Capillary action





Capillary action (sometimes called capillarity, capillary motion, capillary rise, capillary effect, or wicking) is the process of a liquid flowing in a narrow space in opposition to or at least without the assistance of any external forces like 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 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 forces 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 within the liquid) and 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.

History
The first recorded observation of capillary action was by Leonardo da Vinci. 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, page 54 .  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 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 page 551 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; ... ) A former student of Galileo, Niccolò Aggiunti, was said to have investigated capillary action. 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.

Others soon followed Boyle's lead. 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, "Observ. IV.  Of small Glass Canes."
 * Geminiano Montanari, Pensieri fisico-matematici sopra alcune esperienze fatte in Bologna ... [Physical-mathematical ideas about some experiments done in Bologna ... ] (Bologna, (Italy):  1667).
 * George Sinclair, Ars Nova et Magna Gravitatis et Levitatis [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:  "Tentamen VIII.  Canaliculorum angustiorum recens-notata Phænomena, ... "  (Essay 8. Recently noted phenomena of narrow capillaries, ... ), pp. 44–48. Some (e.g., Honoré Fabri, Jacob Bernoulli ) 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, Giovanni Alfonso Borelli, Louis Carré, Francis Hauksbee, Josia Weitbrecht ) 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, 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:  Archive.org.
 * Gaspard Monge (1746–1818) investigated the force between panes of glass that were separated by a film of liquid. See:  Gaspard Monge (1787) "Mémoire sur quelques effets d'attraction ou de répulsion apparente entre les molécules de matière"  (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].) a successful quantitative treatment of capillary action was not attained until 1805 by two investigators: Thomas Young of the United Kingdom and Pierre-Simon Laplace of France. 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). In 1871, the British physicist Sir William Thomson (later Lord Kelvin) determined the effect of the meniscus on a liquid's vapor pressure—a relation known as the Kelvin equation. German physicist Franz Ernst Neumann (1798–1895) subsequently determined the interaction between two immiscible liquids.

Albert Einstein's first paper, which was submitted to Annalen der Physik in 1900, was on capillarity.

Phenomena and physics


Capillary penetration in porous media shares its dynamic mechanism with flow in hollow tubes, as both processes are resisted by viscous forces. 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 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 forces 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.

Examples
In the built environment, evaporation limited capillary penetration is responsible for the phenomenon of 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.

In physiology, capillary action is essential for the drainage of continuously produced tear fluid from the eye. Two canaliculi of tiny diameter are present in the inner corner of the eyelid, also called the lacrimal ducts; their openings can be seen with the naked eye within the lacrymal sacs when the eyelids are everted.

Wicking is the absorption of a liquid by a material in the manner of a candle wick.

Paper towels absorb liquid through capillary action, allowing a fluid to be transferred from a surface to the towel. The small pores of a 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 wicking fabrics, after the capillary properties of candle and lamp wicks.

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.

Capillary action draws ink to the tips of fountain pen nibs from a reservoir or cartridge inside the pen.

With some pairs of materials, such as mercury and glass, the intermolecular forces within the liquid exceed those between the solid and the liquid, so a convex meniscus forms and capillary action works in reverse.

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 potential ($$\Psi_m$$) drive capillary action in soil.

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. 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. 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 lubrication of steam locomotives: wicks of worsted wool are used to draw oil from reservoirs into delivery pipes leading to the bearings.

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 roots.

Capillary action for uptake of water has been described in some small animals, such as Ligia exotica and Moloch horridus.

Capillary rise of liquid in a capillary


The height h of a liquid column is given by Jurin's law
 * $$h={{2 \gamma \cos{\theta}}\over{\rho g r}},$$

where $$\scriptstyle \gamma $$ 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 acceleration due to gravity (length/square of time ), 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, at 20°C, , and. Because water spreads on clean glass, the effective equilibrium contact angle is approximately zero. For these values, the height of the water column is
 * $$h\approx {{1.48 \times 10^{-5} \ \mbox{m}^2}\over r}.$$

Thus for a 2 m radius glass tube in lab conditions given above, the water would rise an unnoticeable 0.007 mm. However, for a 2 cm radius tube, the water would rise 0.7 mm, and for a 0.2 mm radius tube, the water would rise 70 mm.

Capillary rise of liquid between two glass plates
The product of layer thickness (d) and elevation height (h) is constant (d·h = constant), the two quantities are inversely proportional. The surface of the liquid between the planes is hyperbola.

Liquid transport in porous media


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 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
 * $$V = AS\sqrt{t},$$

where S is the sorptivity of the medium, in units of m·s−1/2 or mm·min−1/2. This time dependence relation is similar to Washburn's equation for the wicking in capillaries and porous media. The quantity
 * $$i = \frac{V}{A}$$

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
 * $$x = \frac{i}{f} = \frac{S}{f}\sqrt{t}.$$

Some authors use the quantity S/f as the sorptivity.

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 rising dampness. Some values for the sorptivity of building materials are in the table below.