Editing Capillary action (section)

== 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
|}