capillary action

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Capillary action (sometimes capillarity, capillary motion, capillary effect, or wicking) is the ability of a
liquid A liquid is a nearly incompressible In fluid mechanics or more generally continuum mechanics, incompressible flow (isochoric process, isochoric flow) refers to a fluid flow, flow in which the material density is constant within a fluid parc ...

to flow in narrow spaces without the assistance of, or even in opposition to, external forces like
gravity Gravity (), or gravitation, is a by which all things with or —including s, s, , and even —are attracted to (or ''gravitate'' toward) one another. , gravity gives to s, and the causes the s of the oceans. The gravitational attracti ...

. 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 Carbon fiber reinforced polymer (American English American English (AmE, AE, AmEng, USEng, en-US), sometimes called United States English or U.S. English, is the set of varieties of the English language native to the United States. Curr ...

, or in a
biological cell The cell (from Latin ''cella'', meaning "small room") is the basic structural, functional, and biological unit of all known organisms. Cells are the smallest units of life, and hence are often referred to as the "building blocks of life". The s ...

. It occurs because of
intermolecular force Intermolecular forces (IMF) (or secondary forces) are the forces which mediate interaction between molecules, including forces of attraction or repulsion which act between atoms and other types of neighboring particles, e.g. atom An atom is the ...

s between the liquid and surrounding solid surfaces. If the diameter of the tube is sufficiently small, then the combination of
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(which is caused by cohesion within the liquid) and between the liquid and container wall act to propel the liquid.

# History

The first recorded observation of capillary action was by
Leonardo da Vinci Leonardo di ser Piero da Vinci (15 April 14522 May 1519) was an Italian polymath of the High Renaissance who was active as a painter, Drawing, draughtsman, engineer, scientist, theorist, sculptor and architect. While his fame initially rest ...

. A former student of
Galileo Galileo di Vincenzo Bonaiuti de' Galilei ( , ; 15 February 1564 – 8 January 1642), commonly referred to as Galileo, was an astronomer, physicist and engineer, sometimes described as a polymath, from Pisa, in modern-day Italy. Galileo h ...

, Niccolò Aggiunti, was said to have investigated capillary action. In 1660, capillary action was still a novelty to the Irish chemist
Robert Boyle Robert Boyle (; 25 January 1627 – 31 December 1691) was an Anglo-Irish natural philosopher, chemist, physicist, and inventor. Boyle is largely regarded today as the first modern chemist, and therefore one of the founders of modern che ...

, 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. Some (e.g., ,
Jacob Bernoulli Jacob Bernoulli (also known as James or Jacques; – 16 August 1705) was one of the many prominent mathematicians in the Bernoulli family. He was an early proponent of Leibnizian calculus and sided with Gottfried Wilhelm Leibniz during the Leibn ...
) 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 Isaak Vossius, sometimes anglicised Isaac Voss (1618 in Leiden Leiden (, ; in English language, English and Archaism, archaic Dutch language, Dutch also ''Leyden'') is a List of cities in the Netherlands by province, city and List of munici ...
,
Giovanni Alfonso Borelli Giovanni Alfonso Borelli (; 28 January 1608 – 31 December 1679) was a Renaissance Italy, Italian physiologist, physicist, and mathematician. He contributed to the modern principle of scientific investigation by continuing Galileo Galilei, Galileo ...

, Louis Carré,
Francis Hauksbee Francis Hauksbee the Elder FRS (1660–1713), also known as Francis Hawksbee, was an 18th-century English scientist best known for his work on electricity Electricity is the set of physical phenomena associated with the presence and moti ...
, Josias Weitbrecht, 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, a successful quantitative treatment of capillary action was not attained until 1805 by two investigators: Thomas Young (scientist), 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 William Thomson, 1st Baron Kelvin determined the effect of the Meniscus (liquid), 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 (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 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.

# In plants and animals

Capillary action is seen in many plants. 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''.

# 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. 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. 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 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. 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 nib (pen), nibs from a reservoir or cartridge inside the pen. With some pairs of materials, such as mercury (element), mercury and glass, the
intermolecular force Intermolecular forces (IMF) (or secondary forces) are the forces which mediate interaction between molecules, including forces of attraction or repulsion which act between atoms and other types of neighboring particles, e.g. atom An atom is the ...

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. 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 ($\Psi_m$) 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. 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.

# Height of a meniscus

## Capillary rise of liquid in a capillary

The height ''h'' of a liquid column is given by Jurin's lawGeorge Batchelor, G.K. Batchelor, 'An Introduction To Fluid Dynamics', Cambridge University Press (1967) , :$h=,$ where $\scriptstyle \gamma$ is the liquid-air
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(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), and ''r'' is the radius of tube. Thus the thinner the space in which the water can travel, the further up it goes. For a water-filled glass tube in air at standard laboratory conditions, at 20°C, , and . For these values, the height of the water column is :$h\approx .$ Thus for a radius glass tube in lab conditions given above, the water would rise an unnoticeable . However, for a radius tube, the water would rise , and for a radius tube, the water would rise .

## 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 Proportionality_(mathematics)#Inverse_proportionality, inversely proportional. The surface of the liquid between the planes is hyperbola. 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

# 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 :$V = AS\sqrt,$ 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 :$i = \frac$ 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 :$x = \frac = \frac\sqrt.$ Some authors use the quantity ''S/f'' as the sorptivity.C. Hall, W.D. Hoff, Water transport in brick, stone, and concrete. (2002