Time-Dependent Non-Steady-State Diffusivities of C6 Paraffins in Silicalite by Zero-Length Column Method

1992 ◽  
Vol 57 (4) ◽  
pp. 698-709 ◽  
Author(s):  
Daniel Shavit ◽  
Patrick Voogd ◽  
Herman W. Kouwenhoven
Keyword(s):  
Diffusion Coefficient ◽  
Diffusion Coefficients ◽  
Reasonable Agreement ◽  
Time Dependent ◽  
Fast Diffusion ◽  
Diffusion Anisotropy ◽  
Zeolite Lattice ◽  
Column Method ◽  
Linear Isotherm ◽  
Long Time

Long-time diffusion experiments of n-hexane, 2-methylpentane and 2,3-dimethylbutane in silicalite according to the zero-length column method showed a significant decrease of the diffusion coefficients for longer times. A new and simple model of "uncoupled dual diffusion" is proposed to fit the experimental data. The calculated fast-diffusion coefficients as well as the calculated mean activation energies of diffusion of n-hexane and 2-methylpentane were almost equal and in reasonable agreement with literature data. A decrease of the adsorption partial pressure from 5.5 to 0.6 Torr did not have any influence on the fast-diffusion coefficient of n-hexane, which implies that the decrease of the diffusion coefficient in this range is not simply due to a non-linear isotherm. The proposed dual diffusion model may represent effects such as the presence of multiple energy states available for adsorbed molecules in the zeolite lattice, and/or diffusion anisotropy due to differences in the channel configurations in the three crystallografic directions.

scholarly journals Time-Dependent Diffusion Coefficients for Chaotic Advection due to Fluctuations of Convective Rolls

Fluids ◽  
2018 ◽  
Vol 3 (4) ◽  
pp. 99 ◽  
Author(s):  
Kazuma Yamanaka ◽  
Takayuki Narumi ◽  
Megumi Hashiguchi ◽  
Hirotaka Okabe ◽  
Kazuhiro Hara ◽  
...  
Keyword(s):  
Diffusion Coefficient ◽  
Liquid Crystals ◽  
Diffusion Coefficients ◽  
Coarse Graining ◽  
Chaotic Advection ◽  
Time Dependent ◽  
Local Order ◽  
Weak Turbulence ◽  
Normal Diffusion ◽  
Convective Rolls

The properties of chaotic advection arising from defect turbulence, that is, weak turbulence in the electroconvection of nematic liquid crystals, were experimentally investigated. Defect turbulence is a phenomenon in which fluctuations of convective rolls arise and are globally disturbed while maintaining convective rolls locally. The time-dependent diffusion coefficient, as measured from the motion of a tagged particle driven by the turbulence, was used to clarify the dependence of the type of diffusion on coarse-graining time. The results showed that, as coarse-graining time increases, the type of diffusion changes from superdiffusion → subdiffusion → normal diffusion. The change in diffusive properties over the observed timescale reflects the coexistence of local order and global disorder in the defect turbulence.

scholarly journals The Effect of Particle Drag and Wall Absorption on Mass Transfer in Concentric Annulus Flows

2011 ◽  
Vol 10 (1) ◽  
pp. 1-13
Author(s):  
B. Umadevi ◽  
Dinesh P.A. ◽  
Indira R. Rao ◽  
Vinay C.V.
Keyword(s):  
Mass Transfer ◽  
Diffusion Coefficient ◽  
Diffusion Coefficients ◽  
Dispersion Model ◽  
Transport Coefficients ◽  
Time Dependent ◽  
Exchange Coefficient ◽  
Concentric Annulus ◽  
Annular Gap ◽  
And Diffusion

The effects of the irreversible boundary reaction and the particle drag on mass transfer are studied analytically in concentric annulus flows. The solution of mathematical model, based on the generalized dispersion model brings out the mass transport following by the insertion of catheter on an artery in terms of the three effective transport coefficients, viz., the exchange, convection and diffusion coefficient. A general expression is derived which shows clearly the time dependent nature of the coefficients in the dispersive model. The complete time dependent expression for the exchange coefficient is obtained explicitly and independent of velocity distribution in the flow; however it does depend on the initial solute distribution. Because of the complexity of the problem only asymptotic large time evaluations are made for the convective and diffusion coefficients, but these are sufficient to give the physical insight into the nature of the problem of the effects of drag and absorption parameters. It is found that as absorption parameter increases exchange and convection coefficients will be enhanced, but diffusion coefficient will be reduced. After certain period of time exchange coefficient will be constant for different values annular gap. As the drag parameter increases convection and diffusion coefficients will be reduced. With the enhancement of catheter radius i.e., the annular gap will be reduced then the convection and diffusion coefficients will be decreased.

scholarly journals The Influence of Sorption Pressure on Gas Diffusion in Coal Particles: An Experimental Study

Processes ◽  
2019 ◽  
Vol 7 (4) ◽  
pp. 219 ◽  
Author(s):  
Yang ◽  
Wang ◽  
Zhang ◽  
Ren
Keyword(s):  
Diffusion Coefficient ◽  
Diffusion Coefficients ◽  
Gas Diffusion ◽  
Gas Pressure ◽  
Fast Diffusion ◽  
Pore Characteristic ◽  
Coal Particles ◽  
Pore Size Distributions ◽  
Coal Ranks ◽  
And Diffusion

Gas pressure changes during the process of coal mine gas drainage and CBM recovery. It is of great importance to understand the influence of sorption pressure on gas diffusion; however, the topic remains controversial in past studies. In this study, four samples with different coal ranks were collected and diffusion experiments were conducted under different pressures through the adsorption and desorption processes. Three widely used models, i.e., the unipore diffusion (UD) model, the bidisperse diffusion (BD) model and the dispersive diffusion (DD) model, were adopted to compare the applicability and to calculate the diffusion coefficients. Results show that for all coal ranks, the BD model and DD model can match the experimental results better than the UD model. Concerning the fast diffusion coefficient Dae of the BD model, three samples display a decreasing trend with increasing gas pressure while the other sample shows a V-type trend. The slow diffusion coefficient Die of BD model increases with gas pressure for all samples, while the ratio β is an intrinsic character of coal and remains constant. For the DD model, the characteristic rate parameter kΦ does not change sharply and the stretching parameter α increases with gas pressure. Both Dae and Die are in proportion to kΦ, which reflect the diffusion rate of gas in the coal. The impacts of pore characteristic on gas diffusion were also analyzed. Although pore size distributions and specific surface areas are different in the four coal samples, correlations are not apparent between pore characteristic and diffusion coefficients.

Diffusion coefficients of elastic macromolecules

2019 ◽  
Vol 878 ◽  
Author(s):  
Bogdan Cichocki ◽  
Marcin Rubin ◽  
Anna Niedzwiecka ◽  
Piotr Szymczak
Keyword(s):  
Diffusion Coefficient ◽  
Diffusion Coefficients ◽  
Reference Point ◽  
Brownian Dynamics ◽  
The Other ◽  
Long Time ◽  
Computationally Expensive ◽  
Dynamics Simulations ◽  
Brownian Dynamics Simulations ◽  
Short Time

In elastic macromolecules, the value of the short-time diffusion coefficient depends on the choice of the point the displacement of which is tracked. On the other hand, the experimentally more relevant long-time diffusion coefficient is independent of the reference point, but its estimation usually requires computationally expensive Brownian dynamics simulations. Here we show how to obtain a precise estimate of the long-time diffusion coefficient of elastic macromolecules in a fast and robust manner, without invoking Brownian dynamics.

scholarly journals Prediction of Time-Dependent Chloride Diffusion Coefficients for Slag-Blended Concrete

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Ki-Bong Park ◽  
Han-Seung Lee ◽  
Xiao-Yong Wang
Keyword(s):  
Diffusion Coefficient ◽  
Diffusion Coefficients ◽  
Blended Cement ◽  
Numerical Procedure ◽  
Time Dependent ◽  
Chloride Diffusion ◽  
Chloride Diffusion Coefficient ◽  
Capillary Porosity ◽  
Key Factor ◽  
Hydration Model

The chloride diffusion coefficient is considered to be a key factor for evaluating the service life of ground-granulated blast-furnace slag (GGBS) blended concrete. The chloride diffusion coefficient relates to both the concrete mixing proportions and curing ages. Due to the continuous hydration of the binders, the capillary porosity of the concrete decreases and the chloride diffusion coefficient also decreases over time. To date, the dependence of chloride diffusivity on the binder hydration and curing ages of slag-blended concrete has not been considered in detail. To fill this gap, this study presents a numerical procedure to predict time-dependent chloride diffusion coefficients for slag-blended concrete. First, by using a blended cement hydration model, the degree of the binder reaction for hardening concrete can be calculated. The effects of the water to binder ratios and slag replacement ratios on the degree of the binder reaction are considered. Second, by using the degree of the binder reaction, the capillary porosity of the binder paste at different curing ages can be determined. Third, by using the capillary porosity and aggregate volume, the chloride diffusion coefficients of concrete can be calculated. The proposed numerical procedure has been verified using the experimental results of concrete with different water to binder ratios, slag replacement ratios, and curing ages.

Diffusion in Very Dilute Zr-Fe Alloys

2009 ◽  
Vol 283-286 ◽  
pp. 128-132
Author(s):  
Rodolfo A. Pérez
Keyword(s):  
Diffusion Coefficient ◽  
Diffusion Process ◽  
Ab Initio Calculations ◽  
Diffusion Coefficients ◽  
Fast Diffusion ◽  
Self Diffusion ◽  
Diffusion Enhancement ◽  
Fe Alloys ◽  
Theoretical Results ◽  
Made In

The diffusion process in hcp Zr with low amounts of Fe being in solution or forming very dilute Zr-Fe alloys is analysed and discussed. The enhancement of the diffusion coefficient in alloys with increasing amounts of Fe is studied using both experimental and theoretical results. In contraposition with the assumption made in the literature that the Fe in solution in the hcp Zr lattice is the responsible, this enhancement seems to be more related with the total amount of Fe present in the samples. This idea is supported by measurements of Au diffusion in Zr with 50 to 150 gr/gr of Fe which shows increments in the diffusion coefficients even at the lower temperatures where the reported Fe solubility in -Zr is negligible. Ab initio calculations using SIESTA and WIEN2k codes show several stable and meta-stable configurations for the Fe in the hcp Zr lattice in interstitial and off-centre positions, resembling the last ones a Zr3Fe like arrangement. These configurations are used in order to analyze the mechanism of both, self-diffusion enhancement and ultra-fast diffusion of Fe in -Zr.

scholarly journals Effect of Modification on the Fluid Diffusion Coefficient in Silica Nanochannels

Molecules ◽  
2021 ◽  
Vol 26 (13) ◽  
pp. 4030
Author(s):  
Gengbiao Chen ◽  
Zhiwen Liu
Keyword(s):  
Diffusion Coefficient ◽  
Diffusion Coefficients ◽  
Surface Effect ◽  
Bulk Water ◽  
Self Diffusion ◽  
Average Diffusion Coefficient ◽  
Average Diffusion ◽  
Chain Lengths ◽  
Fluid Diffusion ◽  
Self Diffusion Coefficient

The diffusion behavior of fluid water in nanochannels with hydroxylation of silica gel and silanization of different modified chain lengths was simulated by the equilibrium molecular dynamics method. The diffusion coefficient of fluid water was calculated by the Einstein method and the Green–Kubo method, so as to analyze the change rule between the modification degree of nanochannels and the diffusion coefficient of fluid water. The results showed that the diffusion coefficient of fluid water increased with the length of the modified chain. The average diffusion coefficient of fluid water in the hydroxylated nanochannels was 8.01% of the bulk water diffusion coefficient, and the diffusion coefficients of fluid water in the –(CH2)3CH3, –(CH2)7CH3, and –(CH2)11CH3 nanochannels were 44.10%, 49.72%, and 53.80% of the diffusion coefficients of bulk water, respectively. In the above four wall characteristic models, the diffusion coefficients in the z direction were smaller than those in the other directions. However, with an increase in the silylation degree, the increased self-diffusion coefficient due to the surface effect could basically offset the decreased self-diffusion coefficient owing to the scale effect. In the four nanochannels, when the local diffusion coefficient of fluid water was in the range of 8 Å close to the wall, Dz was greater than Dxy, and beyond the range of 8 Å of the wall, the Dz was smaller than Dxy.

Effect of Macropore Structure on Desorption Diffusion Performance of N-Pentane on 5A Zeolite

2013 ◽  
Vol 634-638 ◽  
pp. 731-735 ◽  
Author(s):  
Lu Shi ◽  
Zong Jian Liu ◽  
Qun Cui ◽  
Hai Yan Wang ◽  
Hu Qing Yao
Keyword(s):  
Diffusion Coefficients ◽  
Diffusion Rate ◽  
Low Pressure ◽  
Fast Diffusion ◽  
Desorption Rate ◽  
Macropore Structure ◽  
5A Zeolite ◽  
Desorption Equilibrium

Desorption rate curves of n-pentane on 5A zeolites at 418 K and 10-0.03 kPa were determined, and the effects of different macropore structure on desorption performance were analyzed. Results show that macropore distribution of 5A-1 concentrates in 0.25-1.25 μm, while that of 5A-2 ranges from mesopore category to 0.3 μm, but 5A-3 contains both pores of 0.01-0.1 μm and 0.2-2 μm inside, reflecting a broadest distribution; 5A-3, 5A-1 and 5A-2 reach desorption equilibrium after 1100 s, 1400 s and 2000 s respectively at 0.03 kPa, indicating that abundant macropores make n-pentane fastest desorbed from 5A-3, but this advantage gradually disappears with the increasing pressure; the effective desorption diffusion coefficients of n-pentane on 5A-1, 5A-2 and 5A-3 are 4.2×10-15-2.2×10-14 m2/s, 2.0×10-15-2.3×10-14 m2/s, 7.4×10-15-2.4×10-14 m2/s respectively, suggesting that plenty macropores make the diffusivity less affected by the changes of pressure, which can guarantee a fast diffusion rate of n-pentane even at low pressure.

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