View source for Capillary action

{{Short description|Ability of a liquid to flow in narrow spaces}}
[[File:Capillary flow brick.jpg|thumb|Capillary water flow up a 225 mm-high porous brick after it was placed in a shallow tray of water. The time elapsed after first contact with water is indicated. From the weight increase, the estimated porosity is 25%.]]
{{Continuum mechanics}}

[[File:Capillarity.svg|thumb|Capillary action of [[water]] (polar) compared to [[Mercury (element)|mercury]] (non-polar), in each case with respect to a polar surface such as glass (≡Si–OH)]]

'''Capillary action''' (sometimes called '''capillarity''', '''capillary motion''', '''capillary rise''', '''capillary effect''', or '''wicking''') is the process of a [[liquid]] flowing in a narrow space without the assistance of external forces like [[Gravitation|gravity]].

The effect can be seen in the drawing up of liquids between the hairs of a paint-brush, in a thin tube such as a [[Drinking straw|straw]], in porous materials such as paper and plaster, in some non-porous materials such as clay and liquefied [[carbon fiber]], or in a [[biological cell]].

It occurs because of [[intermolecular force]]s between the liquid and surrounding solid surfaces. If the diameter of the tube is sufficiently small, then the combination of [[surface tension]] (which is caused by [[Cohesion (chemistry)|cohesion]] within the liquid) and [[Adhesion|adhesive forces]] between the liquid and container wall act to propel the liquid.

==Etymology==
Capillary comes from the Latin word capillaris, meaning "of or resembling hair". The meaning stems from the tiny, hairlike diameter of a capillary.{{cn|date=January 2025}}

== History ==
The first recorded observation of capillary action was by [[Leonardo da Vinci]].<ref>See:
*  Manuscripts of Léonardo de Vinci (Paris), vol. N, folios 11, 67, and 74.
*  Guillaume Libri, ''Histoire des sciences mathématiques en Italie, depuis la Renaissance des lettres jusqu'a la fin du dix-septième siecle'' [History of the mathematical sciences in Italy, from the Renaissance until the end of the seventeenth century] (Paris, France:  Jules Renouard et cie., 1840), vol. 3, [https://archive.org/details/histoiredesscie01librgoog/page/n407 page 54] {{webarchive|url=https://web.archive.org/web/20161224132312/https://books.google.com/books?id=PE8IAAAAIAAJ&pg=PA54 |date=2016-12-24 }}.  From page 54:  ''"Enfin, deux observations capitales, celle de l'action capillaire (7) et celle de la diffraction (8), dont jusqu'à présent on avait méconnu le véritable auteur, sont dues également à ce brillant génie."''  (Finally, two major&nbsp;observations, that of capillary action (7) and that of diffraction (8), the true author of which until now had not been recognized, are also due to this brilliant genius.)
*  C. Wolf (1857) "Vom Einfluss der Temperatur auf die Erscheinungen in Haarröhrchen" (On the influence of temperature on phenomena in capillary tubes) ''Annalen der Physik und Chemie'', '''101''' (177) : 550–576; see footnote on [https://books.google.com/books?id=H17kAAAAMAAJ&pg=PA551 page 551] {{webarchive|url=https://web.archive.org/web/20140629020351/http://books.google.com/books?id=H17kAAAAMAAJ&pg=PA551 |date=2014-06-29 }} by editor Johann C. Poggendorff.  From page 551:  ''" ... nach Libri (''Hist. des sciences math. en Italie'', T. III, p. 54) in den zu Paris aufbewahrten Handschriften des grossen Künstlers Leonardo da Vinci (gestorben 1519) schon Beobachtungen dieser Art vorfinden; ... "'' ( ... according to Libri (''History of the mathematical sciences in Italy'', vol. 3, p. 54) observations of this kind [i.e., of capillary action] are already to be found in the manuscripts of the great artist Leonardo da Vinci (died 1519), which are preserved in Paris; ... )</ref><ref>More detailed histories of research on capillary action can be found in:
*  David Brewster, ed., ''Edinburgh Encyclopaedia'' (Philadelphia, Pennsylvania:  Joseph and Edward Parker, 1832), volume 10, [https://books.google.com/books?id=xQ0bAQAAMAAJ&pg=PA805 pp. 805–823] {{webarchive|url=https://web.archive.org/web/20161224134213/https://books.google.com/books?id=xQ0bAQAAMAAJ&pg=PA805 |date=2016-12-24 }}.
* {{cite EB1911 |first=James Clerk |last=Maxwell |first2=John William |last2=Strutt |wstitle=Capillary Action |volume=5 |pages=256–275}}
*  John Uri Lloyd (1902) [https://books.google.com/books?id=OWBBAAAAYAAJ&pg=RA1-PA102 "References to capillarity to the end of the year 1900,"] {{webarchive|url=https://web.archive.org/web/20141214101739/http://books.google.com/books?id=OWBBAAAAYAAJ&pg=RA1-PA102 |date=2014-12-14 }} ''Bulletin of the Lloyd Library and Museum of Botany, Pharmacy and Materia Medica'', '''1''' (4) : 99–204.</ref> A former student of [[Galileo Galilei|Galileo]], [[Niccolò Aggiunti]], was said to have investigated capillary action.<ref>In his book of 1759, Giovani Batista Clemente Nelli (1725–1793) stated (p. 87) that he had ''"un libro di problem vari geometrici ec. e di speculazioni, ed esperienze fisiche ec."'' (a book of various geometric problems and of speculation and physical experiments, etc.) by Aggiunti.  On pages 91–92, he quotes from this book:  Aggiunti attributed capillary action to ''"moto occulto"'' (hidden/secret motion).  He proposed that mosquitoes, butterflies, and bees feed via capillary action, and that sap ascends in plants via capillary action.  See:    Giovambatista Clemente Nelli, ''Saggio di Storia Letteraria Fiorentina del Secolo XVII'' ... [Essay on Florence's literary history in the 17th century, ... ] (Lucca, (Italy):  Vincenzo Giuntini, 1759), [https://books.google.com/books?id=MV1YAAAAcAAJ&pg=PA91 pp. 91–92.] {{webarchive|url=https://web.archive.org/web/20140727023400/http://books.google.com/books?id=MV1YAAAAcAAJ&pg=PA91 |date=2014-07-27 }}</ref> In 1660, capillary action was still a novelty to the Irish chemist [[Robert Boyle]], when he reported that "some inquisitive French Men" had observed that when a capillary tube was dipped into water, the water would ascend to "some height in the Pipe". Boyle then reported an experiment in which he dipped a capillary tube into red wine and then subjected the tube to a partial vacuum. He found that the vacuum had no observable influence on the height of the liquid in the capillary, so the behavior of liquids in capillary tubes was due to some phenomenon different from that which governed mercury barometers.<ref>Robert Boyle, ''New Experiments Physico-Mechanical touching the Spring of the Air'', ... (Oxford, England:  H. Hall, 1660), pp. 265–270. Available on-line at:  [http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?start=291&resultStart=11&viewLayer=search&url=/permanent/archimedes_repository/large/boyle_exper_013_en_1660/index.meta&pn=297&queryType=fulltextMorph Echo (Max Planck Institute for the History of Science; Berlin, Germany)] {{webarchive|url=https://web.archive.org/web/20140305085036/http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?start=291&resultStart=11&viewLayer=search&url=%2Fpermanent%2Farchimedes_repository%2Flarge%2Fboyle_exper_013_en_1660%2Findex.meta&pn=297&queryType=fulltextMorph |date=2014-03-05 }}.</ref>

Others soon followed Boyle's lead.<ref>See, for example:
*  Robert Hooke (1661) ''An attempt for the explication of the Phenomena observable in an experiment published by the Right Hon. Robert Boyle, in the 35th experiment of his Epistolical Discourse touching the Air, in confirmation of a former conjecture made by R. Hooke.'' [pamphlet].
*  Hooke's ''An attempt for the explication'' ... was reprinted (with some changes) in:  Robert Hooke, ''Micrographia'' ... (London, England:  James Allestry, 1667), pp. 12–22, [https://books.google.com/books?id=SgFMAAAAcAAJ&pg=PA12 "Observ. IV.  Of small Glass Canes."] {{webarchive|url=https://web.archive.org/web/20161224125720/https://books.google.com/books?id=SgFMAAAAcAAJ&pg=PA12 |date=2016-12-24 }}
*  Geminiano Montanari, [https://books.google.com/books?id=5_dbAAAAQAAJ&pg=PA3 ''Pensieri fisico-matematici sopra alcune esperienze fatte in Bologna'' ... ] {{webarchive|url=https://web.archive.org/web/20161229061900/https://books.google.co.uk/books?id=5_dbAAAAQAAJ&pg=PA3 |date=2016-12-29 }} [Physical-mathematical ideas about some experiments done in Bologna ... ] (Bologna, (Italy):  1667).
*  George Sinclair, [https://books.google.com/books?id=844_AAAAcAAJ&pg=PP5 ''Ars Nova et Magna Gravitatis et Levitatis''] {{webarchive|url=https://web.archive.org/web/20171103050207/https://books.google.com/books?id=844_AAAAcAAJ&pg=PP5 |date=2017-11-03 }} [New and great powers of weight and levity] (Rotterdam, Netherlands:  Arnold Leers, Jr., 1669).
*  Johannes Christoph Sturm, ''Collegium Experimentale sive Curiosum'' [Catalog of experiments, or Curiosity] (Nüremberg (Norimbergæ), (Germany):  Wolfgang Moritz Endter & the heirs of Johann Andreas Endter, 1676).  See:  [https://books.google.com/books?id=nbMWAAAAQAAJ&pg=PA44 ''"Tentamen VIII.  Canaliculorum angustiorum recens-notata Phænomena, ... "''] {{webarchive|url=https://web.archive.org/web/20140629034844/http://books.google.com/books?id=nbMWAAAAQAAJ&pg=PA44 |date=2014-06-29 }} (Essay 8. Recently noted phenomena of narrow capillaries, ... ), pp. 44–48.</ref> Some (e.g., [[Honoré Fabri]],<ref>See:
*  Honorato Fabri, ''Dialogi physici'' ... ((Lyon (Lugdunum), France:  1665), [https://books.google.com/books?id=jY4_AAAAcAAJ&pg=PA157 pages 157 ff] {{webarchive|url=https://web.archive.org/web/20161224130147/https://books.google.com/books?id=jY4_AAAAcAAJ&pg=PA157 |date=2016-12-24 }} "Dialogus Quartus.  In quo, de libratis suspensisque liquoribus & Mercurio disputatur.  (Dialogue four.  In which the balance and suspension of liquids and mercury is discussed).
*  Honorato Fabri, ''Dialogi physici'' ... ((Lyon (Lugdunum), France:  Antoine Molin, 1669), [https://books.google.com/books?id=zRJ2rQs730QC&pg=PA267 pages 267 ff] {{webarchive|url=https://web.archive.org/web/20170407062538/https://books.google.com/books?id=zRJ2rQs730QC&pg=PA267 |date=2017-04-07 }} "Alithophilus, Dialogus quartus, in quo nonnulla discutiuntur à D. Montanario opposita circa elevationem Humoris in canaliculis, etc." (Alithophilus, Fourth dialogue, in which Dr. Montanari's opposition regarding the elevation of liquids in capillaries is utterly refuted).</ref> [[Jacob Bernoulli]]<ref>Jacob Bernoulli, [https://books.google.com/books?id=sHw5AAAAcAAJ&pg=PP11 ''Dissertatio de Gravitate Ætheris''] {{webarchive|url=https://web.archive.org/web/20170407062110/https://books.google.com/books?id=sHw5AAAAcAAJ&pg=PP11 |date=2017-04-07 }} (Amsterdam, Netherlands:  Hendrik Wetsten, 1683).</ref>) thought that liquids rose in capillaries because air could not enter capillaries as easily as liquids, so the air pressure was lower inside capillaries. Others (e.g., [[Isaac Vossius]],<ref>Isaac Vossius, ''De Nili et Aliorum Fluminum Origine'' [On the sources of the Nile and other rivers] (Hague (Hagæ Comitis), Netherlands:  Adrian Vlacq, 1666), [https://books.google.com/books?id=FjoVAAAAQAAJ&q=ascendit&pg=PA3 pages 3–7] {{webarchive|url=https://web.archive.org/web/20170407062352/https://books.google.com/books?id=FjoVAAAAQAAJ&pg=PA3 |date=2017-04-07 }} (chapter 2).</ref> [[Giovanni Alfonso Borelli]],<ref>Borelli, Giovanni Alfonso ''De motionibus naturalibus a gravitate pendentibus'' (Lyon, France:  1670), page 385, Cap. 8 Prop. CLXXXV (Chapter 8, Proposition 185.).  Available on-line at:  [http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?highlightQuery=CLXXXV&viewLayer=dict%2Csearch&url=/permanent/archimedes_repository/large/borel_demot_010_la_1670/index.meta&highlightElement=s&highlightElementPos=2&pn=385&queryType=fulltextMorph Echo (Max Planck Institute for the History of Science; Berlin, Germany)] {{webarchive|url=https://web.archive.org/web/20161223092633/http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?highlightQuery=CLXXXV&viewLayer=dict%2Csearch&url=%2Fpermanent%2Farchimedes_repository%2Flarge%2Fborel_demot_010_la_1670%2Findex.meta&highlightElement=s&highlightElementPos=2&pn=385&queryType=fulltextMorph |date=2016-12-23 }}.</ref> [[Louis Carré (mathematician)|Louis Carré]],<ref>Carré (1705) [http://gallica.bnf.fr/ark:/12148/bpt6k3487x/f409.image "Experiences sur les tuyaux Capillaires"] {{webarchive|url=https://web.archive.org/web/20170407064612/http://gallica.bnf.fr/ark:/12148/bpt6k3487x/f409.image |date=2017-04-07 }} (Experiments on capillary tubes), ''Mémoires de l'Académie Royale des Sciences'', pp. 241–254.</ref> [[Francis Hauksbee]],<ref>See:
*  Francis Hauksbee (1708) [https://books.google.com/books?id=qlZOAQAAIAAJ&pg=PA260 "Several Experiments Touching the Seeming Spontaneous Ascent of Water,"] {{webarchive|url=https://web.archive.org/web/20140629071158/http://books.google.com/books?id=qlZOAQAAIAAJ&pg=PA260 |date=2014-06-29 }} ''Philosophical Transactions of the Royal Society of London'', '''26''' :  258–266.
*  Francis Hauksbee, ''Physico-mechanical Experiments on Various Subjects'' ... (London, England: (Self-published), 1709), pages 139–169.
*  Francis Hauksbee (1711) [http://babel.hathitrust.org/cgi/pt?id=ucm.5324351053;view=1up;seq=437;start=1;size=10;page=search;num=374#view=1up;seq=437 "An account of an experiment touching the direction of a drop of oil of oranges, between two glass planes, towards any side of them that is nearest press'd together,"] ''Philosophical Transactions of the Royal Society of London'', '''27''' : 374–375.
*  Francis Hauksbee (1712) [http://babel.hathitrust.org/cgi/pt?id=ucm.5324351053;view=1up;seq=437;start=1;size=10;page=search;num=541#view=1up;seq=589 "An account of an experiment touching the ascent of water between two glass planes, in an hyperbolick figure,"] ''Philosophical Transactions of the Royal Society of London'', '''27''' : 539–540.</ref> [[Josias Weitbrecht|Josia Weitbrecht]]<ref>See:
*  Josia Weitbrecht (1736) [https://books.google.com/books?id=O1o-AAAAcAAJ&pg=PA265 "Tentamen theoriae qua ascensus aquae in tubis capillaribus explicatur"] {{webarchive|url=https://web.archive.org/web/20140629063553/http://books.google.com/books?id=O1o-AAAAcAAJ&pg=PA265 |date=2014-06-29 }} (Theoretical essay in which the ascent of water in capillary tubes is explained), ''Commentarii academiae scientiarum imperialis Petropolitanae'' (Memoirs of the imperial academy of sciences in St. Petersburg), '''8''' :  261–309.
*  Josias Weitbrecht (1737) [https://books.google.com/books?id=vR3oAAAAMAAJ&pg=PA275 "Explicatio difficilium experimentorum circa ascensum aquae in tubis capillaribus"] {{webarchive|url=https://web.archive.org/web/20141105061249/http://books.google.com/books?id=vR3oAAAAMAAJ&pg=PA275 |date=2014-11-05 }} (Explanation of difficult experiments concerning the ascent of water in capillary tubes), ''Commentarii academiae scientiarum imperialis Petropolitanae'' (Memoirs of the imperial academy of sciences in St. Petersburg), '''9''' :  275–309.</ref>) thought that the particles of liquid were attracted to each other and to the walls of the capillary.

Although experimental studies continued during the 18th century,<ref>For example:
* In 1740, Christlieb Ehregott Gellert (1713–1795) observed that like mercury, molten lead would not adhere to glass and therefore the level of molten lead was depressed in a capillary tube.  See:  C. E. Gellert (1740) "De phenomenis plumbi fusi in tubis capillaribus" (On phenomena of molten lead in capillary tubes) ''Commentarii academiae scientiarum imperialis Petropolitanae'' (Memoirs of the imperial academy of sciences in St. Petersburg), '''12''' :  243–251.  Available on-line at:  [https://archive.org/stream/commentariiacade12impe#page/242/mode/2up Archive.org] {{webarchive|url=https://web.archive.org/web/20160317040309/https://archive.org/stream/commentariiacade12impe |date=2016-03-17 }}.
*  [[Gaspard Monge]] (1746–1818) investigated the force between panes of glass that were separated by a film of liquid.  See:  Gaspard Monge (1787) [https://archive.org/stream/histoiredelacad87hist#page/506/mode/1up "Mémoire sur quelques effets d'attraction ou de répulsion apparente entre les molécules de matière"] {{webarchive|url=https://web.archive.org/web/20160316110932/https://archive.org/stream/histoiredelacad87hist |date=2016-03-16 }} (Memoir on some effects of the apparent attraction or repulsion between molecules of matter), ''Histoire de l'Académie royale des sciences, avec les Mémoires de l'Académie Royale des Sciences de Paris'' (History of the Royal Academy of Sciences, with the Memoirs of the Royal Academy of Sciences of Paris), pp. 506–529.  Monge proposed that particles of a liquid exert,  on each other, a short-range force of attraction, and that this force produces the surface tension of the liquid.  From p. 529:  ''"En supposant ainsi que l'adhérence des molécules d'un liquide n'ait d'effet sensible qu'à la surface même, & dans le sens de la surface, il seroit facile de déterminer la courbure des surfaces des liquides dans le voisinage des parois qui les conteinnent; ces surfaces seroient des lintéaires dont la tension, constante dans tous les sens, seroit par-tout égale à l'adhérence de deux molécules; & les phénomènes des tubes capillaires n'auroient plus rein qui ne pût être déterminé par l'analyse."''  (Thus by assuming that the adhesion of a liquid's molecules has a significant effect only at the surface itself, and in the direction of the surface, it would be easy to determine the curvature of the surfaces of liquids in the vicinity of the walls that contain them; these surfaces would be menisci whose tension, [being] constant in every direction, would be everywhere equal to the adhesion of two molecules; and the phenomena of capillary tubes would have nothing that could not be determined by analysis [i.e., calculus].)</ref> a successful quantitative treatment of capillary action<ref>In the 18th century, some investigators did attempt a quantitative treatment of capillary action.  See, for example, [[Alexis Clairaut|Alexis Claude Clairaut]] (1713–1765) ''Theorie de la Figure de la Terre tirée des Principes de l'Hydrostatique'' [Theory of the figure of the Earth based on principles of hydrostatics] (Paris, France:  David fils, 1743), ''Chapitre X. De l'élevation ou de l'abaissement des Liqueurs dans les Tuyaux capillaires'' (Chapter 10.  On the elevation or depression of liquids in capillary tubes), [http://gallica.bnf.fr/ark:/12148/bpt6k62579b/f146.image.r=.langEN pages 105–128.] {{webarchive|url=https://web.archive.org/web/20160409112511/http://gallica.bnf.fr/ark:/12148/bpt6k62579b/f146.image.r=.langEN |date=2016-04-09 }}</ref> was not attained until 1805 by two investigators: [[Thomas Young (scientist)|Thomas Young]] of the United Kingdom<ref>Thomas Young (January 1, 1805) [https://books.google.com/books?id=C5JJAAAAYAAJ&pg=PA65 "An essay on the cohesion of fluids,"] {{webarchive|url=https://web.archive.org/web/20140630152013/http://books.google.com/books?id=C5JJAAAAYAAJ&pg=PA65 |date=2014-06-30 }} ''Philosophical Transactions of the Royal Society of London'', '''95''' :  65–87.</ref> and [[Pierre-Simon Laplace]] of France.<ref>Pierre Simon marquis de Laplace, ''Traité de Mécanique Céleste'', volume 4, (Paris, France:  Courcier, 1805), ''Supplément au dixième livre du Traité de Mécanique Céleste'', [https://books.google.com/books?id=_A8OAAAAQAAJ&pg=RA1-PA1 pages 1–79] {{webarchive|url=https://web.archive.org/web/20161224132517/https://books.google.com/books?id=_A8OAAAAQAAJ&pg=RA1-PA1 |date=2016-12-24 }}.</ref> They derived the [[Young–Laplace equation]] of capillary action.  By 1830, the German mathematician [[Carl Friedrich Gauss]] had determined the boundary conditions governing capillary action (i.e., the conditions at the liquid-solid interface).<ref>Carl Friedrich Gauss, ''Principia generalia Theoriae Figurae Fluidorum in statu Aequilibrii'' [General principles of the theory of fluid shapes in a state of equilibrium] (Göttingen, (Germany):  Dieterichs, 1830).  Available on-line at:  [http://babel.hathitrust.org/cgi/pt?id=nyp.33433069098576#view=1up;seq=9 Hathi Trust].</ref> In 1871, the British physicist [[William Thomson, 1st Baron Kelvin|Sir William Thomson]] (later Lord Kelvin) determined the effect of the [[Meniscus (liquid)|meniscus]] on a liquid's [[vapor pressure]]—a relation known as the [[Kelvin equation]].<ref>William Thomson (1871) [https://books.google.com/books?id=ZeYXAAAAYAAJ&pg=PA448 "On the equilibrium of vapour at a curved surface of liquid,"] {{webarchive|url=https://web.archive.org/web/20141026051156/http://books.google.com/books?id=ZeYXAAAAYAAJ&pg=PA448 |date=2014-10-26 }} ''Philosophical Magazine'', series 4, '''42''' (282) : 448–452.</ref> German physicist [[Franz Ernst Neumann]] (1798–1895) subsequently determined the interaction between two immiscible liquids.<ref>Franz Neumann with A. Wangerin, ed., [http://babel.hathitrust.org/cgi/pt?id=uc1.b4498901;page=root;view=image;size=100;seq=7;num=iii ''Vorlesungen über die Theorie der Capillarität''] [Lectures on the theory of capillarity] (Leipzig, Germany:  B. G. Teubner, 1894).</ref>

[[Albert Einstein]]'s first paper, which was submitted to ''[[Annalen der Physik]]'' in 1900, was on capillarity.<ref>Albert Einstein (1901) [http://gallica.bnf.fr/ark:/12148/bpt6k15314w/f595.image.langFR "Folgerungen aus den Capillaritätserscheinungen"] {{webarchive|url=https://web.archive.org/web/20171025203011/http://gallica.bnf.fr/ark:/12148/bpt6k15314w/f595.image.langFR |date=2017-10-25 }} (Conclusions [drawn] from capillary phenomena), ''Annalen der Physik'', '''309''' (3) : 513–523.</ref><ref>{{cite web |author=Hans-Josef Kuepper |url=http://www.einstein-website.de/z_physics/wisspub-e.html |title=List of Scientific Publications of Albert Einstein |publisher=Einstein-website.de |access-date=2013-06-18 |url-status=live |archive-url=https://web.archive.org/web/20130508071317/http://www.einstein-website.de/z_physics/wisspub-e.html |archive-date=2013-05-08 }}</ref>

== Phenomena and physics ==
[[File:Rising-damp.jpg|thumb|Moderate rising damp on an internal wall]]

[[File:Capillary Flow Experiment.jpg|thumb|Capillary flow experiment to investigate capillary flows and phenomena aboard the [[International Space Station]]]]
Capillary penetration in porous media shares its dynamic mechanism with flow in hollow tubes, as both processes are resisted by viscous forces.<ref name="cappen">{{cite journal |last1=Liu |first1=Mingchao |last2=Wu |first2=Jian |last3=Gan |first3=Yixiang |last4=Hanaor |first4=Dorian A.H. |last5=Chen |first5=C.Q. |title=Tuning capillary penetration in porous media: Combining geometrical and evaporation effects |journal=International Journal of Heat and Mass Transfer |date=August 2018 |volume=123 |pages=239–250 |doi=10.1016/j.ijheatmasstransfer.2018.02.101 |bibcode=2018IJHMT.123..239L |url=https://unsworks.unsw.edu.au/bitstreams/2f5ef787-bf87-4d2c-a9c8-70e55bcff408/download |hdl=1959.4/unsworks_60951 |hdl-access=free }}</ref> Consequently, a common apparatus used to demonstrate the phenomenon is the ''capillary tube''. When the lower end of a glass tube is placed in a liquid, such as water, a concave [[Meniscus (liquid)|meniscus]] forms. [[Adhesion]] occurs between the fluid and the solid inner wall pulling the liquid column along until there is a sufficient mass of liquid for [[gravitational force]]s to overcome these intermolecular forces. The contact length (around the edge) between the top of the liquid column and the tube is proportional to the radius of the tube, while the weight of the liquid column is proportional to the square of the tube's radius. So, a narrow tube will draw a liquid column along further than a wider tube will, given that the inner water molecules cohere sufficiently to the outer ones.{{cn|date=January 2025}}

== Examples ==
In the built environment, evaporation limited capillary penetration is responsible for the phenomenon of [[damp (structural)|rising damp]] in [[concrete]] and [[masonry]], while in industry and diagnostic medicine this phenomenon is increasingly being harnessed in the field of [[paper-based microfluidics]].<ref name="cappen" />

In physiology, capillary action is essential for the drainage of continuously produced [[tears|tear]] fluid from the eye. Two canaliculi of tiny diameter are present in the inner corner of the [[eyelid]], also called the [[Nasolacrimal duct|lacrimal ducts]]; their openings can be seen with the naked eye within the lacrymal sacs when the eyelids are everted.{{cn|date=January 2025}}

Wicking is the absorption of a liquid by a material in the manner of a candle wick.{{cn|date=January 2025}}

[[Paper towel]]s absorb liquid through capillary action, allowing a [[Fluid statics|fluid]] to be transferred from a surface to the towel. The small pores of a [[sponge (tool)|sponge]] act as small capillaries, causing it to absorb a large amount of fluid. Some textile fabrics are said to use capillary action to "wick" sweat away from the skin. These are often referred to as [[layered clothing#wicking-materials|wicking fabrics]], after the capillary properties of [[candle]] and lamp [[Candle wick|wicks]].{{cn|date=January 2025}}

Capillary action is observed in [[thin layer chromatography]], in which a solvent moves vertically up a plate via capillary action. In this case the pores are gaps between very small particles.{{cn|date=January 2025}}

Capillary action draws [[ink]] to the tips of [[fountain pen]] [[nib (pen)|nib]]s from a reservoir or cartridge inside the pen.{{cn|date=January 2025}}

With some pairs of materials, such as [[mercury (element)|mercury]] and glass, the [[intermolecular force]]s within the liquid exceed those between the solid and the liquid, so a [[wikt:convex|convex]] meniscus forms and capillary action works in reverse.{{cn|date=January 2025}}

In [[hydrology]], capillary action describes the attraction of water molecules to soil particles. Capillary action is responsible for moving [[groundwater]] from wet areas of the soil to dry areas. Differences in soil [[water potential|potential]] (<math>\Psi_m</math>) drive capillary action in soil.{{cn|date=January 2025}}

A practical application of capillary action is the capillary action siphon. Instead of utilizing a hollow tube (as in most siphons), this device consists of a length of cord made of a fibrous material (cotton cord or string works well). After saturating the cord with water, one (weighted) end is placed in a reservoir full of water, and the other end placed in a receiving vessel. The reservoir must be higher than the receiving vessel.<ref>{{Cite web |title=Capillary Action and Water {{!}} U.S. Geological Survey |url=https://www.usgs.gov/special-topics/water-science-school/science/capillary-action-and-water |access-date=2024-04-29 |website=www.usgs.gov}}</ref> A related but simplified capillary siphon only consists of two hook-shaped stainless-steel rods, whose surface is hydrophilic, allowing water to wet the narrow grooves between them.<ref>{{cite journal |last1=Wang |first1=Kaizhe |last2=Sanaei |first2=Pejman |last3=Zhang |first3=Jun |last4=Ristroph |first4=Leif |title=Open capillary siphons |journal=Journal of Fluid Mechanics |date=10 February 2022 |volume=932 |doi=10.1017/jfm.2021.1056 |bibcode=2022JFM...932R...1W }}</ref> Due to capillary action and gravity, water will slowly transfer from the reservoir to the receiving vessel. This simple device can be used to water houseplants when nobody is home. This property is also made use of in the [[Automatic lubricator#Wick feed lubricator|lubrication of steam locomotives]]: wicks of [[worsted|worsted wool]] are used to draw oil from reservoirs into delivery pipes leading to the [[Bearing (mechanical)|bearings]].<ref>{{cite book |last1=Ahrons |first1=Ernest Leopold |title=Lubrication of Locomotives |date=1922 |publisher=Locomotive Publishing Company |location=London |oclc=795781750 |page=26}}</ref>

=== In plants and animals ===

Capillary action is seen in many plants, and plays a part in [[transpiration]]. Water is brought high up in trees by branching; evaporation at the leaves creating depressurization; probably by [[osmotic pressure]] added at the roots; and possibly at other locations inside the plant, especially when gathering humidity with [[air root]]s.<ref>[http://npand.wordpress.com/2008/08/05/tree-physics-1/ Tree physics] {{webarchive|url=https://web.archive.org/web/20131128125015/http://npand.wordpress.com/2008/08/05/tree-physics-1/ |date=2013-11-28 }} at "Neat, Plausible And" scientific discussion website.</ref><ref>[http://www.wonderquest.com/Redwood.htm Water in Redwood and other trees, mostly by evaporation] {{webarchive|url=https://web.archive.org/web/20120129122454/http://www.wonderquest.com/Redwood.htm |date=2012-01-29 }} article at wonderquest website.</ref><ref>{{cite journal |last1=Poudel |first1=Sajag |last2=Zou |first2=An |last3=Maroo |first3=Shalabh C. |title=Disjoining pressure driven transpiration of water in a simulated tree |journal=Journal of Colloid and Interface Science |date=June 2022 |volume=616 |pages=895–902 |doi=10.1016/j.jcis.2022.02.108 |pmid=35259719 |arxiv=2111.10927 |bibcode=2022JCIS..616..895P }}</ref>

Capillary action for uptake of water has been described in some small animals, such as ''[[Ligia exotica]]''<ref>{{cite journal |vauthors=Ishii D, Horiguchi H, Hirai Y, Yabu H, Matsuo Y, Ijiro K, Tsujii K, Shimozawa T, Hariyama T, Shimomura M|title=Water transport mechanism through open capillaries analyzed by direct surface modifications on biological surfaces |journal=Scientific Reports |volume=3 |page=3024 |date=October 23, 2013 |doi=10.1038/srep03024 |pmid=24149467 |pmc=3805968 |bibcode=2013NatSR...3.3024I }}</ref> and ''[[Moloch horridus]]''.<ref>{{cite journal |last1=Bentley |first1=P. J. |last2=Blumer |first2=W. F. C. |title=Uptake of Water by the Lizard, Moloch horridus |journal=Nature |date=May 1962 |volume=194 |issue=4829 |pages=699–700 |doi=10.1038/194699a0 |pmid=13867381 |bibcode=1962Natur.194..699B }}</ref>

== Height of a meniscus ==
=== Capillary rise of liquid in a capillary ===
[[File:2014.06.17 Water height capillary.jpg|thumb|Water height in a capillary plotted against capillary diameter]]

The height ''h'' of a liquid column is given by [[Jurin's law]]<ref name="Bachelor">[[George Batchelor|G.K. Batchelor]], 'An Introduction To Fluid Dynamics', Cambridge University Press (1967) {{ISBN|0-521-66396-2}},</ref>
:<math>h={{2 \gamma \cos{\theta}}\over{\rho g r}},</math>
where <math>\scriptstyle \gamma </math> is the liquid-air [[surface tension]] (force/unit length), ''θ'' is the [[contact angle]], ''ρ'' is the [[density]] of liquid (mass/volume), ''g'' is the local [[gravitational acceleration|acceleration due to gravity]] (length/square of time<ref>Hsai-Yang Fang, john L. Daniels, Introductory Geotechnical Engineering: An Environmental Perspective</ref>), and ''r'' is the [[radius]] of tube.

As ''r'' is in the denominator, the thinner the space in which the liquid can travel, the further up it goes. Likewise, lighter liquid and lower gravity increase the height of the column.

For a water-filled glass tube in air at standard laboratory conditions, {{nowrap|''γ'' {{=}} 0.0728 N/m}} at 20{{nbsp}}°C, <!--
It is not possible to have a contact angle of "zero". It would be nice if this equation were to reflect a real world example to help those trying to understand they physics of capillary action.
--> {{nowrap|''ρ'' {{=}} 1000 kg/m<sup>3</sup>}}, and {{nowrap|''g'' {{=}} 9.81&nbsp;m/s<sup>2</sup>}}. Because water [[Wetting|spreads]] on clean glass, the effective equilibrium contact angle is approximately zero.{{fact|date=November 2024}} For these values, the height of the water column is
:<math>h\approx {{1.48 \times 10^{-5} \ \mbox{m}^2}\over r}.</math>

Thus for a {{convert|2|m|ft|abbr=on}} radius glass tube in lab conditions given above, the water would rise an unnoticeable {{convert|0.007|mm|in|abbr=on}}. However, for a {{convert|2|cm|in|abbr=on}} radius tube, the water would rise {{convert|0.7|mm|in|abbr=on}}, and for a {{convert|0.2|mm|in|abbr=on}} radius tube, the water would rise {{convert|70|mm|in|abbr=on}}.

=== Capillary rise of liquid between two glass plates ===
The product of layer thickness (''d'') and elevation height (''h'') is constant (''d''·''h''&nbsp;=&nbsp;constant), the two quantities are [[Proportionality (mathematics)#Inverse proportionality|inversely proportional]]. The surface of the liquid between the planes is [[hyperbola]].
<gallery caption="Water between two glass plates" widths="130px" mode="packed">
file:Kapilláris emelkedés 1.jpg
file:Kapilláris emelkedés 2.jpg
file:Kapilláris emelkedés 3.jpg
file:Kapilláris emelkedés 4.jpg
file:Kapilláris emelkedés 5.jpg
file:Kapilláris emelkedés 6.jpg
</gallery>

== Liquid transport in porous media ==
[[File:Capillary flow brick.jpg|thumb|Capillary flow in a brick, with a sorptivity of 5.0 mm·min<sup>−1/2</sup> and a porosity of 0.25.]]

When a dry porous medium is brought into contact with a liquid, it will absorb the liquid at a rate which decreases over time. When considering evaporation, liquid penetration will reach a limit dependent on parameters of temperature, humidity and permeability. This process is known as evaporation limited capillary penetration<ref name="cappen" /> and is widely observed in common situations including fluid absorption into paper and rising damp in concrete or masonry walls. For a bar shaped section of material with cross-sectional area ''A'' that is wetted on one end, the cumulative volume ''V'' of absorbed liquid after a time ''t'' is
:<math>V = AS\sqrt{t},</math>
where ''S'' is the [[sorptivity]] of the medium, in units of m·s<sup>−1/2</sup> or mm·min<sup>−1/2</sup>. This time dependence relation is similar to [[Washburn's equation]] for the wicking in capillaries and porous media.<ref>{{cite journal |last1=Liu |first1=Mingchao |last2=Wu |first2=Jian |last3=Gan |first3=Yixiang |last4=Hanaor |first4=Dorian A. H. |last5=Chen |first5=C. Q. |title=Evaporation Limited Radial Capillary Penetration in Porous Media |journal=Langmuir |date=27 September 2016 |volume=32 |issue=38 |pages=9899–9904 |doi=10.1021/acs.langmuir.6b02404 |pmid=27583455 }}</ref>  The quantity
:<math>i = \frac{V}{A}</math>
is called the cumulative liquid intake, with the dimension of length. The wetted length of the bar, that is the distance between the wetted end of the bar and the so-called ''wet front'', is dependent on the fraction ''f'' of the volume occupied by voids. This number ''f'' is the [[porosity]] of the medium; the wetted length is then
:<math>x = \frac{i}{f} = \frac{S}{f}\sqrt{t}.</math>
Some authors use the quantity ''S/f'' as the sorptivity.<ref name="hall-hoff">C. Hall, W.D. Hoff, Water transport in brick, stone, and concrete. (2002) [https://books.google.com/books?id=q-QOAAAAQAAJ&pg=PA131 page 131 on Google books] {{webarchive|url=https://web.archive.org/web/20140220042356/http://books.google.com/books?id=q-QOAAAAQAAJ&lpg=PA131&ots=tq5JxlmMUe&pg=PA131 |date=2014-02-20 }}</ref>

The above description is for the case where gravity and evaporation do not play a role.

Sorptivity is a relevant property of building materials, because it affects the amount of [[Damp (structural)#Rising damp|rising dampness]]. Some values for the sorptivity of building materials are in the table below.
{| class="wikitable"
|+Sorptivity of selected materials (source:<ref name="hall-hoff-p122">Hall and Hoff, p. 122</ref>)
|-
! Material || Sorptivity <br> (mm·min<sup>−1/2</sup>)
|-
| Aerated concrete || 0.50
|-
| Gypsum plaster || 3.50
|-
| Clay brick || 1.16
|-
| Mortar || 0.70
|-
| Concrete brick || 0.20
|}

== See also ==
* {{annotated link|Bond number}}
* {{annotated link|Bound water}}
* {{annotated link|Capillary fringe}}
* {{annotated link|Capillary pressure}}
* {{annotated link|Capillary wave}}
* {{annotated link|Capillary bridges}}
* {{annotated link|Damp proofing}}
* {{annotated link|Darcy's law}}
* {{annotated link|Frost flower}}
* {{annotated link|Frost heaving}}
* {{annotated link|Hindu milk miracle}}
* {{annotated link|Krogh model}}
* {{annotated link|Porosimetry}}
* {{annotated link|Needle ice}}
* {{annotated link|Surface tension}}
* {{annotated link|Washburn's equation}}
* {{annotated link|Young–Laplace equation}}

== References ==
{{reflist|30em}}

== Further reading ==
{{Commons category}}
* {{cite book|last1=de Gennes|first1=Pierre-Gilles|last2=Brochard-Wyart|first2=Françoise|last3=Quéré|first3=David|title=Capillarity and Wetting Phenomena|year=2004|doi=10.1007/978-0-387-21656-0|isbn=978-1-4419-1833-8|publisher=Springer New York}}

{{Topics in continuum mechanics}}
{{Authority control}}

[[Category:Fluid dynamics]]
[[Category:Hydrology]]
[[Category:Surface science]]
[[Category:Porous media]]