Editing Porous medium

{{Short description|Material containing fluid-filled voids}}
[[File:porousceramic.jpg|thumb|Open-cell ceramic]]

In [[materials science]], a '''porous medium''' or a '''porous material''' is a material containing [[porosity|pores]] (voids).<ref>{{Cite book|title=Hierarchically Structured Porous Materials: From Nanoscience to Catalysis, Separation, Optics, Energy, and Life Science - Wiley Online Library|language=en|doi=10.1002/9783527639588|year = 2011|isbn = 9783527639588|editor1-last=Su|editor1-first=Bao-Lian|editor2-first=Clément|editor2-last=Sanchez|editor3-first=Xiao-Yu|editor3-last=Yang}}</ref> The skeletal portion of the material is often called the "matrix" or "frame". The pores are typically filled with a [[fluid]] ([[liquid]] or [[gas]]). The skeletal material is usually a [[solid]], but structures like [[foam]]s are often also usefully analyzed using concept of porous media.

A porous medium is most often characterised by its [[porosity]]. Other properties of the medium (e.g. [[Permeability (fluid)|permeability]], [[tensile strength]], [[electrical conductivity]], [[tortuosity]]) can sometimes be derived from the respective properties of its constituents (solid matrix and fluid) and the media porosity and pores structure, but such a derivation is usually complex. Even the concept of porosity is only straightforward for a poroelastic medium.

Often both the solid matrix and the pore network (also known as the pore space) are continuous, so as to form two interpenetrating continua such as in a [[sponge]]. However, there is also a concept of closed porosity and [[effective porosity]], i.e. the pore space accessible to flow.

Many natural substances such as [[rock (geology)|rocks]] and [[soil]] (e.g. [[aquifer]]s, [[petroleum reservoir]]s), [[zeolite]]s, [[biological tissue]]s (e.g. bones, wood, [[cork (material)|cork]]), and man made materials such as [[cement]]s and [[ceramic]]s can be considered as porous media. Many of their important properties can only be rationalized by considering them to be porous media.

The concept of porous media is used in many areas of applied science and engineering: [[filtration]], [[mechanics]] ([[acoustics]], [[geomechanics]], [[soil mechanics]], [[rock mechanics]]), [[engineering]] ([[petroleum engineering]], [[bioremediation]], [[construction engineering]]), [[geosciences]] ([[hydrogeology]], [[petroleum geology]], [[geophysics]]), biology and [[biophysics]], [[material science]]. Two important current fields of application for porous materials are energy conversion and [[energy storage]], where porous materials are essential for superpacitors, (photo-)[[catalysis]],<ref>{{Cite journal | doi= 10.1016/j.jcis.2022.12.033 |last1=Madanu|first1=Thomas L.|last2=Mouchet|first2=Sébastien R.|last3=Deparis|first3=Olivier|last4=Liu|first4=Jing|last5=Li|first5=Yu|last6=Su|first6=Bao-Lian|    title = Tuning and transferring slow photons from TiO2 photonic crystals to BiVO4 nanoparticles for unprecedented visible light photocatalysis | journal=Journal of Colloid and Interface Science | volume= 634 | pages = 290–299 |year=2023|pmid=36535165 | url=https://doi.org/10.1016/j.jcis.2022.12.033|url-access=subscription}}</ref> [[fuel cell]]s,<ref>{{Cite book|last1=Zhang|first1=Tao|url=https://doi.org/10.1142/11909|title=Handbook of Porous Materials|last2=Asefa|first2=Tewodros|publisher=WORLD SCIENTIFIC|year=2020|isbn=978-981-12-2322-8|editor-last=Gitis|editor-first=Vitaly|location=Singapore|language=en|doi=10.1142/11909|editor-last2=Rothenberg|editor-first2=Gadi}}</ref> and [[Electric battery|batteries]].

==Scale==
At the microscopic and macroscopic levels, porous media can be classified. 
At the microscopic scale, the structure is represented statistically by the distribution of pore sizes, the degree of pore interconnection and orientation, the proportion of dead pores, etc.<ref name="Particulate systems">{{cite journal |last1=Chhabra |first1=R. P. |last2=Richardson |first2=J. F. |title=Chapter 5 - Particulate systems |journal=Non-Newtonian Flow and Applied Rheology (Second Edition) |date=1 January 2008 |pages=249–315 |doi=10.1016/b978-0-7506-8532-0.00005-6 |url=https://doi.org/10.1016/B978-0-7506-8532-0.00005-6 |publisher=Butterworth-Heinemann |isbn=9780750685320 |language=en|url-access=subscription }}</ref> 
The macroscopic technique makes use of [[bulk property|bulk properties]] that have been averaged at scales far bigger than pore size.<ref name="Particulate systems"/><ref>{{cite journal |title=3 - Dye transport in fluid systems |journal=Modelling, Simulation and Control of the Dyeing Process |date=1 January 2014 |pages=54–81 |doi=10.1533/9780857097583.54 |url=https://doi.org/10.1533/9780857097583.54 |publisher=Woodhead Publishing |isbn=9780857091338 |language=en|url-access=subscription }}</ref>

Depending on the goal, these two techniques are frequently employed since they are complimentary. It is obvious that the microscopic description is required to comprehend surface phenomena like the adsorption of macromolecules from polymer solutions and the blocking of pores, whereas the macroscopic approach is frequently quite sufficient for process design where [[fluid flow]], heat, and [[mass transfer]] are of highest concern. and the molecular dimensions are significantly smaller than pore size of the porous system.<ref name="Particulate systems"/><ref>{{cite journal |last1=Fu |first1=Jinlong |last2=Thomas |first2=Hywel R. |last3=Li |first3=Chenfeng |title=Tortuosity of porous media: Image analysis and physical simulation |journal=Earth-Science Reviews |date=January 2021 |volume=212 |pages=103439 |doi=10.1016/j.earscirev.2020.103439|s2cid=229386129 |url=https://cronfa.swan.ac.uk/Record/cronfa55808/Download/55808__18817__4aeefe32b0ee4ae7993bff0531362902.pdf }}</ref>

==Fluid flow==
{{main|Fluid flow through porous media}}
[[File:Aquifère Darcy perméabilité.jpg|thumb|Fluid flow through porous media]]
Fluid flow through porous media is a subject of common interest and has emerged a separate field of study. The study of more general behaviour of porous media involving deformation of the solid frame is called [[poromechanics]].

The theory of porous flows has applications in inkjet printing<ref>Stephen D. Hoath, "Fundamentals of Inkjet Printing - The Science of Inkjet and Droplets", Wiley VCH 2016</ref> and nuclear waste disposal<ref>Martinez M.J., McTigue D.F. (1996) Modeling in Nuclear Waste Isolation: Approximate Solutions for Flow in Unsaturated Porous Media. In: Wheeler M.F. (eds) Environmental Studies. The IMA Volumes in Mathematics and its Applications, vol 79. Springer, New York, NY</ref> technologies, among others.

Numerous factors influence fluid flow in porous media, and its fundamental function is to expend energy and create fluid via the wellbore. In flow mechanics via porous medium, the connection between energy and flow rate becomes the most significant issue. The most fundamental law that characterizes this connection is [[Darcy's law]],<ref>{{cite journal |title=Basic theory |journal=Fluid Flow in Porous Media |date=November 2020 |pages=47–67 |doi=10.1142/9789811219535_0002|isbn=978-981-12-1952-8 }}</ref> particularly applicable to fine-porous media. In contrast, Forchheimer's law finds utility in the context of coarse-porous media.<ref>{{cite journal |last1=Mohammadizadeh |first1=SeyedMehdi |last2= Moghaddam |first2= Mehdi Azhdary |last3=Talebbeydokhti |first3=Naser |title=Analysis of Flow in Porous Media using Combined Pressurized-Free surface Network |journal=Journal of Porous Media |date=2021 |volume=24 |issue=10 |pages=1–15 |doi=10.1615/JPorMedia.2021025407 |publisher=Begel House Inc. |language=en}}</ref>

== Models ==
A representation of the void phase that exists inside porous materials using a set or network of pores. It serves as a structural foundation for the prediction of transport parameters and is employed in the context of pore structure characterisation.<ref>{{cite book |last1=Burganos |first1=Vasilis |chapter=Pore Model |title=Encyclopedia of Membranes |date=2015 |pages=1–2 |doi=10.1007/978-3-642-40872-4_1055-2 |chapter-url=https://doi.org/10.1007/978-3-642-40872-4_1055-2 |publisher=Springer |isbn=978-3-642-40872-4 |language=en}}</ref>

There are many idealized models of pore structures. They can be broadly divided into three categories:
* networks of [[capillary|capillaries]]
* arrays of solid particles (e.g., [[random close pack]] of spheres)
* trimodal

Porous materials often have a [[fractal]]-like structure, having a pore surface area that seems to grow indefinitely when viewed with progressively increasing resolution.<ref>{{cite journal|doi=10.1029/2001JB000523 | bibcode=2003JGRB..108.2062D | volume=108 | issue=B2 | pages=2062 | title=Fractal pore structure of sedimentary rocks: Simulation by ballistic deposition | year=2003 | journal=Journal of Geophysical Research: Solid Earth | last1 = Dutta | first1 = Tapati| doi-access=free }}</ref> Mathematically, this is described by assigning the pore surface a [[Hausdorff dimension]] greater than 2.<ref>{{cite journal|doi=10.1111/j.1365-2389.1994.tb00535.x | volume=45 | issue=4 | title=The relationship between structure and the hydraulic conductivity of soil | year=1994 | journal=European Journal of Soil Science | pages=493–502 | last1 = Crawford | first1 = J.W.}}</ref> Experimental methods for the investigation of pore structures include [[confocal microscopy]]<ref>[https://spiral.imperial.ac.uk/bitstream/10044/1/18107/2/Characterisation%20of%20Hadley%20Grains%20by%20Confocal%20Microscopy%20-%20accepted.pdf M. K. Head, H. S. Wong, N. R. Buenfeld, "Characterisation of 'Hadley’ Grains by Confocal Microscopy", Cement & Concrete Research (2006), 36 (8) 1483 -1489]</ref> and [[x-ray tomography]].<ref>{{cite journal| doi=10.1016/j.jhydrol.2012.09.034 | volume=472-473 | title=Using X-ray computed tomography in pore structure characterization for a Berea sandstone: Resolution effect | year=2012 | journal=Journal of Hydrology | pages=254–261 | last1 = Peng | first1 = Sheng | last2 = Hu | first2 = Qinhong | last3 = Dultz | first3 = Stefan | last4 = Zhang | first4 = Ming| bibcode=2012JHyd..472..254P }}</ref>
Porous materials have found some applications in many engineering fields including automotive sectors.<ref>{{cite journal|doi=10.1088/2631-8695/acbfa4 | volume=5 | issue=1 | title=Porous Liner Coated Inlet Duct: A Novel Approach to Attenuate Automotive Turbocharger Inlet Flow-Induced Sound Propagation | year=2023 | journal=Engineering Research Express  | pages=015047 | last1 = Ravanbod | first1 = Mohammad | doi-access=free }}</ref>

== Laws ==
One of the Laws for porous materials is [[Murray's law|the generalized Murray's law]]. The generalized Murray's law is based on optimizing mass transfer by minimizing transport resistance in pores with a given volume, and can be applicable for optimizing mass transfer involving mass variations and chemical reactions involving flow processes, molecule or ion diffusion.<ref>{{Cite journal|last1=Zheng|first1=Xianfeng|last2=Shen|first2=Guofang|last3=Wang|first3=Chao|last4=Li|first4=Yu|last5=Dunphy|first5=Darren|last6=Hasan|first6=Tawfique|author-link6=Tawfique Hasan|last7=Brinker|first7=C. Jeffrey|last8=Su|first8=Bao-Lian|date=2017-04-06|title=Bio-inspired Murray materials for mass transfer and activity|journal=Nature Communications|language=en|volume=8|page=14921|bibcode=2017NatCo...814921Z|doi=10.1038/ncomms14921|issn=2041-1723|pmc=5384213|pmid=28382972}}</ref>

For connecting a parent pipe with radius of '''''r<sub>0</sub>''''' to many children pipes with radius of '''''r<sub>i</sub>''''' , the formula of generalized Murray's law is: <math>r_o^a={1 \over 1-X}\sum_{i=1}^Nr_i^a</math>, where the '''''X''''' is the ratio of mass variation during mass transfer in the parent pore, the exponent '''''α''''' is dependent on the type of the transfer. For laminar flow ''α'' =3; for turbulent flow ''α'' =7/3; for molecule or ionic diffusion ''α'' =2; etc.

==See also==
*[[Cenocell]]
* [[Nanoporous|Nanoporous materials]]
* [[NMR in porous media]]
* [[Percolation theory]]
* [[Percolation threshold]]
* [[Reticulated foam]]
*[[Filtration]]
* [[Poromechanics]]
*[[Reactive transport modeling in porous media|Reactive transport]]
*[[Permeability (Earth sciences)|Permeability]]
*[[Macropore]]

==References==
{{Reflist}}

==Further reading==

*J. Bear; (1972)'' Dynamics of Fluids in Porous Media.'' (Elsevier, New York)

==External links==
* [https://careers.slb.com/inside-schlumberger/transformative-technology/defining-permeability Defining Permeability ]
* [https://imechanica.org/files/JCIS-2019-Tailoring%20porous%20media%20for%20controllable%20capillary%20flow_0.pdf Tailoring porous media to control permeability]
* [http://techalive.mtu.edu/meec/module06/Permeability.htm Graphical depiction of different flow rates through materials of differing permeability]
* [http://perminc.com/resources/fundamentals-of-fluid-flow-in-porous-media/ Fundamentals of Fluid Flow in Porous Media]

{{Earth science}}
{{Authority control}}

{{DEFAULTSORT:Porous Medium}}
[[Category:Porous media|*]]
[[Category:Materials]]