Hydrodynamic dispersion in heterogeneous anisotropic porous media: A simple model for anomalous diffusion emergence

2018 ◽  
Vol 508 ◽  
pp. 424-433 ◽  
Author(s):  
D. Hernández ◽  
F. Ramírez-Alatriste ◽  
J.C.R. Romo-Cruz ◽  
L. Olivares-Quiroz
Keyword(s):  
Porous Media ◽  
Simple Model ◽  
Anomalous Diffusion ◽  
Hydrodynamic Dispersion ◽  
Anisotropic Porous Media

scholarly journals Three-dimensional Hausdorff derivative diffusion model for isotropic/anisotropic fractal porous media

2018 ◽  
Vol 22 (Suppl. 1) ◽  
pp. 1-6 ◽  
Author(s):  
Wei Cai ◽  
Wen Chen ◽  
Fajie Wang
Keyword(s):  
Porous Media ◽  
Fundamental Solution ◽  
Diffusion Equation ◽  
Diffusion Model ◽  
Anomalous Diffusion ◽  
Three Dimensional ◽  
Fractal Structures ◽  
Anisotropic Porous Media ◽  
Convection Diffusion Equation ◽  
Time Space

The anomalous diffusion in fractal isotropic/anisotropic porous media is characterized by the Hausdorff derivative diffusion model with the varying fractal orders representing the fractal structures in different directions. This paper presents a comprehensive understanding of the Hausdorff derivative diffusion model on the basis of the physical interpretation, the Hausdorff fractal distance and the fundamental solution. The concept of the Hausdorff fractal distance is introduced, which converges to the classical Euclidean distance with the varying orders tending to 1. The fundamental solution of the 3-D Hausdorff fractal derivative diffusion equation is proposed on the basis of the Hausdorff fractal distance. With the help of the properties of the Hausdorff derivative, the Huasdorff diffusion model is also found to be a kind of time-space dependent convection-diffusion equation underlying the anomalous diffusion behavior.

HEATLINE VISUALIZATION OF BUOYANCY INDUCED FLOWS FOR NON-DARCY ANISOTROPIC POROUS MEDIA

2020 ◽  
Vol 11 (4) ◽  
pp. 359-379
Author(s):  
Narasimha Suri Tinnaluri ◽  
Lokesh Kalapala ◽  
Jaya Krishna Devanuri
Keyword(s):  
Porous Media ◽  
Anisotropic Porous Media

scholarly journals Pore-Scale Mixing and the Evolution of Hydrodynamic Dispersion in Porous Media

2021 ◽  
Vol 126 (16) ◽  
Author(s):  
Alexandre Puyguiraud ◽  
Philippe Gouze ◽  
Marco Dentz
Keyword(s):  
Porous Media ◽  
Hydrodynamic Dispersion ◽  
Pore Scale

Testing a simple model of gas bubble dynamics in porous media

2015 ◽  
Vol 51 (2) ◽  
pp. 1036-1049 ◽  
Author(s):  
Jorge A. Ramirez ◽  
Andy J. Baird ◽  
Tom J. Coulthard ◽  
J. Michael Waddington
Keyword(s):  
Porous Media ◽  
Simple Model ◽  
Bubble Dynamics ◽  
Gas Bubble

scholarly journals Anomalous diffusion in porous media

2016 ◽  
Vol 40 (3) ◽  
pp. 1850-1862 ◽  
Author(s):  
J.A. Ferreira ◽  
G. Pena ◽  
G. Romanazzi
Keyword(s):  
Porous Media ◽  
Anomalous Diffusion ◽  
Diffusion In Porous Media

Numerical Simulation of Insulin Depot Formation and Absorption in Subcutaneous Tissue Modeled as a Homogeneous Anisotropic Porous Media

2021 ◽  
Author(s):  
Michael Zedelmair ◽  
Abhijit Mukherjee
Keyword(s):  
Porous Media ◽  
Numerical Model ◽  
Insulin Pump ◽  
Subcutaneous Tissue ◽  
Saturated Porous Media ◽  
Anisotropic Porous Media ◽  
Effective Option ◽  
Computational Fluid Dynamics Cfd ◽  
Experimental Findings ◽  
Subcutaneous Adipose

Abstract In this study, a numerical model of the insulin depot formation and absorption in the subcutaneous adipose tissue is developed using the commercial Computational Fluid Dynamics (CFD) software. A better understanding of these mechanisms can be helpful in the development of new devices and cannula geometries as well as predicting the concentration of insulin in the blood. The injection method considered in this simulation is by the use of an insulin pump using a rapid acting U100 insulin analogue. The depot formation is analyzed running Bolus injections ranging from 5-15 units of insulin corresponding to 50-150µl. The insulin is injected into the subcutaneous tissue in the abdominal region. The tissue is modeled as a fluid saturated porous media. An anisotropic approach to define the tissue permeability is studied by varying the value of the porosity in parallel and perpendicular direction having an impact on the viscous resistance to the flow. Following recent experimental findings this configuration results in a disk shaped insulin depot. To be able to run the simulation over longer timeframes the depot formation model has been extended implementing the process of absorption of insulin from the depot. The developed model is then used to analyze the formation of the insulin depot in the tissue when using different flow rates and cannula geometries. The numerical model is an effective option to evaluate new cannula designs prior to the manufacturing and testing of prototypes, which are rather time consuming and expensive.

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