High-Dilution Diffusion of K + , Rb + , Cs + , and Tl + in the Molten System (Li-K)NOs Studied by Wave-Front-Shearing Interferometry

1979 ◽  
Vol 34 (4) ◽  
pp. 504-509 ◽  
Author(s):  
Osamu Odawara ◽  
Isao Okada ◽  
Kazutaka Kawamura
Keyword(s):  
Diffusion Coefficient ◽  
Wave Front ◽  
Diffusion Coefficients ◽  
Free Space ◽  
Experimental Error ◽  
Positive Deviation ◽  
High Dilution ◽  
Ionic Radii ◽  
Shearing Interferometry ◽  
Wide Range

The high-dilution diffusion coefficients of K+, Rb+, Cs+, and Tl+ in molten LiNO3-KNO3 mixtures are measured over a wide range of temperatures and concentrations by means of wavefront- shearing interferometry. A slightly positive deviation from linearity is found for the concentration dependence of the diffusion coefficient of K+ , Rb+, and Tl+, while no deviation is found for Cs+ within the experimental error. This is qualitatively discussed from the viewpoint of the ionic radii, the free space in the solvent, and the interaction between the diffusing and the surrounding ions

High-Dilution Diffusion of Tl+ in Molten NaNO3, KNO3 and RbNO3 Studied by Wave-Front-Shearing Interferometry

1978 ◽  
Vol 33 (4) ◽  
pp. 447-454
Author(s):  
Isao Okada ◽  
Silas E. Gustafsson
Keyword(s):  
Diffusion Coefficient ◽  
Wave Front ◽  
Interdiffusion Coefficient ◽  
Ionic Radius ◽  
Diffusion Rate ◽  
High Dilution ◽  
Shearing Interferometry ◽  
Low Concentrations

The high-dilution diffusion of Tl+ in molten NaNO3 , KNO3 and RbNO3 has been measured with wave-front-shearing interferometry. For very low concentrations of TlNO3 the results areD = 6.21×10-8 exp [-(18400± 800)/RT] in NaNO3 (316-387 °C),D = 5.39×10-8 exp [-(18800±1400)/RT] in KNO3 (341-408 °C),D = 1.87×10-7 exp [-(25800±2200)JRT] in RbNO3 (327-419°C),where D is the diffusion coefficient in m2 s-1, R the gas constant in J K-1 mol-1 and T the temperature in K. Comparisons are made with high-dilution diffusion of Na+, K+, Rb+, Cs+ and Ag+ ions in alkali nitrates, and it is found that both Ag+ and Tl+ diffuse faster than expected if the mass and the ionic radius were the sole parameters of importance, i. e. other parameters such as the polarizability also have an influence on the diffusion rate of an ion. For the system NaNO3 - TlNO3 , the interdiffusion coefficient has also been measured at 88.8, 73.8, 51.5 and 31.6 mol % NaNO3 .

Mutual Diffusion Coefficients for the Systems HD–N2 and HD–Ar at 1 atm Pressure and 300 K

1973 ◽  
Vol 51 (19) ◽  
pp. 2101-2107 ◽  
Author(s):  
K. R. Harris ◽  
T. N. Bell
Keyword(s):  
Diffusion Coefficient ◽  
Diffusion Coefficients ◽  
Experimental Error ◽  
Mutual Diffusion ◽  
Intermolecular Potentials ◽  
Mass Effects

Mutual diffusion coefficients, D12, have been measured as a function of concentration for the systems HD–N2 and HD–Ar at 1 atm pressure and 300 K. The data are compared with previously published measurements for the corresponding H2 and D2 containing systems. After the estimated uncertainties due to experimental error and impurities, and corrections due to quantum and mass effects are taken into account, the mass corrected diffusion coefficient, [Formula: see text], for each system is found to lie above those of the corresponding H2 and D2 systems by up to 2%. These effects are attributed to differences in the intermolecular potentials of H2, D2, and HD.

Effect of moisture content and soil type on self diffusion of 86Rb in soils

1963 ◽  
Vol 60 (2) ◽  
pp. 239-244 ◽  
Author(s):  
I. J. Graham-Bryce
Keyword(s):  
Diffusion Coefficient ◽  
Moisture Content ◽  
Diffusion Coefficients ◽  
Pore Space ◽  
Considerable Effect ◽  
The Self ◽  
Self Diffusion ◽  
Moisture Contents ◽  
Wide Range ◽  
Self Diffusion Coefficient

Self-diffusion coefficients (D) for Rb+ have been measured in a heteroionic Lower Greensand soil over a wide range of moisture contents at three different compactions. The moisture content is shown to have a considerable effect on the value of the self-diffusion coefficient, a rapid rise in the value of D taking place between 5 and 10% moisture content. It is shown that this effect is not simply due to the increased volume of water-filled pore space at higher moisture contents, and other possible factors which could influence the shape of the diffusion coefficient/moisture content curve are discussed. Diffusion coefficients for Rb+ in eight other soils at pF 2 are also reported, but no simple correlation with any of several soil properties measured could be found. A value of 1·0 × 10−7cm2/sec. would seem to be a reasonable generalization for the self-diffusion coefficient of Rb+ in moist calcium-dominated soils.

How to Measure Diffusion Coefficients in Biofilms: A Critical Analysis

2020 ◽  
Author(s):  
Lenno van den Berg ◽  
Mark van Loosdrecht ◽  
Merle de Kreuk
Keyword(s):  
Monte Carlo ◽  
Diffusion Coefficient ◽  
Diffusion Coefficients ◽  
Effective Diffusion ◽  
Granular Sludge ◽  
Monte Carlo Analysis ◽  
Propagation Of Uncertainty ◽  
Relative Standard ◽  
Wide Range

<p>Effective diffusion coefficients are often required for kinetic descriptions of biofilms. Many previous studies have measured diffusion coefficients for specific molecule-biofilm combinations. As a result, many biofilm researchers today rely on literature values of diffusion coefficients for their own biofilm system. However, the reported diffusion coefficients in literature fall within a wide range, even for the same molecule. One potential cause of this range is the accuracy of the methods used to measure diffusion coefficients. The objective of this study was to determine the precision (similarity between repeated experiments) and bias (difference between measured and true diffusion coefficient) of six common methods. The six selected methods were based on determining mass balances and on microelectrode measurements. The precision and bias were quantified based on mathematical models of the six methods, with oxygen diffusion in granular sludge as a case study. The precision was assessed by a Monte Carlo uncertainty analysis, which considers the propagation of uncertainty in the input experimental parameters. The bias was determined for six potential sources of error: solute sorption, biomass deactivation, a concentration boundary layer, granule roughness, granule shape, and granule size distribution. From the Monte Carlo analysis, it followed that the precision of the methods ranged from 4-77% relative standard deviation. The microelectrode methods were more accurate than the mass balance methods. The bias due to the combined effect of the six errors was an underestimation of the diffusion coefficient by 74%. This shows that current methods are unable to accurately determine diffusion coefficients. We do not propose improvements to the current methods, but instead discuss why inaccurate diffusion coefficients are sufficient for accurate engineering of biofilm processes. </p>

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.

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.

Diffusion of Zinc in Two-Phase Mg-Al Alloy

2007 ◽  
Vol 263 ◽  
pp. 189-194
Author(s):  
Ivo Stloukal ◽  
Jiří Čermák
Keyword(s):  
Diffusion Coefficient ◽  
Diffusion Coefficients ◽  
Effective Diffusion ◽  
Residual Activity ◽  
Diffusion Path ◽  
Al Alloy ◽  
Serial Sectioning ◽  
Two Phase ◽  
Interphase Boundaries ◽  
The Mean

Coefficient of 65Zn heterodiffusion in Mg17Al12 intermetallic and in eutectic alloy Mg - 33.4 wt. % Al was measured in the temperature region 598 – 698 K using serial sectioning and residual activity methods. Diffusion coefficient of 65Zn in the intermetallic can be written as DI = 1.7 × 10-2 m2 s-1 exp (-155.0 kJ mol-1 / RT). At temperatures T ≥ 648 K, where the mean diffusion path was greater than the mean interlamellar distance in the eutectic, the effective diffusion coefficient Def = 2.7 × 10-2 m2 s-1 exp (-155.1 kJ mol-1 / RT) was evaluated. At two lower temperatures, the diffusion coefficients 65Zn in interphase boundaries were estimated: Db (623 K) = 1.6 × 10-12 m2 s-1 and Db (598 K) = 4.4 × 10-13 m2 s-1.

Molten Slag Structure and Diffusion Coefficients of Cr3+ and Si4+ during Micro-Carbon Cr-Fe Alloy Production

2011 ◽  
Vol 79 ◽  
pp. 77-82
Author(s):  
Yi Min ◽  
Jian Huang ◽  
Cheng Jun Liu ◽  
Mao Fa Jiang
Keyword(s):  
Diffusion Coefficient ◽  
Diffusion Coefficients ◽  
Molten Slag ◽  
Optimization Method ◽  
Structure Theory ◽  
Average Diffusion Coefficient ◽  
Slag Structure ◽  
Initial Stage ◽  
Silicate Structure ◽  
Average Diffusion

Based on the silicate structure theory, the molten slag structure and the existential state of and during micro-carbon Cr-Fe alloy production process were analysised, and then their diffusion coefficients were calculated. The results showed that, during the initial stage, the average diffusion coeffecient of and is close to the , the reaction process is controlled by the diffusion of () and corporately, during the later stage, the diffusion coefficient of is less than average diffusion coefficient of and , the controlling step is the diffusion of . According to the evolution of diffusion coefficient, molten slag composition optimization method was advised to increase the diffusion ability of and for enhancing the reaction efficiency and the recovery rate of chromium.

Induced polarization and pore radius — A discussion

Geophysics ◽  
2016 ◽  
Vol 81 (5) ◽  
pp. D519-D526 ◽  
Author(s):  
Andreas Weller ◽  
Zeyu Zhang ◽  
Lee Slater ◽  
Sabine Kruschwitz ◽  
Matthias Halisch
Keyword(s):  
Diffusion Coefficient ◽  
Relaxation Time ◽  
Diffusion Coefficients ◽  
Pore Radius ◽  
Mercury Porosimetry ◽  
Induced Polarization ◽  
Reliable Estimate ◽  
Characteristic Relaxation Time ◽  
A Value ◽  
Apparent Diffusion

Permeability estimation from induced polarization (IP) measurements is based on a fundamental premise that the characteristic relaxation time [Formula: see text] is related to the effective hydraulic radius [Formula: see text] controlling fluid flow. The approach requires a reliable estimate of the diffusion coefficient of the ions in the electrical double layer. Others have assumed a value for the diffusion coefficient, or postulated different values for clay versus clay-free rocks. We have examined the link between a widely used single estimate of [Formula: see text] and [Formula: see text] for an extensive database of sandstone samples, in which mercury porosimetry data confirm that [Formula: see text] is reliably determined from a modification of the Hagen-Poiseuille equation assuming that the electrical tortuosity is equal to the hydraulic tortuosity. Our database does not support the existence of one or two distinct representative diffusion coefficients but instead demonstrates strong evidence for six orders of magnitude of variation in an apparent diffusion coefficient that is well-correlated with [Formula: see text] and the specific surface area per unit pore volume [Formula: see text]. Two scenarios can explain our findings: (1) the length scale defined by [Formula: see text] is not equal to [Formula: see text] and is likely much longer due to the control of pore-surface roughness or (2) the range of diffusion coefficients is large and likely determined by the relative proportions of the different minerals (e.g., silica and clays) making up the rock. In either case, the estimation of [Formula: see text] (and hence permeability) is inherently uncertain from a single characteristic IP relaxation time as considered in this study.

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