Capillary action

Capillary action (also known as capillarity, capillary motion, capillary rise, capillary effect, or wicking) describes the phenomenon of liquid movement within confined spaces, occurring independently of external forces like gravity.

This phenomenon is observable in various contexts, including the ascent of liquids between paintbrush bristles, within narrow tubes such as straws, in porous materials like paper and plaster, in certain non-porous substances such as clay and liquefied carbon fiber, and within biological cells.

Its occurrence is attributed to intermolecular interactions between the liquid and adjacent solid surfaces. When the tube's diameter is adequately narrow, the synergistic action of surface tension (resulting from cohesive forces within the liquid) and adhesive forces between the liquid and the container wall drives the liquid's movement.

Etymology

The term 'capillary' derives from the Latin word capillaris, signifying 'of or resembling hair'. This nomenclature reflects the minute, hair-like diameter characteristic of a capillary.

History

Leonardo da Vinci is credited with the earliest documented observation of capillary action. Niccolò Aggiunti, a former student of Galileo, is also reported to have conducted investigations into this phenomenon. By 1660, the Irish chemist Robert Boyle still considered capillary action a novel phenomenon. He documented observations by "some inquisitive French Men" who noted that water ascended to "some height in the Pipe" when a capillary tube was immersed. Boyle subsequently described an experiment involving the immersion of a capillary tube in red wine, followed by its exposure to a partial vacuum. His findings indicated that the vacuum exerted no discernible effect on the liquid's height within the capillary, suggesting that the behavior of liquids in such tubes stemmed from a mechanism distinct from that governing mercury barometers.

Other researchers promptly pursued Boyle's investigations. Certain scholars (e.g., Honoré Fabri, Jacob Bernoulli) posited that liquids ascended in capillaries due to the differential ease of entry for air versus liquids, resulting in reduced air pressure within the capillaries. Conversely, others (e.g., Isaac Vossius, Giovanni Alfonso Borelli, Louis Carré, Francis Hauksbee, Josia Weitbrecht) proposed that liquid particles were mutually attractive and also attracted to the capillary walls.

Despite ongoing experimental investigations throughout the 18th century, a comprehensive quantitative framework for capillary action was not established until 1805 by two researchers: Thomas Young from the United Kingdom and Pierre-Simon Laplace from France. They formulated the Young–Laplace equation, which describes capillary action. By 1830, the German mathematician Carl Friedrich Gauss had elucidated the boundary conditions that govern capillary action, specifically those at the liquid-solid interface. In 1871, the British physicist Sir William Thomson (subsequently Lord Kelvin) quantified the influence of the meniscus on a liquid's vapor pressure, a relationship now recognized as the Kelvin equation. Subsequently, the German physicist Franz Ernst Neumann (1798–1895) investigated the interaction between two immiscible liquids.

Albert Einstein's inaugural scientific publication, submitted to Annalen der Physik in 1900, focused on the subject of capillarity.

Phenomena and physics

The dynamic mechanism of capillary penetration in porous media is analogous to fluid flow within hollow tubes, given that both processes encounter resistance from viscous forces. Therefore, the capillary tube serves as a frequently employed device for illustrating this phenomenon. Upon immersing the lower extremity of a glass tube into a liquid, such as water, a concave meniscus develops. Adhesive forces between the fluid and the solid inner wall draw the liquid column upward until the liquid's mass generates gravitational forces capable of counteracting these intermolecular interactions. The contact perimeter between the liquid column's upper surface and the tube is directly proportional to the tube's radius, whereas the liquid column's weight is proportional to the square of its radius. Consequently, a narrower tube will facilitate a greater ascent of the liquid column compared to a wider tube, provided that the internal liquid molecules exhibit sufficient cohesion with those at the periphery.

Examples

Within the built environment, evaporation-limited capillary penetration contributes to the occurrence of rising damp in concrete and masonry structures. Conversely, in industrial applications and diagnostic medicine, this phenomenon is progressively being utilized within the domain of paper-based microfluidics.

In physiological contexts, capillary action plays a crucial role in the continuous drainage of tear fluid from the eye. The inner corner of the eyelid contains two minute canaliculi, also known as lacrimal ducts, whose openings are visible to the unaided eye within the lacrimal sacs when the eyelids are everted.

Paper towels utilize capillary action to absorb liquids, facilitating the transfer of fluid from a surface to the towel. Similarly, the numerous small pores within a sponge function as capillaries, enabling it to absorb substantial volumes of fluid. Certain textile fabrics are engineered to employ capillary action for "wicking" sweat away from the skin, a property that leads to their designation as "wicking fabrics," drawing an analogy to the capillary characteristics of candle and lamp wicks.

Capillary action is also evident in thin-layer chromatography, where a solvent ascends a plate vertically through this phenomenon. Here, the "pores" are effectively the interstitial spaces between minute particles.

Within fountain pens, capillary action is responsible for drawing ink from an internal reservoir or cartridge to the tips of the nibs.

In specific material combinations, such as mercury and glass, the intermolecular forces within the liquid surpass the adhesive forces between the solid and the liquid. This results in the formation of a convex meniscus and a reversal of the typical capillary action.

Within the field of hydrology, capillary action refers to the attractive forces between water molecules and soil particles. This process facilitates the movement of groundwater from saturated soil regions to drier ones. Variations in soil potential (${\displaystyle \Psi _{m}}$) are the primary drivers of capillary action in soil.

A practical application of capillary action is exemplified by the capillary action siphon. Unlike conventional siphons that employ a hollow tube, this device comprises a length of fibrous cord, such as cotton string. To operate, the cord is saturated with water, and one weighted end is submerged in a water reservoir, while the other end is positioned in a receiving vessel, which must be situated below the reservoir. A simpler, related capillary siphon design features only two hook-shaped stainless-steel rods with hydrophilic surfaces, which allow water to wet the narrow grooves between them. Through the combined effects of capillary action and gravity, water is gradually transferred from the reservoir to the receiving vessel. This straightforward apparatus can be employed for watering houseplants during absences. Furthermore, this principle is utilized in the lubrication systems of steam locomotives, where worsted wool wicks draw oil from reservoirs into delivery pipes that supply the bearings.

In Plants and Animals

Capillary action is observed in numerous plant species and contributes significantly to the process of transpiration. Water ascends to considerable heights in trees through a combination of factors: the branching vascular system, depressurization caused by evaporation from leaves, osmotic pressure generated at the roots, and potentially other internal mechanisms, particularly when air roots absorb humidity.

The uptake of water via capillary action has been documented in certain small animal species, including Ligia exotica and Moloch horridus.

Meniscus Height

Capillary Rise of Liquid

Jurin's law defines the height h of a liquid column as follows:

${\displaystyle h={{2\gamma \cos {\theta }} \over {\rho gr}},}$

In this equation, ${\displaystyle \scriptstyle \gamma }$ represents the liquid-air surface tension (expressed as force per unit length), θ denotes the contact angle, ρ signifies the liquid's density (mass per unit volume), g indicates the local acceleration due to gravity (length per unit time squared), and r refers to the radius of the tube.

Given that r resides in the denominator, a reduction in the liquid's travel space inversely correlates with an increase in its vertical ascent. Similarly, a less dense liquid and diminished gravitational force contribute to a greater column height.

Under standard laboratory conditions, a water-filled glass tube in air exhibits specific parameters: γ = 0.0728 N/m at 20°C, ρ = 1000 kg/m§910§, and g = 9.81 m/s§1516§. Due to water's tendency to spread on clean glass surfaces, the effective equilibrium contact angle approaches zero. Utilizing these specified values, the resulting height of the water column is calculated as:

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

Consequently, for a glass tube with a 2 m (6.6 ft) radius under the aforementioned laboratory conditions, the water would exhibit an imperceptible rise of 0.007 mm (0.00028 in). In contrast, a 2 cm (0.79 in) radius tube would result in a 0.7 mm (0.028 in) water rise, while a 0.2 mm (0.0079 in) radius tube would demonstrate a substantial 70 mm (2.8 in) ascent.

Capillary Rise of Liquid Between Parallel Glass Plates

The product of the layer thickness (d) and the elevation height (h) remains constant (d·h = constant), indicating an inverse proportionality between these two quantities. The liquid's surface situated between the planes assumes a hyperbolic configuration.

Liquid Transport within Porous Media

Upon contact with a liquid, a dry porous medium initiates liquid absorption at a rate that progressively diminishes over time. When evaporation is a factor, liquid penetration ultimately attains a limit determined by temperature, humidity, and permeability parameters. This phenomenon, termed evaporation-limited capillary penetration, is frequently observed in scenarios such as fluid absorption by paper and rising damp in concrete or masonry structures. For a bar-shaped material section with a cross-sectional area A, wetted at one extremity, the cumulative volume V of absorbed liquid after a duration t is expressed as:

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

In this equation, S represents the medium's sorptivity, quantified in units of m·s^−1/2 or mm·min^−1/2. This temporal dependency relationship bears resemblance to Washburn's equation, which describes wicking phenomena in capillaries and porous media. The subsequent quantity,

${\displaystyle i={\frac {V}{A}}}$

is designated as the cumulative liquid intake, possessing the dimension of length. The wetted length of the bar, defined as the distance between its wetted extremity and the wet front, is contingent upon the volumetric fraction f occupied by voids. This value, f, represents the medium's porosity; consequently, the wetted length is determined by:

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

It is noteworthy that certain researchers define sorptivity using the quantity S/f.

The preceding description pertains specifically to scenarios where gravitational forces and evaporative effects are negligible.

Sorptivity constitutes a significant property of building materials, directly impacting the degree of rising dampness. Representative sorptivity values for various construction materials are available.

Bond number – A dimensionless quantity employed in fluid dynamics.Pages displaying short descriptions of redirect targets

• Bond number – Dimensionless number in fluid dynamicsPages displaying short descriptions of redirect targets
• Bound water – A diminutive aqueous layer encapsulating mineral surfaces.
• Capillary action through synthetic mesh.
• Capillary fringe – A subsurface stratum where groundwater ascends from a water table via capillary action.
• Capillary pressure – The pressure differential observed between two fluids, arising from interfacial forces between the fluids and the confining tube walls.
• Capillary wave – A wave propagating on a fluid's surface, primarily governed by surface tension.
• Capillary bridges – A minimized liquid surface connecting two wetted objects.Pages displaying short descriptions of redirect targets
• Damp proofing – A method of moisture management implemented in building construction.
• Darcy's law – An equation delineating the flow characteristics of a fluid traversing a porous medium.
• Frost flower – A delicate ice layer extruded from a plant.
• Frost heaving – The upward expansion of soil occurring during freezing conditions.
• Hindu milk miracle – Alleged miraculous occurrences reported in 1995.Pages displaying short descriptions of redirect targets
• Krogh model.
• Porosimetry – The process of measuring and characterizing a material's porosity.
• Needle ice – An ice column that forms when liquid groundwater ascends into freezing atmospheric conditions.
• Surface tension – The inherent tendency of a liquid surface to contract, thereby minimizing its surface area.
• Washburn's equation – An equation that describes the penetration depth of a liquid into a capillary tube over time.
• Young–Laplace equation – An equation that characterizes the pressure differential across an interface in fluid mechanics.

References

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.

• 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.Source: TORIma Academy Archive