Relaxation time of substance concentration in a medium with an arbitrary space-varying diffusion coefficient

1997 ◽  
Vol 40 (7) ◽  
pp. 591-598
Author(s):  
A. N. Malakhov
Keyword(s):  
Diffusion Coefficient ◽  
Relaxation Time ◽  
Substance Concentration ◽  
Arbitrary Space

1H NMR characterisation of the diffusional properties of methanogenic granular sludge

1999 ◽  
Vol 39 (7) ◽  
pp. 187-194 ◽  
Author(s):  
P. Lens ◽  
F. Vergeldt ◽  
G. Lettinga ◽  
H. Van As
Keyword(s):  
Diffusion Coefficient ◽  
Relaxation Time ◽  
Bacterial Cell ◽  
Granular Sludge ◽  
T2 Relaxation ◽  
Self Diffusion ◽  
Diffusion Analysis ◽  
S Matrix ◽  
Granular Matrix ◽  
Pfg Nmr

The diffusive properties of mesophilic methanogenic granular sludge have been studied using diffusion analysis by relaxation time separated pulsed field gradient nuclear magnetic resonance (DARTS PFG NMR) spectroscopy. NMR measurements were performed at 22°C with 10 ml granular sludge at a magnetic field strength of 0.5 T (20 MHz resonance frequency for protons). Spin-spin relaxation (T2) time measurements indicate that three 1H populations can be distinguished in methanogenic granular sludge beds, corresponding to water in three different environments. The T2 relaxation time measurements clearly differentiate the extragranular water (T2 ≈ 1000 ms) from the water present in the granular matrix (T2 = 40-100 ms) and bacterial cell associated water (T2 = 10-15 ms). Self-diffusion coefficient measurements at 22°C of the different 1H-water populations as the tracer show that methanogenic granular sludge does not contain one unique diffusion coefficient. The observed distribution of self-diffusion coefficients varies between 1.1 × 10−9 m2/s (bacterial cell associated water) and 2.1 × 10−9 m2/s (matrix associated water).

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.

Changes in the apparent diffusion coefficient of water and T2 relaxation time in gerbil hippocampus after mild ischemia

Neuroreport ◽  
2000 ◽  
Vol 11 (15) ◽  
pp. 3333-3336 ◽  
Author(s):  
Lidong Zhu ◽  
Nobuhito Saito ◽  
Osamu Abe ◽  
Toshiyuki Okubo ◽  
Haruyasu Yamada ◽  
...  
Keyword(s):  
Diffusion Coefficient ◽  
Relaxation Time ◽  
Apparent Diffusion Coefficient ◽  
T2 Relaxation Time ◽  
T2 Relaxation ◽  
Apparent Diffusion

scholarly journals Diffusional Properties of Methanogenic Granular Sludge: 1H NMR Characterization

2003 ◽  
Vol 69 (11) ◽  
pp. 6644-6649 ◽  
Author(s):  
Piet N. L. Lens ◽  
Rakel Gastesi ◽  
Frank Vergeldt ◽  
Adriaan C. van Aelst ◽  
Antonio G. Pisabarro ◽  
...  
Keyword(s):  
Diffusion Coefficient ◽  
Relaxation Time ◽  
Nmr Spectroscopy ◽  
Diffusion Coefficients ◽  
Metal Sulfide ◽  
Free Water ◽  
Granular Sludge ◽  
Self Diffusion ◽  
Nmr Characterization ◽  
Self Diffusion Coefficient

ABSTRACT The diffusive properties of anaerobic methanogenic and sulfidogenic aggregates present in wastewater treatment bioreactors were studied using diffusion analysis by relaxation time-separated pulsed-field gradient nuclear magnetic resonance (NMR) spectroscopy and NMR imaging. NMR spectroscopy measurements were performed at 22°C with 10 ml of granular sludge at a magnetic field strength of 0.5 T (20 MHz resonance frequency for protons). Self-diffusion coefficients of H2O in the investigated series of mesophilic aggregates were found to be 51 to 78% lower than the self-diffusion coefficient of free water. Interestingly, self-diffusion coefficients of H2O were independent of the aggregate size for the size fractions investigated. Diffusional transport occurred faster in aggregates growing under nutrient-rich conditions (e.g., the bottom of a reactor) or at high (55°C) temperatures than in aggregates cultivated in nutrient-poor conditions or at low (10°C) temperatures. Exposure of aggregates to 2.5% glutaraldehyde or heat (70 or 90°C for 30 min) modified the diffusional transport up to 20%. In contrast, deactivation of aggregates by HgCl2 did not affect the H2O self-diffusion coefficient in aggregates. Analysis of NMR images of a single aggregate shows that methanogenic aggregates possess a spin-spin relaxation time and self-diffusion coefficient distribution, which are due to both physical (porosity) and chemical (metal sulfide precipitates) factors.

Relaxation behaviors of star polymers in the grid model

2021 ◽  
pp. 2150105
Author(s):  
Xu-Chen Yu ◽  
Ji-Xuan Hou
Keyword(s):  
Diffusion Coefficient ◽  
Relaxation Time ◽  
Star Polymers ◽  
Branch Length ◽  
Linear Polymer ◽  
Star Polymer ◽  
Grid Model ◽  
Dynamical Simulation ◽  
Qualitative Prediction

The tube theory has made a detailed description for the linear polymer entangled system, while the behavior of entangled star polymers is still determined by a qualitative prediction. In this paper, the dynamical simulation of a three-arms star polymer in the grid model is presented. We record the diffusion coefficient [Formula: see text], the relaxation time for the arms of star polymer [Formula: see text] and some other parameters corresponding to different branch length. Therefore, results that are inconsistent with the theoretical begin to emerge.

scholarly journals Analysis of Transport Properties of the Randomly Moving Electrons in Metals

2019 ◽  
Vol 26 (2) ◽  
pp. 147-153
Author(s):  
Villius PALENSKIS ◽  
Evaras ŽITKEVIČIUS
Keyword(s):  
Diffusion Coefficient ◽  
Relaxation Time ◽  
Free Path ◽  
Mean Free Path ◽  
Periodic Lattice ◽  
Simple Method ◽  
Temperature Range ◽  
Average Diffusion Coefficient ◽  
Average Diffusion ◽  
Average Relaxation Time

In this critical analysis on the base of randomly moving (RM) electrons, presented the resistivity dependence on temperature for elemental metals both above and below the Debye’s temperatures. There also are presented the general relationships for estimation of the average diffusion coefficient, the average velocity, mean free path and average relaxation time of RM electrons on the Fermi surface at mentioned temperature range. It is shown that the scattering of RM electrons mainly is due to electronic defects associated with distortion of the periodic potential distribution in the periodic lattice, and accounting the exchange of the thermal energies between phonon and RM electron. The calculation results of resistivity dependence on temperature in the temperature range from 1 K to 900 K are demonstrated for Au and W and compared with the experimental data. There also is presented the simple method for determination of the basic kinetic characteristic dependences on temperature only from the resistivity dependence on temperature. It is at first time determined for Au and W the temperature dependences of the mean free path, average diffusion coefficient, average relaxation time of RM electrons from 1 K to 900 K.

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