What is the ability of a liquid to move through a tube?

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Capillary action can be defined as the ascension of liquids through slim tube, cylinder or permeable substance due to adhesive and cohesive forces interacting between the liquid and the surface. When intermolecular bonding of a liquid itself is substantially inferior to a substances’ surface it is interacting, capillarity occurs. Also, the diameter of the container as well as the gravitational forces will determine amount of liquid raised. While, water possesses this unique property, a liquid like mercury will not display the same attributes due to the fact that it has higher cohesive force than adhesive force.

Three main variables that determine whether a liquid possesses capillary action are:

• Cohesive force: It is the intermolecular bonding of a substance where its mutual attractiveness forces them to maintain a certain shape of the liquid.
• Surface tension: This occurs as a result of like molecules, cohesive forces, banding together to form a somewhat impenetrable surface on the body of water. The surface tension is measured in Newton/meter.
• Adhesive force: When forces of attraction between unlike molecules occur, it is called adhesive forces.

Capillary action only occurs when the adhesive forces are stronger than the cohesive forces, which invariably becomes surface tension, in the liquid.

Figure \(\PageIndex{1}\): It is possible to see that in water, the strength of the adhesive forces are larger than the strength of the cohesive forces. This results in the concave formation of water in the capillary tube; this is known as capillary attraction. Alternatively for mercury, the cohesive forces are stronger than the adhesive forces which allows the the meniscus to bend away from the walls of the capillary tube. This is known as capillary Repulsion. ​ commons.wikimedia.org/wiki/Fi...(PSF)(bjl).svg

A good way to remember the difference between adhesive and cohesive forces is that with adhesive forces you add another set of molecules, the molecules of the surface, for the liquid to bond with. With cohesive forces, the molecules of the liquid will only cooperate with their own kind. Decreased surface tension also increases capillary action. This is because decreased surface tension means that the intermolecular forces are decreased, thus decreasing cohesive forces. As a result, capillary action will be even greater.

Figure \(\PageIndex{2}\): Scalable illustration of capillary action for large and small bore capillaries, and for positive and negative contact angles. (Public Domain; Eduard Konečný via Wikipedia).

Practical use of capillary action is evident in all forms of our daily lives. It makes performing our tasks efficiently and effectively. Some applications of this unique property include:

• The fundamental properties are used to absorb water by using paper towels. The cohesive and adhesive properties draw the fluid into the paper towel. The liquid flows into the paper towel at a certain rate.
• A technique called thin layer chromatography uses capillary action in which a layer of liquid is used to separate mixtures from substances.
• Capillary action helps us naturally by pumping out tear fluid in the eye. This process cleanses the eye and clears all of the dust and particles that are around the ducts of the eye.
• To generate energy: A possible use for capillary action is as a source of renewable energy. By allowing water to climb through capillaries, evaporate once it reaches the top, the condensate and drop back down to the bottom spinning a turbine on its way to create the energy, capillary action can make electricity! Although this idea is still in the works, it goes to show the potential that capillary action holds and how important it is.

Figure \(\PageIndex{3}\): Capillary action is evident in nature all around us. The properties allow the water to be transpired by the xylem in the plant. The water starts in the roots and proceeds upward to the highest branches of the plant. commons.wikimedia.org/wiki/File:GemeineFichte.jpg

When measuring the level of liquid of a test tube or buret, it is imperative to measure at the meniscus line for an accurate reading. It is possible to measure the height (represented by h) of a test tube, buret, or other liquid column using the formula:

\[ h = \dfrac{2\gamma \cos\theta}{\rho\;g\;r} \]

In this formula,

• γ represents the surface tension in a liquid-air environment,
• θ is the angle of contact or the degree of contact,
• ρ is the density of the liquid in the representative column,
• g is the acceleration due to the force of gravity and
• r is the radius of the tube in which the liquid is presented in.

At optimum level, in which a glass tube filled with water is present in air, this formula can determine the height of a specific column of water in meters (m):

\[ h\approx\dfrac{1.4 \times 10^{-5}}{r}\]

However, the following conditions must be met for this formula to occur.

• γ= 0.0728 N/m (when water is at a temperature of 20°C)
• θ= 20°
• ρis 1000 kg/m3
• g= 9.8 m/s2

When certain objects that are porous encounter a liquid medium, it will begin to absorb the liquid at a rate which actually decreases over a period of time. This formula is written as:

\[ V = S*A\sqrt{t} \]

In this specific formula,

• A is the wet area (cross-section),
• S is the sorptivity (capacity of medium to absorb using the process of capillary action),
• V is the volume of liquid absorbed in time, t.

1. Name one way to increase capillary action, and one way to decrease it.
2. If cohesion is greater than adhesion, will the meniscus be convex or concave?
3. What would be the height of a liquid in a column, on earth, with a liquid-air surface tension 0f .0973 N/m, contact angle of 30 degrees, density of 1200 kg/m3? Note that the radius of the tube is 0.2 meters.
4. What would be the height of water in a glass tube with a radius of .6mm?

Solutions

1. Increase capillary action: Increase temperature, decrease capillary tube diameter, perform any number of actions to decrease surface tension, etc…! Decrease capillary action: The opposite of the steps you would take to increase, also, increasing the density of the liquid you're working with.
2. The meniscus will result in a convex formation.
3. Using the formula above, the height of the liquid will be 7.165* 10-5m high.
4. Using the formula above, the height of the water in the glass tube would be .014m high.

References

1. Petrucci, Ralph, and William Harwood. F. Geoffrey Herring. Jeffry Madura. General Chemistry: Principles and Modern Applications. 9th ed. Upper Saddle River, NJ: Pearson, 2007.
2. Cyclical Gravity Greenhouse Liquid Capillary Action Energy Generator, R Smith, 9.11.2005 14:38,
3. Capillary Action, Wikipedia

4. Capillary Action, from USGS Water Science for Schools." USGS Georgia Water Science Center - Home Page. Web. 04 June 2011.

Contributors and Attributions

• Achille Peiris, Becky Stein

Ability of a liquid to flow in narrow spaces

This article is about the physical phenomenon. For the band, see Capillary Action (band).

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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%.

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Capillary action of water (polar) compared to 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, or even in opposition to, 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, in porous materials such as paper and plaster, in some non-porous materials such as sand 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.[citation needed]

Etymology

Capillary comes from the Latin word capillaris, meaning "of or resembling hair." The meaning stems from the tiny, hairlike diameter of a capillary. While capillary is usually used as a noun, the word also is used as an adjective, as in "capillary action," in which a liquid is moved along — even upward, against gravity — as the liquid is attracted to the internal surface of the capillaries.

History

The first recorded observation of capillary action was by Leonardo da Vinci.[1][2] A former student of Galileo, Niccolò Aggiunti, was said to have investigated capillary action.[3] 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.[4]

Others soon followed Boyle's lead.[5] Some (e.g., Honoré Fabri,[6] Jacob Bernoulli[7]) 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,[8] Giovanni Alfonso Borelli,[9] Louis Carré,[10] Francis Hauksbee,[11] Josia Weitbrecht[12]) 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,[13] a successful quantitative treatment of capillary action[14] was not attained until 1805 by two investigators: Thomas Young of the United Kingdom[15] and Pierre-Simon Laplace of France.[16] 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).[17] 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.[18] German physicist Franz Ernst Neumann (1798–1895) subsequently determined the interaction between two immiscible liquids.[19]

Albert Einstein's first paper, which was submitted to Annalen der Physik in 1900, was on capillarity.[20][21]

Phenomena and physics

Moderate rising damp on an internal wall

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.[22] 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.[22]

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 ( Ψ m {\displaystyle \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.[citation needed] 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. [23] 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.[24]

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.[25][26]

Capillary action for uptake of water has been described in some small animals, such as Ligia exotica[27] and Moloch horridus.[28]

Height of a meniscus

Capillary rise of liquid in a capillary

Water height in a capillary plotted against capillary diameter

The height h of a liquid column is given by Jurin's law[29]

h = 2 γ cos ⁡ θ ρ g r , {\displaystyle h={{2\gamma \cos {\theta }} \over {\rho gr}},}

where γ {\displaystyle \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[30]), 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, γ = 0.0728 N/m at 20 °C, ρ = 1000 kg/m3, and g = 9.81 m/s2. Because water spreads on clean glass, the effective equilibrium contact angle is approximately zero.[31] For these values, the height of the water column is

h ≈ 1.48 × 10 − 5   m 2 r . {\displaystyle h\approx {{1.48\times 10^{-5}\ {\mbox{m}}^{2}} \over r}.}

Thus for a 2 m (6.6 ft) radius glass tube in lab conditions given above, the water would rise an unnoticeable 0.007 mm (0.00028 in). However, for a 2 cm (0.79 in) radius tube, the water would rise 0.7 mm (0.028 in), and for a 0.2 mm (0.0079 in) radius tube, the water would rise 70 mm (2.8 in).

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.

• Water between two glass plates

Liquid transport in porous media

Capillary flow in a brick, with a sorptivity of 5.0 mm·min−1/2 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 [22] 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 = A S t , {\displaystyle 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.[32] The quantity

i = V A {\displaystyle 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 = i f = S f t . {\displaystyle x={\frac {i}{f}}={\frac {S}{f}}{\sqrt {t}}.}

Some authors use the quantity S/f as the sorptivity.[33] 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.

Sorptivity of selected materials (source:[34]) Material Sorptivity
(mm·min−1/2)

Aerated concrete	0.50
Gypsum plaster	3.50
Clay brick	1.16
Mortar	0.70
Concrete brick	0.20

See also

• Bond number
• Bound water
• Capillary fringe
• Capillary pressure
• Capillary wave
• Capillary bridges
• Damp-proof course
• Darcy's law
• Frost flowers
• Frost heaving
• Hindu milk miracle
• Krogh model
• Mercury intrusion porosimetry
• Needle ice
• Surface tension
• Washburn's equation
• Young–Laplace equation

References

1. ^ 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 Archived 2016-12-24 at the Wayback Machine. 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 Archived 2014-06-29 at the Wayback Machine 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; ... )
2. ^ 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, pp. 805–823 Archived 2016-12-24 at the Wayback Machine.
   • Maxwell, James Clerk; Strutt, John William (1911). "Capillary Action" . In Chisholm, Hugh (ed.). Encyclopædia Britannica. Vol. 5 (11th ed.). Cambridge University Press. pp. 256–275.
   • John Uri Lloyd (1902) "References to capillarity to the end of the year 1900," Archived 2014-12-14 at the Wayback Machine Bulletin of the Lloyd Library and Museum of Botany, Pharmacy and Materia Medica, 1 (4) : 99–204.
3. ^ 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), pp. 91–92. Archived 2014-07-27 at the Wayback Machine
4. ^ Robert Boyle, New Experiments Physico-Mechanical touching the Spring of the Air, ... (Oxford, England: H. Hall, 1660), pp. 265–270. Available on-line at: Echo (Max Planck Institute for the History of Science; Berlin, Germany) Archived 2014-03-05 at the Wayback Machine.
5. ^ 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." Archived 2016-12-24 at the Wayback Machine
   • Geminiano Montanari, Pensieri fisico-matematici sopra alcune esperienze fatte in Bologna ... Archived 2016-12-29 at the Wayback Machine [Physical-mathematical ideas about some experiments done in Bologna ... ] (Bologna, (Italy): 1667).
   • George Sinclair, Ars Nova et Magna Gravitatis et Levitatis Archived 2017-11-03 at the Wayback Machine [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, ... " Archived 2014-06-29 at the Wayback Machine (Essay 8. Recently noted phenomena of narrow capillaries, ... ), pp. 44–48.
6. ^ See:
   • Honorato Fabri, Dialogi physici ... ((Lyon (Lugdunum), France: 1665), pages 157 ff Archived 2016-12-24 at the Wayback Machine "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), pages 267 ff Archived 2017-04-07 at the Wayback Machine "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).
7. ^ Jacob Bernoulli, Dissertatio de Gravitate Ætheris Archived 2017-04-07 at the Wayback Machine (Amsterdam, Netherlands: Hendrik Wetsten, 1683).
8. ^ Isaac Vossius, De Nili et Aliorum Fluminum Origine [On the sources of the Nile and other rivers] (Hague (Hagæ Comitis), Netherlands: Adrian Vlacq, 1666), pages 3–7 Archived 2017-04-07 at the Wayback Machine (chapter 2).
9. ^ 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: Echo (Max Planck Institute for the History of Science; Berlin, Germany) Archived 2016-12-23 at the Wayback Machine.
10. ^ Carré (1705) "Experiences sur les tuyaux Capillaires" Archived 2017-04-07 at the Wayback Machine (Experiments on capillary tubes), Mémoires de l'Académie Royale des Sciences, pp. 241–254.
11. ^ See:
    • Francis Hauksbee (1708) "Several Experiments Touching the Seeming Spontaneous Ascent of Water," Archived 2014-06-29 at the Wayback Machine 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) "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) "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.
12. ^ See:
    • Josia Weitbrecht (1736) "Tentamen theoriae qua ascensus aquae in tubis capillaribus explicatur" Archived 2014-06-29 at the Wayback Machine (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.
    • Josia Weitbrecht (1737) "Explicatio difficilium experimentorum circa ascensum aquae in tubis capillaribus" Archived 2014-11-05 at the Wayback Machine (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.
13. ^ 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 Archived 2016-03-17 at the Wayback Machine.
    • 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" Archived 2016-03-16 at the Wayback Machine (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].)
14. ^ In the 18th century, some investigators did attempt a quantitative treatment of capillary action. See, for example, 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), pages 105–128. Archived 2016-04-09 at the Wayback Machine
15. ^ Thomas Young (January 1, 1805) "An essay on the cohesion of fluids," Archived 2014-06-30 at the Wayback Machine Philosophical Transactions of the Royal Society of London, 95 : 65–87.
16. ^ Pierre Simon marquis de Laplace, Traité de Mécanique Céleste, volume 4, (Paris, France: Courcier, 1805), Supplément au dixième livre du Traité de Mécanique Céleste, pages 1–79 Archived 2016-12-24 at the Wayback Machine.
17. ^ 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: Hathi Trust.
18. ^ William Thomson (1871) "On the equilibrium of vapour at a curved surface of liquid," Archived 2014-10-26 at the Wayback Machine Philosophical Magazine, series 4, 42 (282) : 448–452.
19. ^ Franz Neumann with A. Wangerin, ed., Vorlesungen über die Theorie der Capillarität [Lectures on the theory of capillarity] (Leipzig, Germany: B. G. Teubner, 1894).
20. ^ Albert Einstein (1901) "Folgerungen aus den Capillaritätserscheinungen" Archived 2017-10-25 at the Wayback Machine (Conclusions [drawn] from capillary phenomena), Annalen der Physik, 309 (3) : 513–523.
21. ^ Hans-Josef Kuepper. "List of Scientific Publications of Albert Einstein". Einstein-website.de. Archived from the original on 2013-05-08. Retrieved 2013-06-18.
22. ^ a b c Liu, Mingchao; Wu, Jian; Gan, Yixiang; Hanaor, Dorian A.H.; Chen, C.Q. (2018). "Tuning capillary penetration in porous media: Combining geometrical and evaporation effects" (PDF). International Journal of Heat and Mass Transfer. 123: 239–250. doi:10.1016/j.ijheatmasstransfer.2018.02.101. S2CID 51914846.
23. ^ Wang, K.; et al. (2022). "Open Capillary Siphons". Journal of Fluid Mechanics. Cambridge University Press. 932. Bibcode:2022JFM...932R...1W. doi:10.1017/jfm.2021.1056. S2CID 244957617.
24. ^ Ahrons, Ernest Leopold (1922). Lubrication of Locomotives. London: Locomotive Publishing Company. p. 26. OCLC 795781750.
25. ^ Tree physics Archived 2013-11-28 at the Wayback Machine at "Neat, Plausible And" scientific discussion website.
26. ^ Water in Redwood and other trees, mostly by evaporation Archived 2012-01-29 at the Wayback Machine article at wonderquest website.
27. ^ Ishii D, Horiguchi H, Hirai Y, Yabu H, Matsuo Y, Ijiro K, Tsujii K, Shimozawa T, Hariyama T, Shimomura M (October 23, 2013). "Water transport mechanism through open capillaries analyzed by direct surface modifications on biological surfaces". Scientific Reports. 3: 3024. Bibcode:2013NatSR...3E3024I. doi:10.1038/srep03024. PMC 3805968. PMID 24149467.
28. ^ Bentley PJ, Blumer WF (1962). "Uptake of water by the lizard, Moloch horridus". Nature. 194 (4829): 699–670 (1962). Bibcode:1962Natur.194..699B. doi:10.1038/194699a0. PMID 13867381. S2CID 4289732.
29. ^ G.K. Batchelor, 'An Introduction To Fluid Dynamics', Cambridge University Press (1967) ISBN 0-521-66396-2,
30. ^ Hsai-Yang Fang, john L. Daniels, Introductory Geotechnical Engineering: An Environmental Perspective
31. ^ "Capillary Tubes - an overview | ScienceDirect Topics". www.sciencedirect.com. Retrieved 2021-10-29.
32. ^ Liu, M.; et al. (2016). "Evaporation limited radial capillary penetration in porous media" (PDF). Langmuir. 32 (38): 9899–9904. doi:10.1021/acs.langmuir.6b02404. PMID 27583455.
33. ^ C. Hall, W.D. Hoff, Water transport in brick, stone, and concrete. (2002) page 131 on Google books Archived 2014-02-20 at the Wayback Machine
34. ^ Hall and Hoff, p. 122

Further reading

Wikimedia Commons has media related to Capillary action.

• de Gennes, Pierre-Gilles; Brochard-Wyart, Françoise; Quéré, David (2004). Capillarity and Wetting Phenomena. Springer New York. doi:10.1007/978-0-387-21656-0. ISBN 978-1-4419-1833-8.

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