scholarly journals Comparison of Sr Transport in Compacted Homoionous Na and Ca Bentonite Using a Planar Source Method Evaluated at Ideal and Non-Ideal Boundary Condition

Water ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 1520
Author(s):  
Lucie Baborová ◽  
Eva Viglašová ◽  
Dušan Vopálka
Keyword(s):  
Diffusion Coefficient ◽  
Surface Diffusion ◽  
Effective Diffusion Coefficient ◽  
Effective Diffusion ◽  
Ideal Boundary ◽  
Batch Sorption ◽  
Compacted Bentonite ◽  
Source Method ◽  
Planar Source ◽  
And Diffusion

With the aim to determine the influence of dominant interlayer cation on the sorption and diffusion properties of bentonite, diffusion experiments with Sr on the compacted homoionous Ca- and Na-forms of Czech natural Mg/Ca bentonite using the planar source method were performed. The bentonite was compacted to 1400 kg·m−3, and diffusion experiments lasted 1, 3 or 5 days. Two methods of apparent diffusion coefficient Da determination based on the analytical solution of diffusion equation for ideal boundary conditions in a linear form were compared and applied. The determined Da value for Ca-bentonite was 1.36 times higher than that for Na-bentonite sample. Values of Kd were determined in independent batch sorption experiments and were extrapolated for the conditions of compacted bentonite. In spite of this treatment, the use of Kd values determined by batch sorption experiments on a loose material for the determination of effective diffusion coefficient De values from planar source diffusion experiments proved to be inconsistent with the standard Fickian description of diffusion taking into account only the pore diffusion in compacted bentonite. Discrepancies between Kd and De values were measured in independent experiments, and those that resulted from the evaluation of planar source diffusion experiments could be well explained by the phenomenon of surface diffusion. The obtained values of surface diffusion coefficients Ds were similar for both studied systems, and the predicted value of total effective diffusion coefficient De(tot) describing Sr transport in the Na-bentonite was four times higher than in the Ca-bentonite.

Augmented Diffusion in Flowing Blood

1975 ◽  
Vol 97 (1) ◽  
pp. 58-60 ◽  
Author(s):  
W. A. Hyman
Keyword(s):  
Diffusion Coefficient ◽  
Shear Rate ◽  
Effective Diffusion Coefficient ◽  
Effective Diffusion ◽  
Simultaneous Action ◽  
Brownian Diffusion ◽  
Cell Rotation ◽  
Flowing Blood ◽  
Linear Addition ◽  
And Diffusion

An analysis of the simultaneous action of Brownian diffusion and diffusion induced by red blood cell rotation is presented in order to illustrate the form of the combined effect of these two processes. The results indicate a nonlinear combination such that the effective diffusion coefficient is smaller than that obtained by linear addition of the separate processes. The dependence of the effective diffusion coefficient on shear rate is also obtained.

Diffusion of Heavy Oil in SiO2 Model Catalyst and FCC Catalyst

2012 ◽  
Vol 550-553 ◽  
pp. 158-163 ◽  
Author(s):  
Zi Yuan Liu ◽  
Sheng Li Chen ◽  
Peng Dong ◽  
Xiu Jun Ge
Keyword(s):  
Diffusion Coefficient ◽  
Pore Size ◽  
Effective Diffusion Coefficient ◽  
Pore Diameter ◽  
Effective Diffusion ◽  
Model Catalyst ◽  
Average Pore ◽  
Diffusion Factor ◽  
Fcc Catalyst ◽  
Fcc Catalysts

Through the measured effective diffusion coefficients of Dagang vacuum residue supercritical fluid extraction and fractionation (SFEF) fractions in FCC catalysts and SiO2model catalysts, the relation between pore size of catalyst and effective diffusion coefficient was researched and the restricted diffusion factor was calculated. The restricted diffusion factor in FCC catalysts is less than 1 and it is 1~2 times larger in catalyst with polystyrene (PS) template than in conventional FCC catalyst without template, indicating that the diffusion of SFEF fractions in the two FCC catalysts is restricted by the pore. When the average molecular diameter is less than 1.8 nm, the diffusion of SFEF fractions in SiO2model catalyst which average pore diameter larger than 5.6 nm is unrestricted. The diffusion is restricted in the catalyst pores of less than 8 nm for SFEF fractions which diameter more than 1.8 nm. The tortuosity factor of SiO2model catalyst is obtained to be 2.87, within the range of empirical value. The effective diffusion coefficient of the SFEF fractions in SiO2model catalyst is two orders of magnitude larger than that in FCC catalyst with the same average pore diameter. This indicate that besides the ratio of molecular diameter to the pore diameter λ, the effective diffusion coefficient is also closely related to the pore structure of catalyst. Because SiO2model catalyst has uniform pore size, the diffusion coefficient can be precisely correlated with pore size of catalyst, so it is a good model material for catalyst internal diffusion investigation.

scholarly journals Effective diffusion coefficient including the Marangoni effect

2018 ◽  
Vol 148 (13) ◽  
pp. 134906 ◽  
Author(s):  
Hiroyuki Kitahata ◽  
Natsuhiko Yoshinaga
Keyword(s):  
Diffusion Coefficient ◽  
Effective Diffusion Coefficient ◽  
Effective Diffusion ◽  
Marangoni Effect

scholarly journals Restricted diffusion of model sulfides over a NiMo/BK catalyst under hydrodesulfurization reaction conditions

RSC Advances ◽  
2017 ◽  
Vol 7 (70) ◽  
pp. 44340-44347 ◽  
Author(s):  
Huadong Wu ◽  
Aijun Duan ◽  
Zhen Zhao ◽  
Chunming Xu ◽  
Guiyuan Jiang ◽  
...  
Keyword(s):  
Diffusion Coefficient ◽  
Effective Diffusion Coefficient ◽  
Effective Diffusion ◽  
Molecular Size ◽  
Restricted Diffusion ◽  
Reaction Conditions ◽  
Effective Factors

The effective factors (η) of a NiMo/BK catalyst are greater than that of the traditional NiMo/Al2O3; the effective diffusion coefficient (De) decreases with the increasing molecular size of the model sulfides.

scholarly journals Characterization of Effective Diffusion within Viscoelastic Fluids with Elastic Instabilities

Fluids ◽  
2022 ◽  
Vol 7 (1) ◽  
pp. 33
Author(s):  
Valerie Hietsch ◽  
Phil Ligrani ◽  
Mengying Su
Keyword(s):  
Diffusion Coefficient ◽  
Couette Flow ◽  
Effective Diffusion Coefficient ◽  
Effective Diffusion ◽  
Flow Shear ◽  
Shear Rates ◽  
Flow Environment ◽  
Disk Rotation ◽  
Elastic Instabilities ◽  
Fluorescein Dye

We considered effective diffusion, characterized by magnitudes of effective diffusion coefficients, in order to quantify mass transport due to the onset and development of elastic instabilities. Effective diffusion coefficient magnitudes were determined using different analytic approaches, as they were applied to tracked visualizations of fluorescein dye front variations, as circumferential advection was imposed upon a flow environment produced using a rotating Couette flow arrangement. Effective diffusion coefficient results were provided for a range of flow shear rates, which were produced using different Couette flow rotation speeds and two different flow environment fluid depths. To visualize the flow behavior within the rotating Couette flow environment, minute amounts of fluorescein dye were injected into the center of the flow container using a syringe pump. This dye was then redistributed within the flow by radial diffusion only when no disk rotation was used, and by radial diffusion and by circumferential advection when disk rotation was present. Associated effective diffusion coefficient values, for the latter arrangement, were compared to coefficients values with no disk rotation, which were due to molecular diffusion alone, in order to quantify enhancements due to elastic instabilities. Experiments were conducted using viscoelastic fluids, which were based on a 65% sucrose solution, with different polymer concentrations ranging from 0 ppm to 300 ppm. Associated Reynolds numbers based on the fluid depth and radially averaged maximum flow velocity ranged from 0.00 to 0.5. The resulting effective diffusion coefficient values for different flow shear rates and polymer concentrations quantified the onset of elastic instabilities, as well as significant and dramatic changes to local mass transport magnitudes, which are associated with the further development of elastic instabilities.

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