane (CBM) is natural gas produced from coal seams. Coal is both the source rock and the reservoir for methane production. The world total CBM resource potential is evaluated at about 143.2 trillion cubic metres(1). CBM reservoirs are naturally fractured reservoirs that are characterized by two distinct porosity systems including:micropores (matrix) with extremely low permeability andmacropores (natural fractures or cleats). Due to the small pore diameter of less than 10 Å, the coal matrix has a large internal surface area of 100 to 300 m(2)/g(2, 3). As a result, substantial quantities of gas can be adsorbed on the surface of the coal grains. Micropores are impermeable to gas and inaccessible to water. However, the desorbed gas can be transported through the primary porosity system by diffusion. The macropores act as a sink to the micropores and provide permeability to fluid flow. In porous media with larger pore size distributions, mass transfer is driven by pressure gradients, whereas in coal, mass transfer is driven by concentration gradients(4, 5). The diffusion through the micropores can be the result of three distinct mechanisms that may act individually or simultaneously(6):bulk diffusion, where molecule/molecule interactions dominate;Knudsen diffusion, where molecule/surface interactions dominate; andtwo-dimensional surface diffusion of the adsorbed gas layer. The steady state diffusion coefficient of methane for most coals is on the order of 10−4 to 10−5 cm(2)/s(6). These experimentally determined diffusion coefficients represent averaged values including the contributions of the bulk, Knudsen and surface diffusion processes. Diffusion effects can be quantified by determining a sorption time. The sorption time is equal to the time required to desorb 63.2% of the initial gas volume. It is determined from whole core canister desorption test. This time is related to fracture spacing and the diffusion coefficient(7). Gas production from the CBM reservoirs is controlled by a four-step process that includes:

Influence of surface charge on ingress of chloride ion in hardened pastes

The amount of free chloride content in concrete is one of major factors in initiating the corrosion process. The material and environmental factors play a key role in diffusing the chloride ion through the cover concrete to reinforcement. Thus, the electrochemical study is indispensable to understand the mechanism of chloride ingress into concrete. Determination of surface charge and its influence on diffusion of chloride ion into cement matrix of concrete are researched for Ordinary Portland Cement (OPC) paste and cement paste containing Ground Granulated Blastfurnace Slag (GGBS). Different kinds of experiments such as measurement of membrane potential, determination of porosity and pore size distribution, determination of pore solution concentration, and steady state diffusion coefficient of chloride and sodium ions are employed to understand the mechanism of chloride ingress. The obtained results show that the positive surface charge on the pore walls of hardened paste regardless of GGBS’s presents. The surface charge of hardened paste mainly depends on pore solution concentration and cement composition. The physiochemical characteristics of the pores are affecting on transporting ions through it. Hardened paste has greater resistance to diffusing sodium ions than chloride ions. Moreover, there is a strong interaction between transport of chloride ion and surface charge in matured hardened paste.

Interpretation of diffusion coefficients in nanostructured materials from random walk numerical simulation

We make use of the numerical simulation random walk (RWNS) method to compute the "jump" diffusion coefficient of electrons in nanostructured materials via mean-square displacement. First, a summary of analytical results is given that relates the diffusion coefficient obtained from RWNS to those in the multiple-trapping (MT) and hopping models. Simulations are performed in a three-dimensional lattice of trap sites with energies distributed according to an exponential distribution and with a step-function distribution centered at the Fermi level. It is observed that once the stationary state is reached, the ensemble of particles follow Fermi-Dirac statistics with a well-defined Fermi level. In this stationary situation the diffusion coefficient obeys the theoretical predictions so that RWNS effectively reproduces the MT model. Mobilities can be also computed when an electrical bias is applied and they are observed to comply with the Einstein relation when compared with steady-state diffusion coefficients. The evolution of the system towards the stationary situation is also studied. When the diffusion coefficients are monitored along simulation time a transition from anomalous to trap-limited transport is observed. The nature of this transition is discussed in terms of the evolution of electron distribution and the Fermi level. All these results will facilitate the use of RW simulation and related methods to interpret steady-state as well as transient experimental techniques.

Temporal evolution of the electron diffusion coefficient in electrolyte-filled mesoporous nanocrystalline TiO 2 films

Electron transport in electrolyte-filled mesoporous TiO 2-based solar cells is described quantitatively from the perspective of the continuous-time random walk model. An analytical expression is derived for the time-dependent diffusion coefficient of electrons, which transforms at a characteristic (Fermi) time from strongly time-dependent values (dispersive transport) at short times to relatively time-independent values (nondispersive transport) at long times. At short times, the diffusion coefficient displays a power-law behavior with time. The timescale for the diffusion coefficient to reach its steady-state value is substantially longer than the Fermi time. The Fermi time and the steepness of the distribution of waiting times associated with trap sites have a strong influence on both the steady-state diffusion coefficient of electrons and on the dispersiveness of electron transport. At short timescales, ionic drag, associated with the ambipolar effect, slows electron transport through the TiO 2 matrix, whereas at steady state, transport is trap limited. Decreasing the electron density lowers the steady-state limit of the diffusion coefficient and increases the timescale over which transport is dispersive.

Time-lags for radial transport with boundary-layer resistance in a ν-dimensional membrane

By means of an extension of the procedure due originally to Frisch [J. Phys. Chem. 61 (1957) 93], expressions have been derived for the ingoing and outgoing time-lags pertaining to radial transport with boundary-layer resistance in slab, hollow cylinder and spherical shell membranes. The derivation relates to a constant diffusion coefficient, D and complements an earlier treatment (for slab membranes only) [J. Membrane Sci. 186 (2001) 63] which employed the Jaeger procedure [J. Membrane Sci. 117 (1996) 79]. For the geometrically asymmetric hollow cylinder and spherical shell membranes both ‘forward’ and ‘reverse’ flow have been considered. Assuming the transfer coefficients ( h 1, h 2) to be unaffected by flow reversal, expressions for the resultant ‘adsorption’ and ‘desorption’ time-lags have been deduced and identities between them evaluated. For the three membrane systems considered there are, in each case, only three distinguishable (boundary) time-lags. Final considerations have been limited to membranes of fixed thickness, l, with equal transfer coefficients ( h 1 = h 2 ≡ h) at the boundaries. The dependence of the ratio of each time-lag to the corresponding limiting ( k → ∞) value upon k (≡ hl/ D) and q (≡ R 2/ R 1) has been investigated. Attention has also been directed towards the utilisation of time-lags for estimating an ‘effective’ (steady-state) diffusion coefficient.

Monte Carlo calculations of hot-electron transport and diffusion noise in GaN and InN

Monte Carlo simulations of high-field transport are used to calculate the spectral density of velocity fluctuations and the diffusion coefficients of hot electrons in GaN and InN. The results of the simulations are complemented by the investigation of the velocity relaxation time through the balance equation method. It is found that the low-frequency noise spectrum remains white up to 100–300 GHz, so that the steady-state diffusion coefficient can be considered as constant in practically the whole millimetre wavelength range. It is shown that the main features of the field dependence of the longitudinal and transverse diffusion coefficients such as initial decrease of the diffusion coefficient followed by a peak near the threshold field for the intervalley transfer, etc are described well both qualitatively and quantitatively by simplified approaches based on velocity relaxation times.

Effect of the application of electrical fields on the interactions between the chloride ions and the cementitious matrix

The application of electrical fields to determine the chloride diffusion coefficients through concrete has become a need in order to obtain the required results in reasonable periods of time. However, this acceleration could modify the complex interactions between the chloride ions and the cementitious matrix, being the coefficients obtained by migration tests not representative of those of natural conditions. This subject is undertaken in this paper by performing steady and non-steady state migration tests for chlorides and natural diffusion for oxygen and chloride ions. As a result it has been stated that when applying an electrical field (until 10.5 V/cm), the transport of chloride ions take place through the same kind of pores, but the interaction to combine chlorides is smaller than when driven by natural diffusion. This is a point to be taken into account when designing the experimental conditions for migration tests to determine the non steady state diffusion coefficient of chloride ions.

An electrochemical method for accelerated chloride migration test of diffusion coefficient in cement-based materials

In this study, the electrochemical technique is applied to accelerate chloride ion migration in cement-based material to estimate its permeability. The plain cement concrete and concrete containing different type of mineral admixtures (slag and fly ash) with water/binder (w/b) ratios of 0.35, 0.45, 0.55, and 0.65 were used. For all test series, the chloride concentration in the anode cell as well as the electrical current were simultaneously monitored in the accelerated chloride migration test (ACMT). The steady-state diffusion coefficient for concrete was calculated using the constant flux on the basis of the Nernst–Planck’s equation and the non-steady-state diffusion coefficient was calculated from the modified second Fick’s law. The charge passed from different conditions were separately defined and derived. The results for all mixtures show that the steady-state diffusion coefficient and charge passed obtained from the accelerated chloride migration test under steady-state condition is linearly correlated.

Measurement of the steady and non-steady-state chloride diffusion coefficients in a migration test by means of monitoring the conductivity in the anolyte chamber. Comparison with natural diffusion tests

Abstract The precise calculation of steady-state chloride diffusion coefficients is laborious, expensive, and time consuming due to the fact that it is necessary to take liquid samples for the chlorides to be analysed. In this paper, the concentration of chlorides is monitored by measuring the conductivity of the anolyte which initially is distilled water. Additionally, the calculation of Ds and Dns is made from the same test using the concept of “time-lag” and of the “equivalent time” between diffusion and migration experiments. The correlation between Ds and the conductivity has been done by testing 10 different cementitious matrixes (concrete and mortar) with different binders, and considering the influence of the type of solution that is the source of chloride ions as well as the variation of the electrodes and the effect of the kind of matrix. The results obtained have been compared with natural diffusion results in order to validate them. As a result, for the possibility of making it automatic, the calculation of Ds and Dns diffusion coefficients has been verified.

Transport through a slab membrane governed by a concentration-dependent diffusion coefficient: Part II. The four time-lags for some particular D( C)

Expressions have been derived for the ‘adsorption’ ( L l a( C 0), L 0 a( C 0)) and ‘desorption’ ( L 0 d( C 0), L l d( C 0)) time-lags corresponding with 13 functional dependencies of the differential diffusion coefficient, D( C). A detailed analysis of the concentration dependence of the time-lags is given. The initial ( C 0 → 0) slope and curvature of a time-lag : (ingoing) concentration curve may be obtained from the corresponding limiting values of d D( C 0)/d C 0 and d 2 D( C 0)/d C 0 2. It is shown how the ‘desorption’ time-lags and ingoing ‘adsorption’ time-lag are related to the (experimentally) more readily determined outgoing ‘adsorption’ time-lag, L l a( C 0) and may be evaluated using a master-plot of steady-state flux of diffusant, J ∞( C 0), against ingoing concentration, C 0. The arithmetic mean of designated time-lag integral diffusion coefficients can, over a limited range of C 0, approximate to the steady-state integral diffusion coefficient D̃( C 0). This finding, combined with determination of the complementary J ∞( C 0) should allow an estimate of C 0 to be made. Following upon experimental observations, attention has been directed towards the concentration dependence of ‘adsorption’ and ‘desorption’ time-lag ratios, R a ( C 0) and R d( C 0) and of the arithmetic mean, R M( C 0) = (1/2)[ R a( C 0) + R d( C 0)]. Departures of R M( αC 0) from the ideal value of 2 were not great and were hardly reflected in the corresponding larger variations of R a( C 0) and R d( C 0).

Influence of potential and time on the dissolution of Sn-In, Sn-Zn, and In-Zn alloys with a low content of the second component in chloride media

The dissolution of low-melting alloys with low contents of the more negative component is investigated as a function of time and potential. It is shown, by taking potentiostatic measurements, that several time intervals exist where steady-state and non-steady-state diffusion coefficients are realized. The main dissolution parameters are potential-dependent, and two ranges exist where the steady-state diffusion coefficient varies with the potential.

Characterization of transport of caesium, strontium, cobalt and iron ions through concrete by steady-state migration and natural diffusion tests

Immobilization of wastes in cement-based matrices is being increasingly used, particularly in the case of elements of medium and low activity. Therefore, characterization of the system in relation to the release of ionic wastes through the cement, and consequently the determination of their diffusion coefficients, becomes of strategic importance. Nowadays, diffusion coefficients of some radioactive elements (mainly of Cs+) can be found in the literature, obtained by natural diffusion tests that are very time-consuming. In the present paper, the calculation of steady-state diffusion coefficients of Cs+, Sr2+, Co2+ and Fe3+ through concrete has been done by migration experiments. The mutual influence of the diffusion coefficients has also been studied, and transference numbers of the different ions have been calculated. The results have been compared with those obtained by natural diffusion tests, having found for Cs+ and Sr2+ that there is a very good accordance between diffusion and migration tests. In contrast for Co2+ and Fe3+ the accordance is not so good, because at migration working conditions they are able to form complex compounds. In consequence, migration tests are reliable for obtaining diffusion coefficients of different elements through concrete, always taking into account the nature of the species that are present at working conditions.

Transport through a slab membrane governed by a concentration-dependent diffusion coefficient. Part I. The four time-lags: some general considerations

Two (equivalent) sets of expressions have been derived for the four time-lags, L a l , L d 0, L d l , L a 0, associated with transport through a slab membrane under `simple' boundary conditions and with the diffusion coefficient, D, a function of the concentration, C, of the diffusing species. The individual sign and relative magnitudes of the time-lags have been determined. Order of magnitude has been derived for two particular classes of D( C): Class (A): D( C) a strictly-increasing function of C and Class (B): D( C) a strictly-decreasing function of C, thereby establishing the two time-lag sequences: ( A) L a 0<L d l<0<L d 0<L a l, ( B) L d l<L a 0<0<L a l<L d 0. The four time-lags have been employed to define four integral diffusion coefficients: D ̃ a L, D d L, D ̃ d L, D a L. Inequalities between these (time-lag) integral diffusion coefficients and the corresponding steady-state integral diffusion coefficient, D̃, have been investigated. For the particular Classes (A) and (B) functions considered, the sequences of time-lag moduli are: ( A) 2L d 0<|L d l|<|L a 0|<2L a l, ( B) 2L d 0>|L d l|>|L a 0|>2L a l.

In Vitro Release and Diffusion Studies of Promethazine Hydrochloride from Polymeric Dermatological Bases Using Cellulose Membrane and Hairless Mouse Skin

The study was designed to investigate the feasibility of developing a transdermal drug dosage form of promethazine hydrochloride (PMH). The in vitro release and diffusion characteristics of PMH from various dermatological polymeric bases were studied using cellulose membrane and hairless mouse skin as the diffusion barriers. These included polyethylene glycol (PEG), hydroxypropyl methylcellulose (HPMC), cross-linked microcrystalline cellulose, and carboxyl methyl cellulose sodium (Avicel® CL-611), and a modified hydrophilic ointment USP. In addition, the effects of several additive ingredients known to enhance the drug release from topical formulations were evaluated. The general rank order for the drug release from these formulations using cellulose membrane was observed to be PEG > HMPC > Avicel CL-611 > hydrophilic ointment base. The inclusion of the additives had little or no effect on the drug diffusion from these bases, except for the hydrophilic ointment formulation containing 15% ethanol, which provided a significant increase in the drug release. However, when these formulations were studied for drug diffusion through the hairless mouse skin, the Avicel CL-611 base containing 15% ethanol exhibited the optimum drug release. The data also revealed that this formulation gave the highest steady-state flux, diffusion, and permeability coefficient values and correlated well with the amount of drug release.