Short-time behavior of the diffusion coefficient as a geometrical probe of porous media

1993 ◽  
Vol 47 (14) ◽  
pp. 8565-8574 ◽  
Author(s):  
Partha P. Mitra ◽  
Pabitra N. Sen ◽  
Lawrence M. Schwartz
Keyword(s):  
Porous Media ◽  
Diffusion Coefficient ◽  
Time Behavior ◽  
Short Time

scholarly journals Cusp of Non-Gaussian Density of Particles for a Diffusing Diffusivity Model

Entropy ◽  
2021 ◽  
Vol 23 (2) ◽  
pp. 231
Author(s):  
M. Hidalgo-Soria ◽  
E. Barkai ◽  
S. Burov
Keyword(s):  
Diffusion Coefficient ◽  
Initial Conditions ◽  
Waiting Times ◽  
Effective Diffusion ◽  
Time Behavior ◽  
Mean Values ◽  
Gaussian Density ◽  
Long Time ◽  
Non Gaussian ◽  
Short Time

We study a two state “jumping diffusivity” model for a Brownian process alternating between two different diffusion constants, D+>D−, with random waiting times in both states whose distribution is rather general. In the limit of long measurement times, Gaussian behavior with an effective diffusion coefficient is recovered. We show that, for equilibrium initial conditions and when the limit of the diffusion coefficient D−⟶0 is taken, the short time behavior leads to a cusp, namely a non-analytical behavior, in the distribution of the displacements P(x,t) for x⟶0. Visually this cusp, or tent-like shape, resembles similar behavior found in many experiments of diffusing particles in disordered environments, such as glassy systems and intracellular media. This general result depends only on the existence of finite mean values of the waiting times at the different states of the model. Gaussian statistics in the long time limit is achieved due to ergodicity and convergence of the distribution of the temporal occupation fraction in state D+ to a δ-function. The short time behavior of the same quantity converges to a uniform distribution, which leads to the non-analyticity in P(x,t). We demonstrate how super-statistical framework is a zeroth order short time expansion of P(x,t), in the number of transitions, that does not yield the cusp like shape. The latter, considered as the key feature of experiments in the field, is found with the first correction in perturbation theory.

Short time behavior and universal relations in polymer cyclization

1991 ◽  
Vol 1 (4) ◽  
pp. 471-486 ◽  
Author(s):  
Barry Friedman ◽  
Ben O'Shaughnessy
Keyword(s):  
Time Behavior ◽  
Short Time

PERMEABILITY AND DIFFUSION COEFFICIENT PREDICTION OF FRACTAL POROUS MEDIA WITH NANOSCALE PORES FOR GAS TRANSPORT

2018 ◽  
Vol 21 (12) ◽  
pp. 1253-1263
Author(s):  
Ruifei Wang ◽  
Hongqing Song ◽  
Jiulong Wang ◽  
Yuhe Wang
Keyword(s):  
Porous Media ◽  
Diffusion Coefficient ◽  
Gas Transport ◽  
And Diffusion

scholarly journals Experimental study of the supercritical CO 2 diffusion coefficient in porous media under reservoir conditions

2019 ◽  
Vol 6 (6) ◽  
pp. 181902 ◽  
Author(s):  
Junchen Lv ◽  
Yuan Chi ◽  
Changzhong Zhao ◽  
Yi Zhang ◽  
Hailin Mu
Keyword(s):  
Porous Media ◽  
Diffusion Coefficient ◽  
Oil Recovery ◽  
Carbon Capture ◽  
Carbon Capture And Storage ◽  
Elevated Pressure ◽  
Experimental Results ◽  
Saturated Porous Media ◽  
Reservoir Conditions ◽  
The Impact

Reliable measurement of the CO 2 diffusion coefficient in consolidated oil-saturated porous media is critical for the design and performance of CO 2 -enhanced oil recovery (EOR) and carbon capture and storage (CCS) projects. A thorough experimental investigation of the supercritical CO 2 diffusion in n -decane-saturated Berea cores with permeabilities of 50 and 100 mD was conducted in this study at elevated pressure (10–25 MPa) and temperature (333.15–373.15 K), which simulated actual reservoir conditions. The supercritical CO 2 diffusion coefficients in the Berea cores were calculated by a model appropriate for diffusion in porous media based on Fick's Law. The results show that the supercritical CO 2 diffusion coefficient increases as the pressure, temperature and permeability increase. The supercritical CO 2 diffusion coefficient first increases slowly at 10 MPa and then grows significantly with increasing pressure. The impact of the pressure decreases at elevated temperature. The effect of permeability remains steady despite the temperature change during the experiments. The effect of gas state and porous media on the supercritical CO 2 diffusion coefficient was further discussed by comparing the results of this study with previous study. Based on the experimental results, an empirical correlation for supercritical CO 2 diffusion coefficient in n -decane-saturated porous media was developed. The experimental results contribute to the study of supercritical CO 2 diffusion in compact porous media.

CLASSICAL DIFFUSION AND QUANTAL LOCALIZATION OF A KICKED PARTICLE IN A WELL

1988 ◽  
Vol 02 (01) ◽  
pp. 103-120 ◽  
Author(s):  
AVRAHAM COHEN ◽  
SHMUEL FISHMAN
Keyword(s):  
Diffusion Coefficient ◽  
Classical Limit ◽  
Approximate Formula ◽  
Quantum Systems ◽  
Potential Well ◽  
Diffusive Growth ◽  
Classical Chaos ◽  
The One ◽  
Short Time ◽  
Infinite Potential Well

The classical and quantal behavior of a particle in an infinite potential well, that is periodically kicked is studied. The kicking potential is K|q|α, where q is the coordinate, while K and α are constants. Classically, it is found that for α > 2 the energy of the particle increases diffusively, for α < 2 it is bounded and for α = 2 the result depends on K. An approximate formula for the diffusion coefficient is presented and compared with numerical results. For quantum systems that are chaotic in the classical limit, diffusive growth of energy takes place for a short time and then it is suppressed by quantal effects. For the systems that are studied in this work the origin of the quantal localization in energy is related to the one of classical chaos.

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