Advection–diffusion in a porous medium with fractal geometry: fractional transport and crossovers on time scales

Meccanica ◽  
2021 ◽  
Author(s):  
Alexey Zhokh ◽  
Peter Strizhak
Keyword(s):  
Porous Medium ◽  
Time Scales ◽  
Fractal Geometry ◽  
Advection Diffusion ◽  
Fractional Transport

scholarly journals Natural convection and the evolution of a reactive porous medium

2011 ◽  
Vol 673 ◽  
pp. 286-317 ◽  
Author(s):  
LINDSEY T. RITCHIE ◽  
DAVID PRITCHARD
Keyword(s):  
Porous Medium ◽  
Time Scales ◽  
Saturated Porous Medium ◽  
Diffusion Mechanism ◽  
Reaction Diffusion ◽  
Onset Of Convection ◽  
Convective Circulation ◽  
Long Time ◽  
Porosity And Permeability ◽  
Rayleigh Numbers

We describe a mathematical model of buoyancy-driven flow and solute transport in a saturated porous medium, the porosity and permeability of which evolve through precipitation and dissolution as a mineral is lost or gained from the pore fluid. Imposing a vertically varying equilibrium solubility creates a density gradient which can drive convective circulation. We characterise the onset of convection using linear stability analysis, and explore the further development of the coupled reaction–convection system numerically. At low Rayleigh numbers, the effect of the reaction–permeability feedback is shown to be destabilising through a novel reaction–diffusion mechanism; at higher Rayleigh numbers, the precipitation and dissolution have a stabilising effect. Over longer time scales, reaction–permeability feedback triggers secondary instabilities in quasi-steady convective circulation, leading to rapid reversals in the direction of circulation. Over very long time scales, characteristic patterns of porosity emerge, including horizontal layering as well as the development of vertical chimneys of enhanced porosity. We discuss the implications of these findings for more comprehensive models of reactive convection in porous media.

Critical time scales for advection-diffusion-reaction processes

2012 ◽  
Vol 85 (4) ◽  
Author(s):  
Adam J. Ellery ◽  
Matthew J. Simpson ◽  
Scott W. McCue ◽  
Ruth E. Baker
Keyword(s):  
Time Scales ◽  
Critical Time ◽  
Diffusion Reaction ◽  
Advection Diffusion ◽  
Reaction Processes

Real-time rainfall prediction at small space-time scales using a two-dimensional stochastic advection-diffusion model

1993 ◽  
Vol 29 (5) ◽  
pp. 1489-1504 ◽  
Author(s):  
Kenji Jinno ◽  
Akira Kawamura ◽  
Ronny Berndtsson ◽  
Magnus Larson ◽  
Janusz Niemczynowicz
Keyword(s):  
Real Time ◽  
Diffusion Model ◽  
Time Scales ◽  
Space Time ◽  
Two Dimensional ◽  
Small Space ◽  
Rainfall Prediction ◽  
Advection Diffusion

scholarly journals A biochemo-mechano coupled, computational model combining membrane transport and pericellular proteolysis in tissue mechanics

2017 ◽  
Vol 473 (2199) ◽  
pp. 20160812 ◽  
Author(s):  
A.-T. Vuong ◽  
A. D. Rauch ◽  
W. A. Wall
Keyword(s):  
Porous Medium ◽  
Computational Model ◽  
Solid Phase ◽  
Chemical Species ◽  
Reaction Rates ◽  
Tissue Mechanics ◽  
Diffusion Reaction ◽  
Advection Diffusion ◽  
Reaction Processes ◽  
Pericellular Proteolysis

We present a computational model for the interaction of surface- and volume-bound scalar transport and reaction processes with a deformable porous medium. The application in mind is pericellular proteolysis, i.e. the dissolution of the solid phase of the extracellular matrix (ECM) as a response to the activation of certain chemical species at the cell membrane and in the vicinity of the cell. A poroelastic medium model represents the extra cellular scaffold and the interstitial fluid flow, while a surface-bound transport model accounts for the diffusion and reaction of membrane-bound chemical species. By further modelling the volume-bound transport, we consider the advection, diffusion and reaction of sequestered chemical species within the extracellular scaffold. The chemo-mechanical coupling is established by introducing a continuum formulation for the interplay of reaction rates and the mechanical state of the ECM. It is based on known experimental insights and theoretical work on the thermodynamics of porous media and degradation kinetics of collagen fibres on the one hand and a damage-like effect of the fibre dissolution on the mechanical integrity of the ECM on the other hand. The resulting system of partial differential equations is solved via the finite-element method. To the best of our knowledge, it is the first computational model including contemporaneously the coupling between (i) advection–diffusion–reaction processes, (ii) interstitial flow and deformation of a porous medium, and (iii) the chemo-mechanical interaction impelled by the dissolution of the ECM. Our numerical examples show good agreement with experimental data. Furthermore, we outline the capability of the methodology to extend existing numerical approaches towards a more comprehensive model for cellular biochemo-mechanics.

Effect of porous structure on rarefied gas flow in porous medium constructed by fractal geometry

2016 ◽  
Vol 34 ◽  
pp. 1446-1452 ◽  
Author(s):  
Jiayi Zheng ◽  
Weibiao Zhang ◽  
Guozhu Zhang ◽  
Yanshun Yu ◽  
Shengqi Wang
Keyword(s):  
Porous Medium ◽  
Porous Structure ◽  
Fractal Geometry ◽  
Gas Flow ◽  
Rarefied Gas ◽  
Rarefied Gas Flow

scholarly journals Impact of Synthetic Porous Medium Geometric Properties on Solute Transport Using Direct 3D Pore-Scale Simulations

Geofluids ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-13
Author(s):  
Paolo Roberto Di Palma ◽  
Nicolas Guyennon ◽  
Andrea Parmigiani ◽  
Christian Huber ◽  
Falk Heβe ◽  
...  
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Effective Diffusion ◽  
Volume Averaging ◽  
Transport Processes ◽  
Hydrodynamic Dispersion ◽  
Pore Scale ◽  
Geometric Properties ◽  
Advection Diffusion ◽  
The Impact

Transport processes in porous media have been traditionally studied through the parameterization of macroscale properties, by means of volume-averaging or upscaling methods over a representative elementary volume. The possibility of upscaling results from pore-scale simulations, to obtain volume-averaging properties useful for practical purpose, can enhance the understanding of transport effects that manifest at larger scales. Several studies have been carried out to investigate the impact of the geometric properties of porous media on transport processes for solute species. However, the range of pore-scale geometric properties, which can be investigated, is usually limited to the number of samples acquired from microcomputed tomography images of real porous media. The present study takes advantage of synthetic porous medium generation to propose a systematic analysis of the relationships between geometric features of the porous media and transport processes through direct simulations of fluid flow and advection-diffusion of a non-reactive solute. Numerical simulations are performed with the lattice Boltzmann method on synthetic media generated with a geostatistically based approach. Our findings suggest that the advective transport is primarily affected by the specific surface area and the mean curvature of the porous medium, while the effective diffusion coefficient scales as the inverse of the tortuosity squared. Finally, the possibility of estimating the hydrodynamic dispersion coefficient knowing only the geometric properties of porous media and the applied pressure gradient has been tested, within the range of tested porous media, against advection-diffusion simulations at low Reynolds (<10-1) and Peclet numbers ranging from 101 to 10-2.

Fractal Feature of Microstructure of Porous Medium in Effective Stress

2013 ◽  
Vol 827 ◽  
pp. 394-399
Author(s):  
Hao Li
Keyword(s):  
Porous Medium ◽  
Fractal Dimension ◽  
Effective Stress ◽  
Fractal Geometry ◽  
Calculation Model ◽  
The Relationship ◽  
Pore Number

Basing on fractal geometry theory, establish fractal calculation model in effective stress, analyze and discuss the relationship between microstructure of porous medium and effective stress, reveal the influence law of the latter on the former. The results of the study show that the fractal calculation model of effective stress can describe the relationship between them. With the increase of effective stress, the fractal dimension of porous medium increases exponentially, porosity and pore number in porous medium decrease exponentially and mean radius of pore decreases.

LVSEM: Past Present and Future

1990 ◽  
Vol 48 (1) ◽  
pp. 364-365
Author(s):  
James B. Pawley
Keyword(s):  
Field Emission ◽  
Line Width ◽  
Time Scales ◽  
Silicon Oxide ◽  
Beam Current ◽  
High Brightness ◽  
High Beam ◽  
Fixed Charges ◽  
Beam Voltage ◽  
Deposited Metal

Past: In 1960 Thornley published the first description of SEM studies carried out at low beam voltage (LVSEM, 1-5 kV). The aim was to reduce charging on insulators but increased contrast and difficulties with low beam current and frozen biological specimens were also noted. These disadvantages prevented widespread use of LVSEM except by a few enthusiasts such as Boyde. An exception was its use in connection with studies in which biological specimens were dissected in the SEM as this process destroyed the conducting films and produced charging unless LVSEM was used.In the 1980’s field emission (FE) SEM’s came into more common use. The high brightness and smaller energy spread characteristic of the FE-SEM’s greatly reduced the practical resolution penalty associated with LVSEM and the number of investigators taking advantage of the technique rapidly expanded; led by those studying semiconductors. In semiconductor research, the SEM is used to measure the line-width of the deposited metal conductors and of the features of the photo-resist used to form them. In addition, the SEM is used to measure the surface potentials of operating circuits with sub-micrometer resolution and on pico-second time scales. Because high beam voltages destroy semiconductors by injecting fixed charges into silicon oxide insulators, these studies must be performed using LVSEM where the beam does not penetrate so far.

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