Editing Percolation

{{short description|Filtration of fluids through porous materials}}
{{for|the mathematical study of percolation|percolation theory}}
[[File:Manual coffee preperation.jpg|thumb|In coffee percolation, soluble compounds leave the coffee grounds and join the water to form [[coffee]]. Insoluble compounds (and granulates) remain within the [[coffee filter]].]]
[[File:Percolation.gif|thumb|Percolation in a square lattice.]]

In [[physics]], [[chemistry]], and [[materials science]], '''percolation''' ({{etymology|la|{{wikt-lang|la|percolare}}|to filter, trickle through}}) refers to the movement and [[filtration|filtering]] of fluids through porous materials. It is described by [[Darcy's law]]. Broader applications have since been developed that cover connectivity of many systems modeled as lattices or graphs, analogous to connectivity of lattice components in the filtration problem that modulates capacity for percolation.

==Background==
During the last decades, [[percolation theory]], the mathematical study of percolation, has brought new understanding and techniques to a broad range of topics in physics, materials science, [[complex network]]s, [[epidemiology]], and other fields. For example, in [[geology]], percolation refers to filtration of water through soil and permeable rocks. The water flows to [[groundwater recharge|recharge]] the [[groundwater]] in the [[water table]] and [[aquifer]]s. In places where [[infiltration basin]]s or [[septic drain field]]s are planned to dispose of substantial amounts of water, a [[percolation test]] is needed beforehand to determine whether the intended structure is  likely to succeed or fail.
In two dimensional square lattice  percolation is defined as follows. A site is "occupied" with
probability p or "empty" (in which case its edges are removed) with probability 1 – p; the
corresponding problem is called site percolation, see Fig. 2.

Percolation typically exhibits [[universality (dynamical systems)|universality]]. [[Statistical physics]] concepts such as scaling theory, [[renormalization]], [[phase transition]], [[critical phenomena]] and [[fractal]]s are used to characterize percolation properties.
[[Combinatorics]] is commonly employed to study [[percolation threshold]]s.

Due to the complexity involved in obtaining exact results from analytical models of percolation, computer simulations are typically used.  The current fastest algorithm for percolation was published in 2000 by [[Mark Newman]] and Robert Ziff.<ref name="newman">{{cite journal |last1=Newman |first1=Mark |author-link=Mark Newman |last2=Ziff |first2=Robert |title=Efficient Monte Carlo Algorithm and High-Precision Results for Percolation |journal=[[Physical Review Letters]] |volume=85 |issue=19 |pages=4104–4107 |year=2000 |doi=10.1103/PhysRevLett.85.4104 |pmid=11056635 |arxiv=cond-mat/0005264 |bibcode=2000PhRvL..85.4104N |citeseerx=10.1.1.310.4632 |s2cid=747665 }}</ref>

==Examples==
* Coffee percolation (see Fig. 1), where the solvent is water, the permeable substance is the coffee grounds, and the soluble constituents are the chemical compounds that give coffee its color, taste, and aroma.
* Movement of weathered material down on a slope under the earth's surface.
* Cracking of trees with the presence of two conditions, sunlight and pressure.
* Collapse and robustness of biological virus shells to random subunit removal (experimentally-verified fragmentation of viruses).<ref name="Brunk Twarock p. ">{{cite journal | last1=Brunk | first1=Nicholas E. | last2=Twarock | first2=Reidun | title=Percolation Theory Reveals Biophysical Properties of Virus-like Particles | journal=ACS Nano | publisher=American Chemical Society (ACS) | date=2021-07-23 | volume=15 | issue=8 | pages=12988–12995 | issn=1936-0851 | doi=10.1021/acsnano.1c01882 | pmid=34296852 | pmc=8397427 | doi-access=free }}</ref><ref>{{Cite journal |doi = 10.1088/1478-3975/aac194|pmid = 29714713|pmc = 6004236|title = Molecular jenga: The percolation phase transition (collapse) in virus capsids|journal = Physical Biology|volume = 15|issue = 5|pages = 056005|year = 2018|last1 = Brunk|first1 = Nicholas E.|last2 = Lee|first2 = Lye Siang|last3 = Glazier|first3 = James A.|last4 = Butske|first4 = William|last5 = Zlotnick|first5 = Adam|bibcode = 2018PhBio..15e6005B}}</ref><ref>{{Cite journal |doi = 10.1002/pro.3265|pmid = 28795465|pmc = 5654856|title = A molecular breadboard: Removal and replacement of subunits in a hepatitis B virus capsid|journal = Protein Science|volume = 26|issue = 11|pages = 2170–2180|year = 2017|last1 = Lee|first1 = Lye Siang|last2 = Brunk|first2 = Nicholas|last3 = Haywood|first3 = Daniel G.|last4 = Keifer|first4 = David|last5 = Pierson|first5 = Elizabeth|last6 = Kondylis|first6 = Panagiotis|last7 = Wang|first7 = Joseph Che-Yen|last8 = Jacobson|first8 = Stephen C.|last9 = Jarrold|first9 = Martin F.|last10 = Zlotnick|first10 = Adam}}</ref>
* Transport in porous media.
* Spread of diseases.<ref>{{cite journal |last1=Grassberger |first1=Peter |author-link1=Peter Grassberger |title=On the Critical Behavior of the General Epidemic Process and Dynamical Percolation |journal=Mathematical Biosciences |volume=63 |issue=2 <!-- |month=April -->|pages=157–172 |year=1983 |doi=10.1016/0025-5564(82)90036-0 }}</ref><ref>{{cite journal |doi=10.1103/PhysRevE.66.016128|title=Spread of epidemic disease on networks|year=2002|last1=Newman|first1=M. E. J.|journal=Physical Review E|volume=66|issue=1 Pt 2|page=016128|pmid=12241447|arxiv=cond-mat/0205009|bibcode=2002PhRvE..66a6128N|s2cid=15291065}}</ref>
* Surface roughening.{{citation needed|date=October 2014}}
* Dental percolation, increase rate of decay under crowns because of a conducive environment for strep mutants and lactobacillus
* Potential sites for septic systems are tested by the "[[Percolation test|perc test]]". Example/theory: A hole (usually 6–10 inches in diameter) is dug in the ground surface (usually 12–24" deep). Water is filled in to the hole, and the time is measured for a drop of one inch in the water surface. If the water surface quickly drops, as usually seen in poorly-graded sands, then it is a potentially good place for a septic "[[Septic drain field|leach field]]". If the hydraulic conductivity of the site is low (usually in clayey and loamy soils), then the site is undesirable.

==See also==
{{colbegin|colwidth=18em}}
* [[Branched polymer]]
* [[Conductance (graph)|Conductance]]
* [[Critical exponents]]
* [[Fragmentation (chemistry)|Fragmentation]]
* [[Gelation]]
* [[Giant component]]
* [[Groundwater recharge]]
* [[Immunization]]
* [[Network theory]]
* [[Percolation critical exponents]]
* [[Percolation theory]]
* [[Percolation threshold]]
* [[Polymerization]]
* [[Self-organization]]
* [[Self-organized criticality]]
* [[Septic tank]]
* [[Supercooled water]]
* [[Water pipe percolator]]
{{colend}}

==References==
{{Reflist}}

==Further reading==
* [[Harry Kesten|Kesten, Harry]]; [https://www.ams.org/notices/200605/what-is-kesten.pdf "What is percolation?"], in ''[[Notices of the AMS]]'', May 2006.
* Sahimi, Muhammad; ''Applications of Percolation Theory'', Taylor & Francis, 1994. {{ISBN|0-7484-0075-3}} (cloth), {{ISBN|0-7484-0076-1}} (paper).
* [[Geoffrey Grimmett|Grimmett, Geoffrey]]; ''[http://www.statslab.cam.ac.uk/~grg/papers/perc/perc.html Percolation (2. ed).]'' Springer Verlag, 1999.
* [[Dietrich Stauffer|Stauffer, Dietrich]]; and Aharony, Ammon; ''Introduction to Percolation Theory'', Taylor & Francis, 1994, revised second edition, {{ISBN|9780748402533}}.
* Kirkpatrick, Scott; [https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.45.574 "Percolation and Conduction"], in ''Reviews of Modern Physics'', 45, 574, 1973.
* Rodrigues, Edouard; [http://www.jeudhex.com Remarkable properties of pawns on a hexboard] {{Webarchive|url=https://web.archive.org/web/20211209222014/http://jeudhex.com/ |date=2021-12-09 }}
* [[Béla Bollobás|Bollobás, Béla]]; [[Oliver Riordan|Riordan, Oliver]]; ''Percolation'', Cambridge University Press, 2006, {{ISBN|0521872324}}.
* Grimmett, Geoffrey; ''Percolation'', Springer, 1999

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[[Category:Systems theory]]
[[Category:Combinatorics]]