View source for Liquid

{{Short description|State of matter}}
{{Other uses}}
{{pp-semi-indef}}
[[File:Water drop 001.jpg|thumb|300px|The formation of a spherical [[drop (liquid)|droplet]] of liquid [[water]] minimizes the [[surface area]], which is the natural result of [[surface tension]] in liquids.]]
{{Continuum mechanics|fluid}}

A '''liquid''' is a nearly [[compressibility|incompressible]] [[fluid]] that conforms to the shape of its container but retains a nearly constant volume independent of pressure. It is one of [[State of matter#Four fundamental states|the four fundamental states of matter]] (the others being [[solid]], [[gas]], and [[Plasma (physics)|plasma]]), and is the only state with a definite volume but no fixed shape.

The [[density]] of a liquid is usually close to that of a solid, and much higher than that of a gas. Therefore, liquid and solid are both termed [[Condensed matter physics|condensed matter]]. On the other hand, as liquids and gases share the ability to flow, they are both called fluids.

A liquid is made up of tiny vibrating particles of matter, such as atoms, held together by [[intermolecular bonds]]. Like a gas, a liquid is able to flow and take the shape of a container. Unlike a gas, a liquid maintains a fairly constant density and does not disperse to fill every space of a container.

Although liquid water is abundant on Earth, this state of matter is actually the least common in the known universe, because liquids require a relatively narrow temperature/pressure range to exist. Most known matter in the universe is either gas (as [[interstellar cloud]]s) or plasma (as [[star]]s).

{{toclimit|limit=3}}

==Introduction==
[[File:Hot and cold water immiscibility thermal image.jpg|thumb|Thermal image of a sink full of hot water with cold water being added, showing how the hot and the cold water flow into each other]]
Liquid is one of the [[state of matter|four primary states of matter]], with the others being solid, gas and [[Plasma (physics)|plasma]]. A liquid is a [[fluid]]. Unlike a solid, the [[molecule]]s in a liquid have a much greater freedom to move. The forces that bind the molecules together in a solid are only temporary in a liquid, allowing a liquid to flow while a solid remains rigid.

A liquid, like a gas, displays the properties of a fluid. A liquid can flow, assume the shape of a container, and, if placed in a sealed container, will distribute applied pressure evenly to every surface in the container. If liquid is placed in a bag, it can be squeezed into any shape. Unlike a gas, a liquid is nearly incompressible, meaning that it occupies nearly a constant volume over a wide range of pressures; it does not generally expand to fill available space in a container but forms its own surface, and it may not always mix readily with another liquid. These properties make a liquid suitable for applications such as [[hydraulics]].

Liquid particles are bound firmly but not rigidly. They are able to move around one another freely, resulting in a limited degree of particle mobility. As the temperature increases, the increased vibrations of the molecules causes distances between the molecules to increase. When a liquid reaches its [[boiling point]], the cohesive forces that bind the molecules closely together break, and the liquid changes to its gaseous state (unless [[superheating]] occurs). If the temperature is decreased, the distances between the molecules become smaller. When the liquid reaches its [[Melting point|freezing point]] the molecules will usually lock into a very specific order, called crystallizing, and the bonds between them become more rigid, changing the liquid into its solid state (unless [[supercooling]] occurs).

==Examples==
Only two [[chemical element|elements]] are liquid at [[standard conditions for temperature and pressure]]: [[mercury (element)|mercury]] and [[bromine]]. Four more elements have melting points slightly above [[room temperature]]: [[francium]], [[caesium]], [[gallium]] and [[rubidium]].<ref>Theodore Gray, The Elements: A Visual Exploration of Every Known Atom in the Universe New York: Workman Publishing, 2009, p. 127 {{ISBN|1-57912-814-9}}</ref> In addition, certain mixtures of elements are liquid at room temperature, even if the individual elements are solid under the same conditions (see [[eutectic mixture]]). An example is the sodium-potassium metal alloy [[NaK]].<ref name="Leonchuk2022">{{cite journal | last1=Leonchuk | first1=Sergei S. | last2=Falchevskaya | first2=Aleksandra S. | last3=Nikolaev | first3=Vitaly | last4=Vinogradov | first4=Vladimir V. | title=NaK alloy: underrated liquid metal | journal=Journal of Materials Chemistry A | publisher=Royal Society of Chemistry (RSC) | volume=10 | issue=43 | year=2022 | issn=2050-7488 | doi=10.1039/d2ta06882f | pages=22955–22976| s2cid=252979251 }}</ref> Other metal alloys that are liquid at room temperature include [[galinstan]], which is a gallium-indium-tin alloy that melts at {{convert|-19|°C|°F}}, as well as some [[amalgam (chemistry)|amalgams]] (alloys involving mercury).<ref name="Surmann2005">{{cite journal | last1=Surmann | first1=Peter | last2=Zeyat | first2=Hanan | title=Voltammetric analysis using a self-renewable non-mercury electrode | journal=Analytical and Bioanalytical Chemistry | publisher=Springer Science and Business Media LLC | volume=383 | issue=6 | date=2005-10-15 | issn=1618-2642 | doi=10.1007/s00216-005-0069-7 | pages=1009–1013| pmid=16228199 | s2cid=22732411 }}</ref>

Pure substances that are liquid under normal conditions include water, [[ethanol]] and many other organic solvents. Liquid water is of vital importance in chemistry and biology, and it is necessary for all known forms of life.<ref name="MottlGlazerKaiser2007">{{cite journal | last1 = Mottl | first1 = Michael J. | last2 = Glazer | first2 = Brian T. | last3 = Kaiser | first3 = Ralf I. | last4 = Meech | first4 = Karen J. | title = Water and astrobiology | journal = Geochemistry | date = December 2007 | volume = 67 | issue = 4 | pages = 253–282 | issn = 0009-2819 | doi = 10.1016/j.chemer.2007.09.002 | bibcode = 2007ChEG...67..253M | url = https://www.soest.hawaii.edu/oceanography/glazer/Brian_T._Glazer/downloads/Mottl07a.pdf}}</ref><ref name="ChybaHand2005">{{cite journal | last1 = Chyba | first1 = Christopher F. | last2 = Hand | first2 = Kevin P. | title = Astrobiology: The Study of the Living Universe | journal = Annual Review of Astronomy and Astrophysics | date = 1 September 2005 | volume = 43 | issue = 1 | pages = 31–74 | issn = 0066-4146 | eissn = 1545-4282 | doi = 10.1146/annurev.astro.43.051804.102202 | bibcode = 2005ARA&A..43...31C }}</ref>

Inorganic liquids include water, [[magma]], [[inorganic nonaqueous solvent]]s and many [[acid]]s.

Important everyday liquids include [[aqueous solution]]s like household [[bleach]], other [[mixture]]s of different substances such as [[mineral oil]] and gasoline, [[emulsion]]s like [[vinaigrette]] or [[mayonnaise]], [[suspension (chemistry)|suspensions]] like blood, and [[colloid]]s like [[paint]] and [[milk]].

Many gases can be [[Liquefaction of gases|liquefied]] by cooling, producing liquids such as [[liquid oxygen]], [[liquid nitrogen]], [[liquid hydrogen]] and [[liquid helium]]. Not all gases can be liquified at atmospheric pressure, however. [[Carbon dioxide]], for example, can only be liquified at pressures above 5.1 [[Atmosphere (unit)|atm]].<ref>{{Citation
| last1  = Silberberg
| first1 = Martin S.
| title     = Chemistry: The Molecular Nature of Matter and Change
| publisher = McGraw-Hill Higher Education
| year    = 2009
| isbn    = 978-0-07-304859-8
| pages=448–449
}}</ref>

Some materials cannot be classified within the classical three states of matter. For example, [[liquid crystal]]s (used in [[liquid-crystal display]]s) possess both solid-like and liquid-like properties, and belong to their own state of matter distinct from either liquid or solid.<ref name="Andrienko2018">{{cite journal | last1 = Andrienko | first1 = Denis | title = Introduction to liquid crystals | journal = Journal of Molecular Liquids | date = October 2018 | volume = 267 | pages = 520–541 | issn = 0167-7322 | doi = 10.1016/j.molliq.2018.01.175 |doi-access=free}}</ref>

==Applications==
[[File:Blue Lava lamp.JPG|thumb|A [[lava lamp]] contains two immiscible liquids (a molten wax and a watery solution) which add movement due to convection. In addition to the top surface, surfaces also form between the liquids, requiring a tension breaker to recombine the wax droplets at the bottom.]]

=== Lubrication ===
{{See also | Tribology}}
Liquids are useful as [[lubricant]]s due to their ability to form a thin, freely flowing layer between solid materials. Lubricants such as oil are chosen for [[viscosity]] and flow characteristics that are suitable throughout the [[operating temperature]] range of the component. Oils are often used in engines, [[gear box]]es, [[metalworking]], and hydraulic systems for their good lubrication properties.<ref>Theo Mang, Wilfried Dressel [https://books.google.com/books?id=UTdfxf2rkNcC& ''Lubricants and lubrication''], Wiley-VCH 2007 {{ISBN|3-527-31497-0}}</ref>

=== Solvation ===
Many liquids are used as [[solvent]]s, to dissolve other liquids or solids. [[Solution (chemistry)|Solution]]s are found in a wide variety of applications, including [[paint]]s, [[sealant]]s, and [[adhesive]]s. [[Naphtha]] and [[acetone]] are used frequently in industry to clean oil, grease, and tar from parts and machinery. [[Body fluid]]s are water-based solutions.

[[Surfactant]]s are commonly found in soaps and [[detergent]]s. Solvents like alcohol are often used as [[antimicrobial]]s. They are found in cosmetics, [[ink]]s, and liquid [[dye laser]]s. They are used in the food industry, in processes such as the extraction of [[vegetable oil]].<ref>George Wypych [https://books.google.com/books?id=NzhUTvUkpDQC&pg=PA847 ''Handbook of solvents''] William Andrew Publishing 2001 pp. 847–881 {{ISBN|1-895198-24-0}}</ref>

=== Cooling ===
{{See also | Water cooling | Immersion cooling}}
Liquids tend to have better [[thermal conductivity]] than gases, and the ability to flow makes a liquid suitable for removing excess heat from mechanical components. The heat can be removed by channeling the liquid through a [[heat exchanger]], such as a [[radiator]], or the heat can be removed with the liquid during [[evaporation]].<ref>N. B. Vargaftik ''Handbook of thermal conductivity of liquids and gases'' CRC Press 1994 {{ISBN|0-8493-9345-0}}</ref> Water or [[glycol]] coolants are used to keep engines from overheating.<ref>Jack Erjavec [https://books.google.com/books?id=U4TBoJB2zgsC&pg=PA309 ''Automotive technology: a systems approach''] Delmar Learning 2000 p. 309 {{ISBN|1-4018-4831-1}}</ref> The coolants used in [[nuclear reactor]]s include water or liquid metals, such as [[sodium]] or [[bismuth]].<ref>Gerald Wendt ''The prospects of nuclear power and technology'' D. Van Nostrand Company 1957 p. 266</ref> [[Liquid propellant]] films are used to cool the thrust chambers of [[rocket]]s.<ref>''Modern engineering for design of liquid-propellant rocket engines'' by Dieter K. Huzel, David H. Huang – American Institute of Aeronautics and Astronautics 1992 p. 99 {{ISBN|1-56347-013-6}}</ref> In [[machining]], water and oils are used to remove the excess heat generated, which can quickly ruin both the work piece and the tooling. During [[perspiration]], sweat removes heat from the human body by evaporating. In the [[heating, ventilation, and air-conditioning]] industry (HVAC), liquids such as water are used to transfer heat from one area to another.<ref>Thomas E Mull ''HVAC principles and applications manual'' McGraw-Hill 1997 {{ISBN|0-07-044451-X}}</ref>

=== Cooking ===
Liquids are often used in [[cooking]] due to their excellent heat-transfer capabilities. In addition to thermal conduction, liquids transmit energy by convection. In particular, because warmer fluids expand and rise while cooler areas contract and sink, liquids with low [[kinematic viscosity]] tend to transfer heat through [[convection]] at a fairly constant temperature, making a liquid suitable for [[Blanching (cooking)|blanching]], [[boiling]], or [[frying]]. Even higher rates of heat transfer can be achieved by condensing a gas into a liquid. At the liquid's boiling point, all of the heat energy is used to cause the phase change from a liquid to a gas, without an accompanying increase in temperature, and is stored as chemical [[potential energy]]. When the gas condenses back into a liquid this excess heat-energy is released at a constant temperature. This phenomenon is used in processes such as [[steaming]].

=== Distillation ===
Since liquids often have different boiling points, mixtures or solutions of liquids or gases can typically be separated by [[distillation]], using heat, cold, [[vacuum]], pressure, or other means. Distillation can be found in everything from the production of [[alcoholic beverage]]s, to [[oil refinery|oil refineries]], to the [[air separation|cryogenic distillation]] of gases such as [[argon]], [[oxygen]], [[nitrogen]], [[neon]], or [[xenon]] by [[liquefaction]] (cooling them below their individual boiling points).<ref name="Earle1983">{{cite book | last=Earle | first=R. L. | title=Unit operations in food processing | publisher=Pergamon Press | publication-place=Oxford | date=1983 | isbn=0-08-025537-X | oclc=8451210 | pages=56–62, 138–141}}</ref>

=== Hydraulics ===
Liquid is the primary component of [[hydraulic]] systems, which take advantage of [[Pascal's law]] to provide [[fluid power]]. Devices such as [[pump]]s and [[waterwheel]]s have been used to change liquid motion into [[mechanical work]] since ancient times. Oils are forced through [[hydraulic pump]]s, which transmit this force to [[hydraulic cylinder]]s. Hydraulics can be found in many applications, such as [[automotive brakes]] and [[automotive transmission|transmissions]], [[heavy equipment (construction)|heavy equipment]], and airplane control systems. Various [[hydraulic press]]es are used extensively in repair and manufacturing, for lifting, pressing, clamping and forming.<ref>R. Keith Mobley [https://books.google.com/books?id=8DyLdlfJzoMC&pg=PA1 ''Fluid power dynamics''] Butterworth-Heinemann 2000 p. vii {{ISBN|0-7506-7174-2}}</ref>

=== Liquid metals ===
{{See also|Liquid metal#Applications}}
Liquid metals have several properties that are useful in [[Sensor|sensing]] and [[Actuator|actuation]], particularly their [[electrical conductivity]] and ability to transmit forces (incompressibility). As freely flowing substances, liquid metals retain these bulk properties even under extreme deformation. For this reason, they have been proposed for use in [[soft robotics|soft robots]] and [[Wearable technology|wearable healthcare devices]], which must be able to operate under repeated deformation.<ref name="Dickey2017">{{cite journal | last=Dickey | first=Michael D. | title=Stretchable and Soft Electronics using Liquid Metals | journal=Advanced Materials | publisher=Wiley | volume=29 | issue=27 | date=2017-04-18 | issn=0935-9648 | doi=10.1002/adma.201606425 | page=1606425| pmid=28417536 | bibcode=2017AdM....2906425D | s2cid=205276487 | doi-access=free }}</ref><ref name="ColeKhoshmaneshTang2021">{{cite journal | last1=Cole | first1=Tim | last2=Khoshmanesh | first2=Khashayar | last3=Tang | first3=Shi-Yang | title=Liquid Metal Enabled Biodevices | journal=Advanced Intelligent Systems | publisher=Wiley | volume=3 | issue=7 | date=2021-05-04 | issn=2640-4567 | doi=10.1002/aisy.202000275 | page=2000275| s2cid=235568215 }}</ref> The metal [[gallium]] is considered to be a promising candidate for these applications as it is a liquid near room temperature, has low toxicity, and evaporates slowly.<ref name="TangTaborKalantar-ZadehDickey2021">{{cite journal | last1=Tang | first1=Shi-Yang | last2=Tabor | first2=Christopher | last3=Kalantar-Zadeh | first3=Kourosh | last4=Dickey | first4=Michael D. | title=Gallium Liquid Metal: The Devil's Elixir | journal=Annual Review of Materials Research | publisher=Annual Reviews | volume=51 | issue=1 | date=2021-07-26 | issn=1531-7331 | doi=10.1146/annurev-matsci-080819-125403 | pages=381–408| bibcode=2021AnRMS..51..381T | s2cid=236566966 | doi-access=free }}</ref>

===Miscellaneous===
Liquids are sometimes used in measuring devices. A [[thermometer]] often uses the [[thermal expansion]] of liquids, such as [[mercury (element)|mercury]], combined with their ability to flow to indicate temperature. A [[manometer]] uses the weight of the liquid to indicate [[air pressure]].<ref>Bela G. Liptak [https://books.google.com/books?id=pPMursVsxlMC&pg=PA807 ''Instrument engineers' handbook: process control''] CRC Press 1999 p. 807 {{ISBN|0-8493-1081-4}}</ref>

The free surface of a rotating liquid forms a circular [[paraboloid]] and can therefore be used as a [[telescope]]. These are known as [[liquid-mirror telescope]]s.<ref name="Hickson1994">{{cite journal | last1=Hickson | first1=Paul | last2=Borra | first2=Ermanno F. | last3=Cabanac | first3=Remi | last4=Content | first4=Robert | last5=Gibson | first5=Brad K. | last6=Walker | first6=Gordon A. H. | title=UBC/Laval 2.7 meter liquid mirror telescope | journal=The Astrophysical Journal | publisher=American Astronomical Society | volume=436 | year=1994 | issn=0004-637X | doi=10.1086/187667 | page=L201 | arxiv = astro-ph/9406057| bibcode=1994ApJ...436L.201H }}</ref> They are significantly cheaper than conventional telescopes,<ref name="Hickson2007">{{cite journal | last1=Hickson | first1=Paul | last2=Racine | first2=Réne | title=Image Quality of Liquid‐Mirror Telescopes | journal=Publications of the Astronomical Society of the Pacific | publisher=IOP Publishing | volume=119 | issue=854 | year=2007 | issn=0004-6280 | doi=10.1086/517619 | pages=456–465| bibcode=2007PASP..119..456H | s2cid=120735632 | doi-access=free }}</ref> but can only point straight upward ([[zenith telescope]]). A common choice for the liquid is mercury.

==Mechanical properties==
===Volume===
[[File:Cavitating-prop.jpg|thumb|Cavitation in water from a boat propeller]]
Quantities of liquids are measured in units of [[volume]]. These include the [[International System of Units|SI]] unit cubic metre (m<sup>3</sup>) and its divisions, in particular the cubic decimeter, more commonly called the litre (1 dm<sup>3</sup> = 1 L = 0.001 m<sup>3</sup>), and the cubic centimetre, also called millilitre (1&nbsp;cm<sup>3</sup> = 1 mL = 0.001 L = 10<sup>−6</sup> m<sup>3</sup>).<ref>{{Citation |last1     = Knight
 |first1    = Randall D.
 |title     = Physics for Scientists and Engineers: A Strategic Approach (With Modern Physics)
 |publisher = Addison-Wesley
 |year      = 2008
 |isbn      = 978-0-8053-2736-6
 |page      = [https://archive.org/details/physicsforscient0000knig/page/443 443]
 |url       = https://archive.org/details/physicsforscient0000knig/page/443
}}</ref>

The volume of a quantity of liquid is fixed by its temperature and [[pressure]]. Liquids generally expand when heated, and contract when cooled. Water between 0&nbsp;°C and 4&nbsp;°C is a notable exception.<ref>{{Citation
| last1  = Silberberg
| first1 = Martin S.
| title     = Chemistry: The Molecular Nature of Matter and Change
| publisher = McGraw-Hill Higher Education
| year    = 2009
| isbn    = 978-0-07-304859-8
| page=461
}}</ref>

On the other hand, liquids have little [[compressibility]]. Water, for example, will compress by only 46.4 parts per million for every unit increase in [[standard atmospheric pressure|atmospheric pressure]] (bar).<ref>{{cite web|url=http://hyperphysics.phy-astr.gsu.edu/hbase/tables/compress.html|title=Compressibility of Liquids|website=hyperphysics.phy-astr.gsu.edu|access-date=8 May 2018|url-status=live|archive-url=https://web.archive.org/web/20171207161845/http://hyperphysics.phy-astr.gsu.edu/hbase/Tables/compress.html|archive-date=7 December 2017}}</ref> At around 4000 bar (400 [[megapascal]]s or 58,000 [[pounds per square inch|psi]]) of pressure at room temperature water experiences only an 11% decrease in volume.<ref name="ReferenceA">''Intelligent Energy Field Manufacturing: Interdisciplinary Process Innovations'' By Wenwu Zhang -- CRC Press 2011 Page 144</ref> Incompressibility makes liquids suitable for [[hydraulics|transmitting hydraulic power]], because a change in pressure at one point in a liquid is transmitted undiminished to every other part of the liquid and very little energy is lost in the form of compression.<ref>Knight (2008) p. 454</ref>

However, the negligible compressibility does lead to other phenomena. The banging of pipes, called [[water hammer]], occurs when a valve is suddenly closed, creating a huge pressure-spike at the valve that travels backward through the system at just under the speed of sound. Another phenomenon caused by liquid's incompressibility is [[cavitation]]. Because liquids have little [[elasticity (physics)|elasticity]] they can literally be pulled apart in areas of high turbulence or dramatic change in direction, such as the trailing edge of a boat propeller or a sharp corner in a pipe. A liquid in an area of low pressure (vacuum) vaporizes and forms bubbles, which then collapse as they enter high pressure areas. This causes liquid to fill the cavities left by the bubbles with tremendous localized force, eroding any adjacent solid surface.<ref>''Fluid Mechanics and Hydraulic Machines'' by S. C. Gupta -- Dorling-Kindersley 2006 Page 85</ref>

===Pressure and buoyancy===
{{Main|Fluid statics}}

In a [[gravitational field]], liquids exert [[pressure]] on the sides of a container as well as on anything within the liquid itself. This pressure is transmitted in all directions and increases with depth. If a liquid is at rest in a uniform gravitational field, the pressure <math>p</math> at depth <math>z</math> is given by<ref>Knight (2008) p. 448</ref> 
:<math>p=p_0+\rho g z\,</math>
where:
:<math>p_0\,</math> is the pressure at the surface
:<math>\rho\,</math> is the [[density]] of the liquid, assumed uniform with depth
:<math>g\,</math> is the [[gravity|gravitational acceleration]]

For a body of water open to the air, <math>p_0</math> would be the [[atmospheric pressure]].

Static liquids in uniform gravitational fields also exhibit the phenomenon of [[buoyancy]], where objects immersed in the liquid experience a net force due to the pressure variation with depth. The magnitude of the force is equal to the weight of the liquid displaced by the object, and the direction of the force depends on the average density of the immersed object. If the density is ''smaller'' than that of the liquid, the buoyant force points ''upward'' and the object floats, whereas if the density is ''larger'', the buoyant force points ''downward'' and the object sinks. This is known as [[Archimedes' principle]].<ref>Knight (2008) pp. 455-459</ref>

===Surfaces===
{{Main|Surface tension|Surface science}}

[[File:2006-01-14 Surface waves.jpg|thumb|250px|[[Surface wave]]s in water]]

Unless the volume of a liquid exactly matches the volume of its container, one or more surfaces are observed. The presence of a surface introduces new phenomena which are not present in a bulk liquid. This is because a molecule at a surface possesses bonds with other liquid molecules only on the inner side of the surface, which implies a net force pulling surface molecules inward. Equivalently, this force can be described in terms of energy: there is a fixed amount of energy associated with forming a surface of a given area. This quantity is a material property called the [[surface tension]], in units of energy per unit area (SI units: [[Joule|J]]/[[Meter|m]]<sup>2</sup>). Liquids with strong intermolecular forces tend to have large surface tensions.<ref>{{Citation
| last1  = Silberberg
| first1 = Martin S.
| title     = Chemistry: The Molecular Nature of Matter and Change
| publisher = McGraw-Hill Higher Education
| year    = 2009
| isbn    = 978-0-07-304859-8
| page=457
}}</ref>

A practical implication of surface tension is that liquids tend to minimize their surface area, forming spherical [[drop (liquid)|drop]]s and [[bubble (physics)|bubble]]s unless other constraints are present. Surface tension is responsible for a range of other phenomena as well, including [[surface wave]]s, [[capillary action]], [[wetting]], and [[capillary wave|ripples]]. In liquids under [[Confined liquid|nanoscale confinement]], surface effects can play a dominating role since – compared with a macroscopic sample of liquid – a much greater fraction of molecules are located near a surface.

The surface tension of a liquid directly affects its [[wettability]]. Most common liquids have tensions ranging in the tens of mJ/m<Sup>2</sup>, so droplets of oil, water, or glue can easily merge and adhere to other surfaces, whereas liquid metals such as mercury may have tensions ranging in the hundreds of mJ/m<Sup>2</sup>, thus droplets do not combine easily and surfaces may only wet under specific conditions.

The surface tensions of common liquids occupy a relatively narrow range of values when exposed to changing conditions such as temperature, which contrasts strongly with the enormous variation seen in other mechanical properties, such as viscosity.<ref name="Bormashenko2018">{{cite book|author1-link=Edward Bormashenko|author=Edward Yu. Bormashenko|title=Wetting of Real Surfaces|url=https://books.google.com/books?id=fwh2DwAAQBAJ&pg=PA3|date=5 November 2018|publisher=De Gruyter|isbn=978-3-11-058314-4|pages=3–5}}</ref>

The [[free surface]] of a liquid is disturbed by [[gravity]] ([[flatness (liquids)|flatness]]) and [[water waves|waves]] ([[surface roughness]]).

===Flow===
[[File:Viscosities.gif|thumb|A simulation of [[viscosity]]. The fluid on the left has a lower viscosity and Newtonian behavior while the liquid on the right has higher viscosity and non-Newtonian behavior.]]
{{Main|Fluid mechanics|Fluid dynamics}}

An important physical property characterizing the flow of liquids is [[viscosity]]. Intuitively, viscosity describes the resistance of a liquid to flow.

More technically, viscosity measures the resistance of a liquid to deformation at a given rate, such as when it is being sheared at finite velocity.<ref>{{Citation
| last1  = Landau
| first1 = L.D.
| last2  = Lifshitz
| first2 = E.M.
| title     = Fluid Mechanics
| publisher = Pergamon Press
| edition = 2nd
| year    = 1987
| isbn    = 978-0-08-033933-7
| pages = 44–45
}}</ref> A specific example is a liquid flowing through a
pipe: in this case the liquid undergoes shear deformation since it flows more slowly near the walls of the pipe
than near the center. As a result, it exhibits viscous resistance to flow. In order to maintain flow, an external force must be applied, such as a pressure difference between the ends of the pipe.

The viscosity of liquids decreases with increasing temperature.<ref>{{Citation
| last1  = Bird
| first1 = R. Byron
| last2  = Stewart
| first2 = Warren E.
| last3  = Lightfoot
| first3 = Edwin N.
| title     = Transport Phenomena
| publisher = John Wiley & Sons, Inc.
| edition = 2nd
| year    = 2007
| isbn    = 978-0-470-11539-8
| page = 21
}}
</ref>

Precise control of viscosity is important in many applications, particularly the lubrication industry. One way to achieve such control is by blending two or more liquids of differing viscosities in precise ratios.<ref name="Zhmud2014">{{Citation
| last1       = Zhmud
| first1      = Boris
| year       = 2014
| title      = Viscosity Blending Equations
| journal    = Lube-Tech
| volume     = 93
| url        = http://www.lube-media.com/wp-content/uploads/2017/11/Lube-Tech093-ViscosityBlendingEquations.pdf
}}</ref> 
In addition, various additives exist which can modulate the temperature-dependence of the
viscosity of lubricating oils. This capability is important since machinery often operate over a range of 
temperatures (see also [[viscosity index]]).<ref>{{cite web |url=https://wiki.anton-paar.com/en/viscosity-index/ |archive-url=https://web.archive.org/web/20200309134610/https://wiki.anton-paar.com/en/viscosity-index/  |archive-date=March 9, 2020 |title=Viscosity Index |publisher=Anton Paar |location=UK |access-date=29 August 2018 }}</ref>

The viscous behavior of a liquid can be either [[Newtonian fluid|Newtonian]] or [[non-Newtonian fluid|non-Newtonian]]. A Newtonian liquid exhibits a linear strain/stress curve, meaning its viscosity is independent of time, shear rate, or shear-rate history. Examples of Newtonian liquids include water, [[glycerin]], [[motor oil]], [[honey]], or mercury. A non-Newtonian liquid is one where the viscosity is not independent of these factors and either thickens (increases in viscosity) or thins (decreases in viscosity) under shear. Examples of non-Newtonian liquids include [[ketchup]], [[custard]], or [[starch]] solutions.<ref>''Honey in Traditional and Modern Medicine'' by Laid Boukraa -- CRC Press 2014 Page 22--24</ref>

===Sound propagation===
{{Main|Speed of sound#Speed of sound in liquids}}

The speed of sound in a liquid is given by <math>c = \sqrt {K/\rho}</math> where <math>K</math> is the [[bulk modulus]] of the liquid and <math>\rho</math> the density. As an example, water has a bulk modulus of about 2.2&nbsp;[[Pascal (unit)|GPa]] and a density of 1000&nbsp;kg/m<sup>3</sup>, which gives ''c'' = 1.5&nbsp;km/s.<ref>{{Citation
| last1  = Taylor
| first1 = John R.
| title     = Classical Mechanics
| publisher = University Science Books
| year    = 2005
| isbn    = 978-1-891389-22-1
| pages=727–729
}}</ref>

==Thermodynamics==

===Phase transitions===
{{Main|Boiling|Boiling point|Melting|Melting point}}
[[File:Phase-diag2.svg|thumb|300px|A typical [[phase diagram]]. The dotted line gives the anomalous behaviour of water. The green lines show how the [[freezing point]] can vary with pressure, and the blue line shows how the [[boiling point]] can vary with pressure. The red line shows the boundary where [[sublimation (chemistry)|sublimation]] or [[deposition (physics)|deposition]] can occur.]]

At a temperature below the [[boiling point]], any matter in liquid form will evaporate until reaching equilibrium with the reverse process of condensation of its vapor. At this point the vapor will condense at the same rate as the liquid evaporates. Thus, a liquid cannot exist permanently if the evaporated liquid is continually removed.<ref>{{Citation|last1=March|first1=N.H.|last2=Tosi|first2=M.P.|title=Introduction to Liquid State Physics|publisher=World Scientific|year=2002|doi=10.1142/4717|isbn=978-981-3102-53-8|page=7|bibcode=2002ilsp.book.....M}}</ref> A liquid at or above its boiling point will normally boil, though [[superheating]] can prevent this in certain circumstances.

At a temperature below the freezing point, a liquid will tend to [[crystallization|crystallize]], changing to its solid form. Unlike the transition to gas, there is no equilibrium at this transition under constant pressure,{{citation needed|date=February 2021}} so unless [[supercooling]] occurs, the liquid will eventually completely crystallize. However, this is only true under constant pressure, so that (for example) water and ice in a closed, strong container might reach an equilibrium where both phases coexist. For the opposite transition from solid to liquid, see [[melting]].

===Liquids in space===
The phase diagram explains why liquids do not exist in space or any other vacuum. Since the pressure is essentially zero (except on surfaces or interiors of planets and moons) water and other liquids exposed to space will either immediately boil or freeze depending on the temperature. In regions of space near the Earth, water will freeze if the sun is not shining directly on it and vaporize (sublime) as soon as it is in sunlight. If water exists as ice on the Moon, it can only exist in shadowed holes where the sun never shines and where the surrounding rock does not heat it up too much. At some point near the orbit of Saturn, the light from the Sun is too faint to sublime ice to water vapor. This is evident from the longevity of the ice that composes Saturn's rings.<ref>{{Cite web|last=Siegel|first=Ethan|date=2014-12-11|title=Does water freeze or boil in space?|url=https://medium.com/starts-with-a-bang/does-water-freeze-or-boil-in-space-7889856d7f36|access-date=2022-02-10|website=Starts With A Bang!|language=en}}</ref>

===Solutions===
{{Main|Solution (chemistry)}}

Liquids can form [[Solution (chemistry)|solution]]s with gases, solids, and other liquids.

Two liquids are said to be [[miscible]] if they can form a solution in any proportion; otherwise they are immiscible. As an example, water and [[ethanol]] (drinking alcohol) are miscible whereas water and [[gasoline]] are immiscible.<ref>Silberberg, pp. 188 and 502</ref> In some cases a mixture of otherwise immiscible liquids can be stabilized to form an [[emulsion]], where one liquid is dispersed throughout the other as microscopic droplets. Usually this requires the presence of a [[surfactant]] in order to stabilize the droplets. A familiar example of an emulsion is [[mayonnaise]], which consists of a mixture of water and oil that is stabilized by [[lecithin]], a substance found in [[yolk|egg yolks]].<ref>{{Citation
| last1  = Miodownik
| first1 = Mark
| author-link = Mark Miodownik
| title     = Liquid rules: The Delightful and Dangerous Substances that Flow Through Our Lives
| publisher = Houghton Mifflin Harcourt
| year    = 2019
| isbn    = 978-0-544-85019-4
| page=124
}}</ref>

==Microscopic description==
{{See also|Structure of liquids and glasses}}
The microscopic structure of liquids is complex and historically has been the subject of intense research and debate.<ref name="Chandler2017">{{cite journal | last=Chandler | first=David | title=From 50 Years Ago, the Birth of Modern Liquid-State Science | journal=Annual Review of Physical Chemistry | publisher=Annual Reviews | volume=68 | issue=1 | date=2017-05-05 | issn=0066-426X | doi=10.1146/annurev-physchem-052516-044941 | pages=19–38| pmid=28375691 | arxiv=1609.04837 | bibcode=2017ARPC...68...19C | s2cid=37248336 }}</ref><ref name="TrachenkoBrazhkin2015">{{cite journal | last1=Trachenko | first1=K | last2=Brazhkin | first2=V V | title=Collective modes and thermodynamics of the liquid state | journal=Reports on Progress in Physics | publisher=IOP Publishing | volume=79 | issue=1 | date=2015-12-22 | issn=0034-4885 | doi=10.1088/0034-4885/79/1/016502 | page=016502 | pmid=26696098 | arxiv = 1512.06592| s2cid=42203015 }}</ref><ref name="Ben-Naim2009">{{cite book | last=Ben-Naim | first=Arieh | title=Molecular theory of water and aqueous solutions. Part 1, Understanding water | publisher=World Scientific | publication-place=Singapore | date=2009 | isbn=978-981-283-761-5 | oclc=696342117 }}</ref><ref name="Pothoczki2015">{{cite journal | last1=Pothoczki | first1=Szilvia | last2=Temleitner | first2=László | last3=Pusztai | first3=László | title=Structure of Neat Liquids Consisting of (Perfect and Nearly) Tetrahedral Molecules | journal=Chemical Reviews | publisher=American Chemical Society (ACS) | volume=115 | issue=24 | date=2015-12-01 | issn=0009-2665 | doi=10.1021/acs.chemrev.5b00308 | pages=13308–13361| pmid=26624528 }}</ref> A few of the key ideas are explained below.

=== General description===
Microscopically, liquids consist of a dense, disordered packing of molecules. This contrasts with the other two common phases of matter, gases and solids. Although gases are disordered, the molecules are well-separated in space and interact primarily through molecule-molecule collisions. Conversely, although the molecules in solids are densely packed, they usually fall into a regular structure, such as a [[crystalline lattice]] ([[glass]]es are a notable
exception).

=== Short-range ordering ===
[[File:Teilchenmodell Flüssigkeit.svg|thumb|right|200px|Structure of a classical monatomic liquid. Atoms have many nearest neighbors in contact, yet no long-range order is present.]]
While liquids do not exhibit [[Order and disorder#Long-range order|long-range ordering]] as in a crystalline lattice, they do possess [[Short range order|short-range order]], which persists over a few molecular diameters.<ref name="Maitland1981">{{cite book | last1=Maitland | first1=Geoffrey C. | last2=Rigby | first2=Maurice | last3=Smith | first3=E. Brian | last4=Wakeham | first4=W. A. | title=Intermolecular forces: their origin and determination | publication-place=Oxford | date=1981 | isbn=0-19-855611-X | oclc=8139179 }}</ref><ref name="GalloRovere2021">{{cite book | last1=Gallo | first1=Paola | last2=Rovere | first2=Mauro | title=Physics of liquid matter | publisher=Springer | publication-place=Cham | date=2021 | isbn=978-3-030-68349-8 | oclc=1259588062 }}</ref>

In all liquids, excluded volume interactions induce short-range order in molecular positions (center-of-mass coordinates). Classical monatomic liquids like argon and krypton are the simplest examples. Such liquids can be modeled as disordered "heaps" of closely packed spheres, and the short-range order corresponds to the fact that nearest and next-nearest neighbors in a packing of spheres tend to be separated by integer multiples of the diameter.<ref name="Chandler1987">{{cite book | last=Chandler | first=David | title=Introduction to modern statistical mechanics | publisher=Oxford University Press | publication-place=New York | date=1987 | isbn=0-19-504276-X | oclc=13946448 }}</ref><ref name="Finney2013">{{cite journal | last=Finney | first=John L. | title=Bernal's road to random packing and the structure of liquids | journal=Philosophical Magazine | publisher=Informa UK Limited | volume=93 | issue=31–33 | date=2013-02-22 | issn=1478-6435 | doi=10.1080/14786435.2013.770179 | pages=3940–3969| bibcode=2013PMag...93.3940F | s2cid=55689631 | doi-access=free }}</ref>

In most liquids, molecules are not spheres, and intermolecular forces possess a directionality, i.e., they depend on the relative orientation of molecules. As a result, there is short-ranged orientational order in addition to the positional order mentioned above. Orientational order is especially important in [[Hydrogen bond|hydrogen-bonded]] liquids like water.<ref name="Finney2015">{{cite book | last=Finney | first=J. L. | title=Water: a very short introduction | publication-place=Oxford, United Kingdom | date=2015 | isbn=978-0-19-870872-8 | oclc=914537747 | pages=48–52}}</ref><ref name="Ludwig2005">{{cite journal | last=Ludwig | first=Ralf | title=The Structure of Liquid Methanol | journal=ChemPhysChem | publisher=Wiley | volume=6 | issue=7 | date=2005-07-11 | issn=1439-4235 | doi=10.1002/cphc.200400663 | pages=1369–1375| pmid=15991270 }}</ref> The strength and directional nature of hydrogen bonds drives the formation of local "networks" or "clusters" of molecules. Due to the relative importance of thermal fluctuations in liquids (compared with solids), these structures are highly dynamic, continuously deforming, breaking, and reforming.<ref name="Chandler1987"/><ref name="Finney2015"/>

=== Energy and entropy ===
The microscopic features of liquids derive from an interplay between attractive intermolecular forces and [[entropic force]]s.<ref name="Chandler2009">{{cite journal | last=Chandler | first=David | title=Liquids: Condensed, disordered, and sometimes complex | journal=Proceedings of the National Academy of Sciences | volume=106 | issue=36 | date=2009-09-08 | issn=0027-8424 | doi=10.1073/pnas.0908029106 | pages=15111–15112 | pmid=19805248 | pmc=2741213 | doi-access=free }}</ref>

The attractive forces tend to pull molecules close together, and along with short-range repulsive interactions, they are the dominant forces behind the regular structure of solids. The entropic forces are not "forces" in the mechanical sense; rather, they describe the tendency of a system to maximize its [[entropy]] at fixed energy (see [[microcanonical ensemble]]). Roughly speaking, entropic forces drive molecules apart from each other, maximizing the volume they occupy. Entropic forces dominant in gases and explain the tendency of gases to fill their containers. In liquids, by contrast, the intermolecular and entropic forces are comparable, so it is not possible to neglect one in favor of the other. Quantitatively, the binding energy between adjacent molecules is the same order of magnitude as the thermal energy <math>k_{\text{B}} T</math>.<ref name="HansenMcDonald2013">{{cite book | last1=Hansen | first1=Jean-Pierre | last2=McDonald | first2=Ian R. | title=Theory of simple liquids: with applications to soft matter | publication-place=Amsterdam | date=2013 | isbn=978-0-12-387033-9 | oclc=855895733 }}</ref>

==== No small parameter ====
The competition between energy and entropy makes liquids difficult to model at the molecular level, as there is no idealized "reference state" that can serve as a starting point for tractable theoretical descriptions. Mathematically, there is no small parameter from which one can develop a systematic [[perturbation theory]].<ref name="TrachenkoBrazhkin2015"/> This situation contrasts with both gases and solids. For gases, the reference state is the [[ideal gas]], and the density can be used as a small parameter to construct a theory of real (nonideal) gases (see [[virial expansion]]).<ref name="Kardar 2007 p. ">{{cite book | last=Kardar | first=Mehran | title=Statistical physics of particles | publisher=Cambridge University Press | publication-place=New York, NY | date=2007 | isbn=978-0-521-87342-0 | oclc=148639922 | page=130}}</ref> For crystalline solids, the reference state is a perfect crystalline lattice, and possible small parameters are thermal motions and [[lattice defect]]s.<ref name="Finney2015"/>

===Role of quantum mechanics===
Like all known forms of matter, liquids are fundamentally [[quantum mechanical]]. However, under standard conditions (near room temperature and pressure), much of the macroscopic behavior of liquids can be understood in terms of [[classical mechanics]].<ref name="HansenMcDonald2013"/><ref name="Gray1984">{{cite book | last1=Gray | first1=C. G. | last2=Gubbins | first2=Keith E. | last3=Joslin | first3=C. G. | title=Theory of molecular fluids | publisher=Oxford University Press | publication-place=Oxford | date=1984–2011 | isbn=0-19-855602-0 | oclc=10145548 }}</ref> The "classical picture" posits that the constituent molecules are discrete entities that interact through intermolecular forces according to [[Newton's laws of motion]]. As a result, their macroscopic properties can be described using [[classical statistical mechanics]]. While the intermolecular force law technically derives from quantum mechanics, it is usually understood as a model input to classical theory, obtained either from a fit to experimental data or from the [[classical limit]] of a quantum mechanical description.<ref name="MarxHutter 2012">{{cite book | last1=Marx | first1=Dominik | last2=Hutter | first2=Jürg | title=Ab initio molecular dynamics: basic theory and advanced methods | publication-place=Cambridge | date=2012 | isbn=978-0-521-89863-8 | oclc=869135580 }}</ref><ref name="Maitland1981"/> An illustrative, though highly simplified example is a collection of spherical molecules interacting through a [[Lennard-Jones potential]].<ref name="HansenMcDonald2013"/>

{| class="wikitable floatright"
|+ Table 1: Thermal de Broglie wavelengths <math>\Lambda</math> of selected liquids.<ref name="HansenMcDonald2013"/>  Quantum effects are negligible when the ratio <math>\Lambda / a</math> is small, where <math>a</math> is the average distance between molecules.
! Liquid
! Temperature (K)
! <math>\Lambda</math> (nm)
! <math>\Lambda / a</math>
|-
| Hydrogen (H<sub>2</sub>)
| 14.1
| 0.33
| 0.97
|-
| Neon
| 24.5
| 0.078
| 0.26
|-
| Krypton
| 116
| 0.018
| 0.046
|-
| [[Carbon tetrachloride]] (CCl<sub>4</sub>)
| 250
| 0.009
| 0.017
|-
|}

For the classical limit to apply, a necessary condition is that the thermal [[de Broglie wavelength]], 
:<math>
\Lambda = \left(\frac{2 \pi \hbar^2}{m k_{\text{B}} T} \right)^{1/2}
</math> 
is small compared with the length scale under consideration.<ref name="HansenMcDonald2013"/><ref>{{Citation|last1 = Fisher| first1 = I.Z.| title = Statistical Theory of Liquids| publisher = The University of Chicago Press| year =1964}}</ref> Here, <math>\hbar</math> is the [[Planck constant]] and <math>m</math> is the molecule's mass. Typical values of <math>\Lambda</math> are about 0.01-0.1 nanometers (Table 1). Hence, a high-resolution model of liquid structure at the nanoscale may require quantum mechanical considerations. A notable example is hydrogen bonding in associated liquids like water,<ref name="Ceriotti2013">{{cite journal | last1=Ceriotti | first1=Michele | last2=Cuny | first2=Jérôme | last3=Parrinello | first3=Michele | last4=Manolopoulos | first4=David E. | title=Nuclear quantum effects and hydrogen bond fluctuations in water | journal=Proceedings of the National Academy of Sciences | volume=110 | issue=39 | date=2013-09-06 | issn=0027-8424 | doi=10.1073/pnas.1308560110 | pages=15591–15596 | pmid=24014589 | pmc=3785726 | bibcode=2013PNAS..11015591C | doi-access=free }}</ref><ref name="Markland Ceriotti2018">{{cite journal | last1=Markland | first1=Thomas E. | last2=Ceriotti | first2=Michele | title=Nuclear quantum effects enter the mainstream | journal=Nature Reviews Chemistry | publisher=Springer Science and Business Media LLC | volume=2 | issue=3 | date=2018-02-28 | issn=2397-3358 | doi=10.1038/s41570-017-0109 | arxiv = 1803.01037| s2cid=4938804 }}</ref> where, due to the small mass of the proton, inherently quantum effects such as [[zero-point motion]] and [[quantum tunneling|tunneling]] are important.<ref name="Li2011">{{cite journal | last1=Li | first1=Xin-Zheng | last2=Walker | first2=Brent | last3=Michaelides | first3=Angelos | title=Quantum nature of the hydrogen bond | journal=Proceedings of the National Academy of Sciences | volume=108 | issue=16 | date=2011-04-04 | issn=0027-8424 | doi=10.1073/pnas.1016653108 | pages=6369–6373 | bibcode=2011PNAS..108.6369L | doi-access=free | pmc=3081025 }}</ref>

For a liquid to behave classically at the macroscopic level, <math>\Lambda</math> must be small compared with the average distance <math>a \approx \rho^{-1/3}</math> 
between molecules.<ref name="HansenMcDonald2013"/> That is, 
:<math>
\frac{\Lambda}{a} \ll 1
</math>
Representative values of this ratio for a few liquids are given in Table 1. The conclusion is that quantum effects are important for liquids at low temperatures and with small [[molecular mass]].<ref name="HansenMcDonald2013"/><ref name="Gray1984"/> For dynamic processes, there is an additional timescale constraint:
:<math>
\tau \gg \frac{h}{k_B T}
</math>
where <math>\tau</math> is the timescale of the process under consideration. For room-temperature liquids, the right-hand side is about 10<sup>−14</sup> seconds, which generally means that time-dependent processes involving translational motion can be described classically.<ref name="HansenMcDonald2013"/>

At extremely low temperatures, even the macroscopic behavior of certain liquids deviates from classical mechanics. Notable examples are hydrogen and helium. Due to their low temperature and mass, such liquids have a thermal de Broglie wavelength comparable to the average distance between molecules.<ref name="HansenMcDonald2013"/>

===Dynamic phenomena===
The expression for the sound velocity of a liquid,
:<math>
c = \sqrt {K/\rho}
</math>, 
contains the [[bulk modulus]] ''K''. If ''K'' is frequency-independent, then the liquid behaves as a linear medium, so that sound propagates without [[dissipation]] or [[mode coupling]]. In reality, all liquids show some [[Acoustic dispersion|dispersion]]: with increasing frequency, ''K'' crosses over from the low-frequency, liquid-like limit <math>K_0</math> to the high-frequency, solid-like limit <math>K_\infty</math>. In normal liquids, most of this crossover takes place at frequencies between GHz and THz, sometimes called [[hypersound]].

At sub-GHz frequencies, a normal liquid cannot sustain [[shear wave]]s: the zero-frequency limit of the [[shear modulus]] is 0. This is sometimes seen as the defining property of a liquid.<ref>{{cite journal |last1=Born |first1=Max |year=1940 |title=On the stability of crystal lattices |journal=[[Mathematical Proceedings of the Cambridge Philosophical Society]] |volume=36 |issue=2 |pages=160–172 |doi=10.1017/S0305004100017138 |bibcode=1940PCPS...36..160B |s2cid=104272002 }}</ref><ref>{{cite journal |last1=Born |first1=Max |year=1939 |title=Thermodynamics of Crystals and Melting |journal=Journal of Chemical Physics |volume=7 |issue=8 |pages=591–604 |doi=10.1063/1.1750497 |url=http://jcp.aip.org/resource/1/jcpsa6/v7/i8/p591_s1?isAuthorized=no |bibcode=1939JChPh...7..591B  |archive-url=http://arquivo.pt/wayback/20160515021512/http://jcp.aip.org/resource/1/jcpsa6/v7/i8/p591_s1?isAuthorized=no |archive-date=2016-05-15 }}</ref> 
However, like the bulk modulus ''K'', the shear modulus ''G'' is also frequency-dependent and exhibits a similar crossover at hypersound frequencies.

According to [[linear response theory]], the Fourier transform of ''K'' or ''G'' describes how the system returns to equilibrium after an external perturbation; for this reason, the dispersion step in the GHz to THz region is also called [[Relaxation (physics)|relaxation]]. As a liquid is supercooled toward the glass transition, the structural relaxation time exponentially increases, which explains the viscoelastic behavior of glass-forming liquids.
[[File:Lennard-Jones Radial Distribution Function.svg|thumb|300px|Radial distribution function of the [[Lennard-Jones potential|Lennard-Jones model fluid]] ]]

===Experimental methods===
The absence of long-range order in liquids is mirrored by the absence of [[Bragg peak]]s in [[X-ray diffraction|X-ray]] and [[neutron diffraction]]. Under normal conditions, the diffraction pattern has circular symmetry, expressing the [[isotropy]] of the liquid. Radially, the diffraction intensity smoothly oscillates. This can be described by the [[static structure factor]] <math>S(q)</math>, with wavenumber <math>q =(4 \pi / \lambda)\sin \theta</math> given by the wavelength <math>\lambda</math> of the probe (photon or neutron) and the [[Bragg angle]] <math>\theta</math>. The oscillations of <math>S(q)</math> express the short-range order of the liquid, i.e., the correlations between a molecule and "shells" of nearest neighbors, next-nearest neighbors, and so on.

An equivalent representation of these correlations is the [[radial distribution function]] <math>g(r)</math>, which is related to the [[Fourier transform]] of <math>S(q)</math>.<ref name="Chandler1987"/> It represents a spatial average of a temporal snapshot of pair correlations in the liquid.

==Prediction of liquid properties==
{{See also|Computational materials science}}
Methods for predicting liquid properties can be organized by their "scale" of description, that is, the [[length scale]]s and time scales over which they apply.<ref name="Krüger2016">{{cite book | last1=Krüger | first1=Timm | last2=Kusumaatmaja | first2=Halim | last3=Kuzmin | first3=Alexandr | last4=Shardt | first4=Orest | last5=Silva | first5=Goncalo | last6=Viggen | first6=Erlend Magnus | title=The lattice Boltzmann method: principles and practice | publication-place=Switzerland | date=2016 | isbn=978-3-319-44649-3 | oclc=963198053 }}</ref><ref name="Steinhauser2022">{{cite book | last=Steinhauser | first=M. O. | title=Computational multiscale modeling of fluids and solids: theory and applications | publisher=Springer | publication-place=Cham, Switzerland | date=2022 | isbn=978-3-030-98954-5 | oclc=1337924123 }}</ref>

*'''Macroscopic methods''' use equations that directly model the large-scale behavior of liquids, such as their thermodynamic properties and flow behavior. 
*'''Microscopic methods''' use equations that model the dynamics of individual molecules.
*'''Mesoscopic methods''' fall in between, combining elements of both continuum and particle-based models.

===Macroscopic===

====Empirical correlations==== 
Empirical correlations are simple mathematical expressions intended to approximate a liquid's properties over a range of experimental conditions, such as varying temperature and pressure.<ref name="Poling2001">{{cite book | last1=Poling | first1=Bruce E. | last2=Prausnitz | first2=J. M. | last3=O'Connell | first3=John P. | title=The properties of gases and liquids | publisher=McGraw-Hill | publication-place=New York | date=2001 | isbn=0-07-011682-2 | oclc=44712950 }}</ref> They are constructed by [[Regression analysis|fitting]] simple functional forms to experimental data. For example, the [[Temperature dependence of viscosity|temperature-dependence of liquid viscosity]] is sometimes approximated by the function <math>\eta(T) = A e^{B/T}</math>, where <math>A</math> and <math>B</math> are fitting constants.<ref>{{cite book
 |last1        = Bird
 |first1       = R. Byron
 |last2        = Stewart
 |first2       = Warren E.
 |last3        = Lightfoot
 |first3       = Edwin N.
 |url          = https://books.google.com/books?id=L5FnNlIaGfcC
 |title        = Transport Phenomena
 |publisher    = John Wiley & Sons, Inc.
 |edition      = 2nd
 |year         = 2007
 |isbn         = 978-0-470-11539-8
 |access-date  = 2019-09-18
 |archive-date = 2020-03-02
 |archive-url  = https://web.archive.org/web/20200302151358/https://books.google.com/books?id=L5FnNlIaGfcC
 |url-status   = live
}}</ref> Empirical correlations allow for extremely efficient estimates of physical properties, which can be useful in thermophysical simulations. However, they require high quality experimental data to obtain a good fit and cannot reliably extrapolate beyond the conditions covered by experiments.

====Thermodynamic potentials====
{{See also | Equation of state}}
Thermodynamic potentials are functions that characterize the [[equilibrium state]] of a substance. An example is the [[Gibbs free energy]] <math>G(p, T)</math>, which is a function of pressure and temperature. Knowing any one thermodynamic potential <math>\mathcal{F}</math> is sufficient to compute all equilibrium properties of a substance, often simply by taking [[derivative]]s of <math>\mathcal{F}</math>.<ref name="Kardar 2007 p. "/> Thus, a single correlation for <math>\mathcal{F}</math> can replace separate correlations for individual properties.<ref name="Span2000">{{cite book | last=Span | first=R. | title=Multiparameter Equations of State: An Accurate Source of Thermodynamic Property Data | publisher=Springer | series=Engineering online library | year=2000 | isbn=978-3-540-67311-8 | url=https://books.google.com/books?id=dd410GGw8wUC&pg=PA1 | access-date=2023-04-01 | page=1}}</ref><ref name="Huber2022">{{cite journal | last1=Huber | first1=Marcia L. | last2=Lemmon | first2=Eric W. | last3=Bell | first3=Ian H. | last4=McLinden | first4=Mark O. | title=The NIST REFPROP Database for Highly Accurate Properties of Industrially Important Fluids | journal=Industrial & Engineering Chemistry Research | publisher=American Chemical Society (ACS) | volume=61 | issue=42 | date=2022-06-22 | issn=0888-5885 | doi=10.1021/acs.iecr.2c01427 | pages=15449–15472| pmid=36329835 | s2cid=249968848 | pmc=9619405 }}</ref> Conversely, a variety of experimental measurements (e.g., density, heat capacity, vapor pressure) can be incorporated into the same fit; in principle, this would allow one to predict hard-to-measure properties like heat capacity in terms of other, more readily available measurements (e.g., vapor pressure).<ref name="Tillner-Roth1998">{{cite journal | last1=Tillner-Roth | first1=Reiner | last2=Friend | first2=Daniel G. | title=A Helmholtz Free Energy Formulation of the Thermodynamic Properties of the Mixture {Water + Ammonia} | journal=Journal of Physical and Chemical Reference Data | publisher=AIP Publishing | volume=27 | issue=1 | year=1998 | issn=0047-2689 | doi=10.1063/1.556015 | pages=63–96}}</ref>

====Hydrodynamics====
{{Main|Fluid dynamics|Computational fluid dynamics}}
Hydrodynamic theories describe liquids in terms of space- and time-dependent macroscopic [[field (physics)|fields]], such as density, velocity, and temperature. These fields obey [[partial differential equation]]s, which can be linear or [[nonlinear partial differential equation|nonlinear]].<ref name="PrincetonCompanion">{{Citation|last=Moffatt|first=H.K.|year=2015|title=Fluid Dynamics|editor=Nicholas J. Higham|display-editors=etal|encyclopedia=The Princeton Companion to Applied Mathematics|pages=467–476|publisher=Princeton University Press}}</ref> Hydrodynamic theories are more general than equilibrium thermodynamic descriptions, which assume that liquids are approximately [[homogeneous]] and time-independent. The Navier-Stokes equations are a well-known example: they are partial differential equations giving the time evolution of density, velocity, and temperature of a viscous fluid. There are numerous methods for numerically solving the Navier-Stokes equations and its variants.<ref name="Wendt2008">{{cite book | last1=Wendt | first1=John F. | last2=Anderson | first2=John D. Jr. | author3=Von Karman Institute for Fluid Dynamics | title=Computational fluid dynamics: an introduction | publisher=Springer | publication-place=Berlin | date=2008 | isbn=978-3-540-85056-4 | oclc=656397653 }}</ref><ref name="Pozrikidis2011">{{cite book | last=Pozrikidis | first=C. | title=Introduction to theoretical and computational fluid dynamics | publisher=Oxford University Press | publication-place=New York | date=2011 | isbn=978-0-19-990912-4 | oclc=812917029 }}</ref>

===Mesoscopic===
{{See also | Mesoscopic physics}}
Mesoscopic methods operate on length and time scales between the particle and continuum levels. For this reason, they combine elements of particle-based dynamics and continuum hydrodynamics.<ref name="Krüger2016"/>

An example is the [[Lattice Boltzmann methods|lattice Boltzmann method]], which models a fluid as a collection of fictitious particles that exist on a lattice.<ref name="Krüger2016"/> The particles evolve in time through streaming (straight-line motion) and [[collision]]s. Conceptually, it is based on the [[Boltzmann equation]] for dilute gases, where the dynamics of a molecule consists of free motion interrupted by discrete binary collisions, but it is also applied to liquids. Despite the analogy with individual molecular trajectories, it is a coarse-grained description that typically operates on length and time scales larger than those of true molecular dynamics (hence the notion of "fictitious" particles).
	
Other methods that combine elements of continuum and particle-level dynamics include [[smoothed-particle hydrodynamics]],<ref name="Monaghan2005">{{cite journal | last=Monaghan | first=J J | title=Smoothed particle hydrodynamics | journal=Reports on Progress in Physics | publisher=IOP Publishing | volume=68 | issue=8 | date=2005-07-05 | issn=0034-4885 | doi=10.1088/0034-4885/68/8/r01 | pages=1703–1759| bibcode=2005RPPh...68.1703M | s2cid=5987481 }}</ref><ref name="Lind2020">{{cite journal | last1=Lind | first1=Steven J. | last2=Rogers | first2=Benedict D. | last3=Stansby | first3=Peter K. | title=Review of smoothed particle hydrodynamics: towards converged Lagrangian flow modelling | journal=Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences | publisher=The Royal Society | volume=476 | issue=2241 | year=2020 | issn=1364-5021 | doi=10.1098/rspa.2019.0801 | pmid=33071565 | s2cid=221538477 | pmc=7544338 | bibcode=2020RSPSA.47690801L }}</ref> [[dissipative particle dynamics]],<ref name="Español2017">{{cite journal | last1=Español | first1=Pep | last2=Warren | first2=Patrick B. | title=Perspective: Dissipative particle dynamics | journal=The Journal of Chemical Physics | publisher=AIP Publishing | volume=146 | issue=15 | date=2017-04-21 | issn=0021-9606 | doi=10.1063/1.4979514 | page=150901| pmid=28433024 | s2cid=961922 | arxiv=1612.04574 | bibcode=2017JChPh.146o0901E }}</ref> and [[multiparticle collision dynamics]].<ref name="Gompper2008">{{cite book | last1=Gompper | first1=G. | last2=Ihle | first2=T. | last3=Kroll | first3=D. M. | last4=Winkler | first4=R. G. | title=Advanced Computer Simulation Approaches for Soft Matter Sciences III | chapter=Multi-Particle Collision Dynamics: A Particle-Based Mesoscale Simulation Approach to the Hydrodynamics of Complex Fluids | year=2009 | publisher=Springer Berlin Heidelberg | publication-place=Berlin, Heidelberg | isbn=978-3-540-87705-9 | doi=10.1007/978-3-540-87706-6_1 | pages=1–87 | arxiv=0808.2157| s2cid=8433369 }}</ref>

===Microscopic===
Microscopic simulation methods work directly with the equations of motion (classical or quantum) of the constituent molecules.

====Classical molecular dynamics====
{{Main | Molecular dynamics | Molecular mechanics}}
Classical molecular dynamics (MD) simulates liquids using Newton's law of motion; from [[Newton's second law]] (<math>F = m \ddot{x}</math>), the trajectories of molecules can be traced out explicitly and used to compute macroscopic liquid properties like density or viscosity. However, classical MD requires expressions for the [[interatomic potential|intermolecular forces]] ("''F''" in Newton's second law). Usually, these must be approximated using experimental data or some other input.<ref name="Maitland1981"/>

====Ab initio (quantum) molecular dynamics====
{{See also | Car–Parrinello molecular dynamics}}
Ab initio quantum mechanical methods simulate liquids using only the laws of quantum mechanics and fundamental atomic constants.<ref name="MarxHutter 2012"/> In contrast with classical molecular dynamics, the intermolecular force fields are an output of the calculation, rather than an input based on experimental measurements or other considerations. In principle, ab initio methods can simulate the properties of a given liquid without any prior experimental data. However, they are very expensive computationally, especially for large molecules with internal structure.

==See also==
{{Columns-list|colwidth=20em|
* [[Ionic liquid]]
* [[Heavy liquid]]
* [[Liquid dielectric]]
* [[Liquid marbles]]
* [[Liquid breathing]]
* [[Liquid resistor]]
* [[Microfluidics]]
* [[Fluidized bed]]
* [[Supercritical fluid]]
}}

==References==
{{Reflist|30em}}
{{State of matter}}

{{Authority control}}

[[Category:Liquids| ]]
[[Category:Phases of matter|*Liq]]
[[Category:Viscosity]]