Hello friends of Steemit! In this opportunity I will share with you a post where I will explain the steps to carry out a simulation of the phenomenon of the diffusion in porous media. It should be noted that such a procedure is also valid for the simulation of other physical phenomena, such as thermal conduction, fluid flow, among others.
In the previous posts about diffusion in porous media (I leave the links at the end of the post), I mentioned that "there are two different forms to study the phenomenon of diffusion, the phenomenological approach and the physical-statistical approach" [1] [a]. In the phenomenological point of view are used the so-called Fick's laws of diffusion, and in the physical-statistical point of view, is considered the random path of the diffusing particles propelled by their thermal energy and the collisions between them and the collisions with the surface of the porous medium. The approach that I have used in my research is the phenomenological one, since it allows obtaining the diffusivity or diffusion coefficient depending on the geometric properties of the medium.
I also mentioned that in porous media, the equations used for the description of the diffusion, called Fick's equations, are no longer valid and must be modified to include the effects of the geometry of the medium on the movement of the diffused particles.
Now, in view of the above, to study the diffusion and other phenomena of transport in porous media (and in general, in heterogeneous media, those media composed of two or more substances of different nature, of which the porous media are a type), a series of previous steps must be followed that lead to the modified Fick's equations, which will finally be solved for the description of the phenomenon.
Figure 1: Diffusion simulation in a three-dimensional porous medium
On the other hand, it is convenient to clarify that the scientific study of a natural phenomenon can be carried out directly, as it is presented in nature, or through a simulation, which consists in the design or creation of a experimental or theoretical-computational model of a real system to carry out experiences for the qualitative and quantitative description of the behavior of the system or of some phenomenon that happens in it. In the works on diffusion in porous media I have carried out theoretical-computational simulations.
To simulate the diffusion in porous media, and other transport phenomena, the following steps can be followed, which I have used in the research work in this area [2-5]:
In the first place, we proceed to the generation of a model of the porous medium, either experimentally, theoretically or computationally. In the works I have done, and of which I will show some results, the porous media used have been designed theoretically and computationally.
Then to the structural characterization the porous medium, which consists of the determination by means of various experimental, theoretical and computational techniques of the geometric or structural properties of the porous medium, such as porosity, specific surface and pore size.
In third place, we have the physical characterization of the porous medium, which consists in the determination of the transport coefficient, in this case the diffusivity or diffusion coefficient. Such determination shows the influence of the structure of the medium on the diffusivity, which can be expressed by formulas obtained through the application of methods that modify the Fick's equations valid in homogeneous media to obtain valid equations in the porous media. The method I used is called Method of Volumetric Averaging (MPV).
Finally, to the simulation itself. If this is experimental, we proceed to the measurement of the concentration of the diffused substance in several points of the porous system and in several instants of time, but if it is theoretical-computational, like the ones that I have carried out, we proceed to the resolution of the new diffusion equations obtained in the previous step, using the expressions of diffusivity, called effective diffusivity, obtained in step two.
Figure 2: Curve effective diffusivity versus porosity
In figure 2, I show one of the graphs that I have elaborated with the results obtained during my research in the area. In it, it is observed as the diffusion constant changes according to the type of porous medium used, hence the importance of studying diffusion in a variety of porous media in order to obtain the most general results possible.
In the next installment of the series, I will talk about the techniques used for generation of porous media models, and also, I will show you some of the models of porous media used in my research work in the area.
Thanks for your kind reading. I hope this post was liked. I wait for you in the next installment.
If you wish to obtain additional information about the phenomenon of diffusion in porous media, I invite you to read the previous posts of the series:
Diffusion in Porous Media – A world of applications – Part 1
Diffusion in Porous Media – A world of applications – Part 2
Diffusion in Porous Media – A world of applications – Part 3
Diffusion in Porous Media – A world of applications – Part 4
Sources:
[1] Philibert, J., 2005. One and a half century of diffusion: Fick, Einstein, before and beyond. Diffusion Fundamentals, 2, pp. 1.1–1.10.
[2] Borges da Silva, E. A.; Souza, D. P. y Ulson da Souza, A. A., 2007. Prediction of effective diffusivity tensors for bulk diffusion with chemical reactions in porous media. Brazilian Journal of Chemical Engineering, 24, pp. 47-60.
[3] Dullien, F. A. L., 2000. Porous Media: Fluid transport and pore structure, 2da edic., Academic Press Inc., Londres, Reino Unido, pp. 6-110, 288-297, 501-562.
[4] Kim, J. H.; Ochoa, J. A. y Whitaker, S., 1987. Diffusion in anisotropic media, Transport in Porous Media, 2, pp. 327-356.
[5] Whitaker, S., 1967. Diffusion and dispersion in porous media, AIChE (Am. Inst. Chem. Eng.), J. 13, pp.420-426.
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