Diffusivity: A Review on Research and Studies with Insight into Affecting Parameters (original) (raw)
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Diffusion Research with Nanoporous Material
Chemistry International, 2021
Owing to their potential for eco-friendly matter upgrading by molecular sieving and shape-selective conversion, nanoporous materials are among the pioneers of green chemistry. The performance of their application is often controlled by diffusion, i.e. the rate of mass transfer within these materials. This mass transfer, however, is rather complex and subject to numerous influences. Unambiguous diffusion measurement has thus remained a challenge to this day with errors in the interpretation of experimental data being all too common. The present feature reports the efforts of an IUPAC initiative to overcome these limitations.
1st International Conference on Diffusion in Solids and Liquids “DSL-2005”
Abstract It has been shown very recently that the diffusion non-linearity, due to the strong composition dependence of the diffusion coefficients, can lead to surprising effects on nanoscale: i) non parabolic shift of interfaces (both in ideal and phase separating systems), ii) sharpening of an initially diffuse interface in ideal systems. Some of these can not be interpreted even qualitatively from Fick s classical equations.
Analytical method for evaluating the effective molecular diffusion coefficient within porous media
Chemical Engineering Science, 1993
This paper presents an original analytical method for calculating the value of the effective molecular diffusion coefficient of an inert tracer transported within a saturated porous medium, D,, in terms of the bulk diffusion constant, Do. A simple three-step sequence in the tracer core or packed-bed flood is proposed involving (i) a (convection-dominate) tracer slug injection, (ii) a shut in to allow the slug to spread by diffusion and, finally, (iii) a postflush of the tracer slug by tracer-free solvent. The effluent profile from this sequence can be compared with a profile where no diffusive step [stage (ii)] was present. The difference in the effluents-the diffusive case. will be more spread out in time-is purely due to the effects of molecular diffusion within the porous medium. The flood sequence is described by the convection-dispersion equation in stages (i) and (iii) and by the diffusion equation for stage (ii). Green's function propagator and anaIytica1 solutions for each step in the above process are well known for certain boundary conditions. We apply Green's function method to propagate the solution through each stage of the process using the final solution to the previous stage as the initial conditions for the next. The final expression for the effluent profile is complex but can easily be evaluated in closed form, and we have confirmed this by comparison with numerical results. The method is applied to sample experimental tracer effluent results in order to evaluate D, of chloride within a sand pack. This comparison showed that a reasonable match to the effluent was found for D, x 0.75Do. INTRODUCI-ION Because of the influence of both diffusion and disoersion on miscible displacement processes in porous rocks, these phenomena are of interest in the oil industry (
On the effective diffusivity under chemical reaction in porous media
Chemical Engineering Science, 2010
This paper addresses the question of whether effective diffusivities in porous materials under reactive and nonreactive conditions are equal. Previous studies have considered the problem with first-order reactions, suggesting that the effective diffusivity is unaffected by the reaction mechanisms. However, these studies were made under the assumption of heterogeneous reaction (i.e., the reaction takes place on the solid surface). In contrast to such studies, the present work shows that the effective diffusivity is affected by homogeneous reaction (i.e., the reaction takes place in the fluid phase bulk). The results, obtained from volume-averaging methods for first-order kinetics, show that the effective diffusivity is an increasing function of the Thiele modulus.
The Canadian Journal of Chemical Engineering, 1986
The diffusion coefficient of benzoic acid in water at 25°C has been measured as a function of concentration using the Taylor dispersion technique. The diffusion coefficient was found to decrease from 1.25 x lo-' m'/s to I .07 x lo-' m'/s when the concentration increased from 0.27 mol/m' to 5.44 mol/m3. Two different models describing the concentration dependence of the diffusion coefficient have been develo d. They are fitted to the measured data and experimental data from literature at infinite dilution (D = I .57 X 10-m'/s) and at higher concentrations up to 20 mol/mg (D = 0.75 X m'/s). The significance of the concentration dependence is evaluated by measurement and by computer simulations of liquid-solid mass transfer in a tube. The simulations show that 0.80 X m'/s is the constant diffusivity that gives the best approximation in dissolution studies.
Geofluids
In order to investigate in more detail the relation between the size of diffusing molecules and their diffusion coefficients (and geometric factors), diffusion experiments with gases of different size and tritiated water (HTO) have been performed on different clayey samples (Boom Clay, Eigenbilzen Sands, Opalinus Clay, Callovo-Oxfordian Clay, and bentonite with different dry densities). We observed that, for unreactive gases in clayey materials, the effective diffusion coefficient varies with the size of the diffusing molecule and this variation can be described by an exponential or a power law function. The variation of the geometric factor can also be described by an exponential function. The observed experimental relations can be used to estimate diffusion coefficients; by measuring experimentally in clay the effective diffusion coefficient of two unreactive dissolved gases with a different size, the diffusion coefficients of other dissolved gases (with a size in between the two ...
Chemical Engineering Science, 1995
A simple theory is derived for predicting multicomponent diffusion on solid surfaces and in molecular sieves with energetic heterogeneity. The energetic heterogeneity is represented by the uniform energy distribution and the equilibrium adsorption is assumed to follow the Langmuirian behavior. Multicomponent Fickian diffusivities can be predicted from pure-component Fickian diffusivities. The required information for the calculation includes the concentration-dependent pure-component diffusivities and the pure-component adsorption isotherms. The effects of the energetic heterogeneity can be significant, depending on the mutual direction of diffusion (co-diffusion or counter-diffusion), the initial and final surface coverages, and the relative diffusivities of the components. The effects of heterogeneity are stronger on the faster diffusing component. The effect of heterogeneity becomes stronger as the total surface coverage increases. The theory compares favorably with the available experimental data.
The Effect of Molecular Weight on the Rate of Diffusion
The effect of molecular weight on the rate of diffusion was verified using two kinds of test; the glass tube test and the agarwater gel test. Two cottons were moistened with two different substances, HCl and ammonium hydroxide NH 4 OH, and then were simultaneously placed at the end of the glass tube set-up. The ammonium (NH 3(g) ) diffused at a faster rate compared to hydrochloric acid (HCl (g) ) then the reaction between substances formed a white ring smoke, ammonium chloride (NH 4 Cl (s) ), that is near the hydrochloric acid (HCl). In the agar-water gel test, 3 kinds of different substances, namely KMnO4, K2Cr2O7 and methylene blue, were dropped into three wells with the same amount. Methylene blue, having the largest molecular weight between the three, exhibited the smallest diameter meaning it had the slowest rate of diffusion. Thus, when a substance has higher molecular weight it will have a slower rate compared to other substances.