Liquid - Knowledge

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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.

2266:). 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 6769: 1411: 983: 40: 2061: 1850: 752: 2092:, 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. A liquid at or above its boiling point will normally boil, though 779:

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

1814:. Most common liquids have tensions ranging in the tens of mJ/m, 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, thus droplets do not combine easily and surfaces may only wet under specific conditions. 3633:

can replace separate correlations for individual properties. 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

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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

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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

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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

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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,

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Ab initio quantum mechanical methods simulate liquids using only the laws of quantum mechanics and fundamental atomic constants. 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

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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,

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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. In addition, various additives exist which can modulate the temperature-dependence of

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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. 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

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are fitting constants. 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

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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.

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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

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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.

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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, where, due to the small mass of the proton, inherently quantum effects

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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

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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

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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

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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.

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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

1714:, 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 2241:

liquids like water. 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,

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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

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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

1195:. 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 734:

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

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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.

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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

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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.

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is the timescale of the process under consideration. For room-temperature liquids, the right-hand side is about 10 seconds, which generally means that time-dependent processes involving translational motion can be described classically.

1913:, 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 1174:

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

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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

1464:, 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 1426:

unit cubic metre (m) and its divisions, in particular the cubic decimeter, more commonly called the litre (1 dm = 1 L = 0.001 m), and the cubic centimetre, also called millilitre (1 cm = 1 mL = 0.001 L = 10 m).

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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. They are constructed by

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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

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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.

2345:. 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 3683:

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.

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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.

731:. 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. 3782:), 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 3205: 2882: 1901:. 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, 124: 2827: 6638:

Gompper, G.; Ihle, T.; Kroll, D. M.; Winkler, R. G. (2009). "Multi-Particle Collision Dynamics: A Particle-Based Mesoscale Simulation Approach to the Hydrodynamics of Complex Fluids".

3711: 3088:. As a liquid is supercooled toward the glass transition, the structural relaxation time exponentially increases, which explains the viscoelastic behavior of glass-forming liquids. 2791: 2959: 1975: 1457:, 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. 799:

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

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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

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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

3044: 2483: 2403: 3225: 2747: 2715: 2453: 2375: 3248: 1640: 1617: 3555: 2671: 1807:, 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. 3017: 2905: 2019: 1701: 3345: 3312: 3277: 3153: 3690:, which models a fluid as a collection of fictitious particles that exist on a lattice. The particles evolve in time through streaming (straight-line motion) and 2188:

The microscopic structure of liquids is complex and historically has been the subject of intense research and debate. A few of the key ideas are explained below.

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Hickson, Paul; Borra, Ermanno F.; Cabanac, Remi; Content, Robert; Gibson, Brad K.; Walker, Gordon A. H. (1994). "UBC/Laval 2.7 meter liquid mirror telescope".

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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.

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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

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Pothoczki, Szilvia; Temleitner, László; Pusztai, László (2015-12-01). "Structure of Neat Liquids Consisting of (Perfect and Nearly) Tetrahedral Molecules".

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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.

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Tillner-Roth, Reiner; Friend, Daniel G. (1998). "A Helmholtz Free Energy Formulation of the Thermodynamic Properties of the Mixture {Water + Ammonia}".

1199:. 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 2333:. However, under standard conditions (near room temperature and pressure), much of the macroscopic behavior of liquids can be understood in terms of 847:. In addition, certain mixtures of elements are liquid at room temperature, even if the individual elements are solid under the same conditions (see 2349:

of a quantum mechanical description. An illustrative, though highly simplified example is a collection of spherical molecules interacting through a

1857:. 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. 1350:

is considered to be a promising candidate for these applications as it is a liquid near room temperature, has low toxicity, and evaporates slowly.

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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.

6113: 5781: 5659: 5493: 5313: 2337:. The "classical picture" posits that the constituent molecules are discrete entities that interact through intermolecular forces according to 6033: 4703: 673: 3891:

Leonchuk, Sergei S.; Falchevskaya, Aleksandra S.; Nikolaev, Vitaly; Vinogradov, Vladimir V. (2022). "NaK alloy: underrated liquid metal".

2103:, changing to its solid form. Unlike the transition to gas, there is no equilibrium at this transition under constant pressure, so unless 6706: 2317:). For crystalline solids, the reference state is a perfect crystalline lattice, and possible small parameters are thermal motions and 1159: 1886:

the viscosity of lubricating oils. This capability is important since machinery often operate over a range of temperatures (see also

974:) possess both solid-like and liquid-like properties, and belong to their own state of matter distinct from either liquid or solid. 4879: 3664:. Hydrodynamic theories are more general than equilibrium thermodynamic descriptions, which assume that liquids are approximately 1154:, water and oils are used to remove the excess heat generated, which can quickly ruin both the work piece and the tooling. During 755:

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

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Theodore Gray, The Elements: A Visual Exploration of Every Known Atom in the Universe New York: Workman Publishing, 2009, p. 127

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This causes liquid to fill the cavities left by the bubbles with tremendous localized force, eroding any adjacent solid surface.

1453:) of pressure at room temperature water experiences only an 11% decrease in volume. Incompressibility makes liquids suitable for 720:

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

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use equations that directly model the large-scale behavior of liquids, such as their thermodynamic properties and flow behavior.

1434:. Liquids generally expand when heated, and contract when cooled. Water between 0 °C and 4 °C is a notable exception. 3722:

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

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Structure of a classical monatomic liquid. Atoms have many nearest neighbors in contact, yet no long-range order is present.

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Since liquids often have different boiling points, mixtures or solutions of liquids or gases can typically be separated by

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occurs). If the temperature is decreased, the distances between the molecules become smaller. When the liquid reaches its

791:, the cohesive forces that bind the molecules closely together break, and the liquid changes to its gaseous state (unless 3404: 1010:

due to their ability to form a thin, freely flowing layer between solid materials. Lubricants such as oil are chosen for

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unless other constraints are present. Surface tension is responsible for a range of other phenomena as well, including

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that conforms to the shape of its container but retains a nearly constant volume independent of pressure. It is one of

2158:, where one liquid is dispersed throughout the other as microscopic droplets. Usually this requires the presence of a 6169: 5721: 5374: 5289: 4519: 4332: 4298: 4277: 4257: 4225: 4203: 4183: 4161: 3879: 666: 3158: 2183: 6080:

Krüger, Timm; Kusumaatmaja, Halim; Kuzmin, Alexandr; Shardt, Orest; Silva, Goncalo; Viggen, Erlend Magnus (2016).

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A practical implication of surface tension is that liquids tend to minimize their surface area, forming spherical

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Surmann, Peter; Zeyat, Hanan (2005-10-15). "Voltammetric analysis using a self-renewable non-mercury electrode".

3703: 3356: 2342: 80: 2799: 7043: 6968: 6699: 1304: 639: 7155: 6983: 3707: 3657: 3046:. In normal liquids, most of this crossover takes place at frequencies between GHz and THz, sometimes called 1442: 1423: 340: 177: 4035:

Chyba, Christopher F.; Hand, Kevin P. (1 September 2005). "Astrobiology: The Study of the Living Universe".

3790:" in Newton's second law). Usually, these must be approximated using experimental data or some other input. 7165: 7038: 6783: 3647: 3283: 2752: 2197:

although the molecules in solids are densely packed, they usually fall into a regular structure, such as a

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The microscopic features of liquids derive from an interplay between attractive intermolecular forces and

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Methods for predicting liquid properties can be organized by their "scale" of description, that is, the

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is frequency-independent, then the liquid behaves as a linear medium, so that sound propagates without

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if they can form a solution in any proportion; otherwise they are immiscible. As an example, water and

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Markland, Thomas E.; Ceriotti, Michele (2018-02-28). "Nuclear quantum effects enter the mainstream".

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Trachenko, K; Brazhkin, V V (2015-12-22). "Collective modes and thermodynamics of the liquid state".

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of the liquid. Radially, the diffraction intensity smoothly oscillates. This can be described by the

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are immiscible. In some cases a mixture of otherwise immiscible liquids can be stabilized to form an

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Cole, Tim; Khoshmanesh, Khashayar; Tang, Shi-Yang (2021-05-04). "Liquid Metal Enabled Biodevices".

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by Dieter K. Huzel, David H. Huang – American Institute of Aeronautics and Astronautics 1992 p. 99

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is 0. This is sometimes seen as the defining property of a liquid. However, like the bulk modulus

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However, the negligible compressibility does lead to other phenomena. The banging of pipes, called

1393:. They are significantly cheaper than conventional telescopes, but can only point straight upward ( 721: 546: 541: 330: 323: 156: 4695: 724:. On the other hand, as liquids and gases share the ability to flow, they are both called fluids. 7084: 3124: 3096: 3022: 2350: 2263: 2077: 1390: 1334: 1300: 751: 609: 604: 273: 31: 4648: 4642: 2460: 2380: 7109: 7099: 6849: 6844: 3741: 3073: 1450: 1311:

are used extensively in repair and manufacturing, for lifting, pressing, clamping and forming.

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Tang, Shi-Yang; Tabor, Christopher; Kalantar-Zadeh, Kourosh; Dickey, Michael D. (2021-07-26).

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Some materials cannot be classified within the classical three states of matter. For example,

859:, which is a gallium-indium-tin alloy that melts at −19 °C (−2 °F), as well as some 6569:

Español, Pep; Warren, Patrick B. (2017-04-21). "Perspective: Dissipative particle dynamics".

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Chandler, David (2017-05-05). "From 50 Years Ago, the Birth of Modern Liquid-State Science".

3783: 3347:. It represents a spatial average of a temporal snapshot of pair correlations in the liquid. 3233: 3091: 2558: 2309:. This situation contrasts with both gases and solids. For gases, the reference state is the 1624: 1594: 1015: 936: 584: 202: 6232: 4804: 4322: 4048: 3525: 2656: 7028: 6788: 6588: 6509: 6454: 6266:"The NIST REFPROP Database for Highly Accurate Properties of Industrially Important Fluids" 6045: 5998: 5943: 5823: 5810:

Ceriotti, Michele; Cuny, Jérôme; Parrinello, Michele; Manolopoulos, David E. (2013-09-06).

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larger than those of true molecular dynamics (hence the notion of "fictitious" particles).

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is sufficient to compute all equilibrium properties of a substance, often simply by taking

3557:, which is a function of pressure and temperature. Knowing any one thermodynamic potential 3085: 2995: 2890: 2535: 2136: 2130: 2081: 2004: 1704: 1679: 1469: 1219:, pressure, or other means. Distillation can be found in everything from the production of 1162:

industry (HVAC), liquids such as water are used to transfer heat from one area to another.

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A liquid is made up of tiny vibrating particles of matter, such as atoms, held together by

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Hydrodynamic theories describe liquids in terms of space- and time-dependent macroscopic

3400: 3119:. Under normal conditions, the diffraction pattern has circular symmetry, expressing the 3116: 2985: 2334: 2306: 2198: 1898: 1651: 1488: 1343: 1184: 1176: 860: 624: 472: 365: 71: 6592: 6513: 6498:"Review of smoothed particle hydrodynamics: towards converged Lagrangian flow modelling" 6458: 6049: 6002: 5947: 5827: 5415: 5161: 5089: 4974: 4601: 4554: 4469: 4361: 4005: 3069:

is also frequency-dependent and exhibits a similar crossover at hypersound frequencies.

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are used frequently in industry to clean oil, grease, and tar from parts and machinery.

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Wendt, John F.; Anderson, John D. Jr.; Von Karman Institute for Fluid Dynamics (2008).

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Mottl, Michael J.; Glazer, Brian T.; Kaiser, Ralf I.; Meech, Karen J. (December 2007).

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Classical molecular dynamics (MD) simulates liquids using Newton's law of motion; from

3731: 3695: 3678: 3483: 3463: 2680: 2408: 2330: 2068:. The dotted line gives the anomalous behaviour of water. The green lines show how the 1980: 1830: 1519: 1499: 1292: 1220: 736: 644: 278: 234: 229: 4151: 7180: 7175: 7145: 7104: 6993: 6945: 6930: 6823: 6793: 6661: 6612: 6604: 6555: 6543: 6525: 6470: 6466: 6427: 6417: 6394: 6384: 6346: 6315: 6303: 6285: 6238: 6200: 6175: 6165: 6142: 6132: 6095: 6085: 6018: 5961: 5904: 5859: 5841: 5763: 5753: 5727: 5717: 5691: 5681: 5641: 5631: 5591: 5573: 5532: 5524: 5475: 5465: 5429: 5380: 5370: 5342: 5332: 5295: 5285: 5257: 5249: 5214: 5204: 5173: 5165: 5109: 5101: 5047: 4986: 4946: 4859: 4835: 4810: 4781: 4676: 4652: 4627: 4615: 4566: 4515: 4495: 4483: 4438: 4426: 4395: 4383: 4375: 4328: 4304: 4294: 4273: 4253: 4221: 4199: 4179: 4157: 4133: 4091: 4068: 4017: 3959: 3951: 3920: 3908: 3875: 3825: 3702:

Other methods that combine elements of continuum and particle-level dynamics include

3520: 3516: 3510: 3315: 3112: 2723: 2719: 2643:{\displaystyle \Lambda =\left({\frac {2\pi \hbar ^{2}}{mk_{\text{B}}T}}\right)^{1/2}} 2226: 1838: 1367: 1363: 1296: 1143: 1105: 960: 820: 261: 212: 6378: 6234:

Multiparameter Equations of State: An Accurate Source of Thermodynamic Property Data

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Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

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Moffatt, H.K. (2015), "Fluid Dynamics", in Nicholas J. Higham; et al. (eds.),

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Huber, Marcia L.; Lemmon, Eric W.; Bell, Ian H.; McLinden, Mark O. (2022-06-22).

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Liquid rules: The Delightful and Dangerous Substances that Flow Through Our Lives

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Physics for Scientists and Engineers: A Strategic Approach (With Modern Physics)

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fall in between, combining elements of both continuum and particle-based models.

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Computational multiscale modeling of fluids and solids: theory and applications

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Maitland, Geoffrey C.; Rigby, Maurice; Smith, E. Brian; Wakeham, W. A. (1981).

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Static liquids in uniform gravitational fields also exhibit the phenomenon of

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Intelligent Energy Field Manufacturing: Interdisciplinary Process Innovations

4619: 4570: 4487: 4430: 4379: 4137: 4072: 4064: 4021: 3955: 3912: 3850: 3845: 3058: 2981: 2238: 2089: 2073: 2065: 2055: 2047: 2022: 1780: 1482: 1339: 1101: 1089: 1088:. They are used in the food industry, in processes such as the extraction of 1077: 952: 940: 796: 788: 634: 467: 44: 6179: 5956: 5900: 5836: 5731: 5568: 5384: 5201:

Molecular theory of water and aqueous solutions. Part 1, Understanding water

2557:

For the classical limit to apply, a necessary condition is that the thermal

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The absence of long-range order in liquids is mirrored by the absence of

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in order to stabilize the droplets. A familiar example of an emulsion is

1834: 1811: 1359: 1272: 1130:

coolants are used to keep engines from overheating. The coolants used in

1123: 909: 901: 629: 532: 7033: 7008: 6935: 6905: 6839: 6818: 3904: 3582: 3108: 3054: 3047: 2163: 2159: 2021:

the density. As an example, water has a bulk modulus of about 2.2

1875:. Intuitively, viscosity describes the resistance of a liquid to flow. 1465: 1454: 1446: 1382: 1280: 1180: 1069: 1063: 913: 866:

Pure substances that are liquid under normal conditions include water,

780: 551: 447: 6600: 6057: 3890: 2836:. For dynamic processes, there is an additional timescale constraint: 1346:, which must be able to operate under repeated deformation. The metal 6342: 3691: 2310: 2166:, which consists of a mixture of water and oil that is stabilized by 1906: 1872: 1871:

An important physical property characterizing the flow of liquids is

1854: 1386: 1371: 1264: 1151: 1085: 1073: 1011: 1007: 1001: 987: 856: 523: 518: 352: 6768: 6640:

Advanced Computer Simulation Approaches for Soft Matter Sciences III

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of selected liquids. Quantum effects are negligible when the ratio

713:), and is the only state with a definite volume but no fixed shape. 7170: 6998: 6583: 5891: 5152: 5080: 4610: 4585: 4562: 3634:

other, more readily available measurements (e.g., vapor pressure).

3120: 2653:

is small compared with the length scale under consideration. Here,

2341:. As a result, their macroscopic properties can be described using 2167: 2155: 2151: 2143: 1902: 1711: 1492: 1431: 1430:

The volume of a quantity of liquid is fixed by its temperature and

1330: 1240: 1200: 1119: 1051: 1019: 955:. Not all gases can be liquified at atmospheric pressure, however. 905: 844: 832: 772: 502: 407: 387: 373: 6648: 5809: 1410: 7130: 7018: 6953: 6870: 6865: 6642:. Berlin, Heidelberg: Springer Berlin Heidelberg. pp. 1–87. 5930:

Li, Xin-Zheng; Walker, Brent; Michaelides, Angelos (2011-04-04).

5812:"Nuclear quantum effects and hydrogen bond fluctuations in water" 4982: 4445: 4250:

Modern engineering for design of liquid-propellant rocket engines

2259: 2147: 2109: 2099:

At a temperature below the freezing point, a liquid will tend to

2051: 2043: 1918: 1914: 1826: 1796: 1670: 1643: 1370:, combined with their ability to flow to indicate temperature. A 1347: 1188: 1171: 1139: 1059: 1055: 1047: 1035: 982: 921: 897: 867: 855:. Other metal alloys that are liquid at room temperature include 840: 836: 824: 717: 256: 39: 6496:

Lind, Steven J.; Rogers, Benedict D.; Stansby, Peter K. (2020).

6193:

Bird, R. Byron; Stewart, Warren E.; Lightfoot, Edwin N. (2007).

4854:

Bird, R. Byron; Stewart, Warren E.; Lightfoot, Edwin N. (2007),

3656:, such as density, velocity, and temperature. These fields obey 1882:

The viscosity of liquids decreases with increasing temperature.

1158:, sweat removes heat from the human body by evaporating. In the 6445:

Monaghan, J J (2005-07-05). "Smoothed particle hydrodynamics".

6160:

Poling, Bruce E.; Prausnitz, J. M.; O'Connell, John P. (2001).

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simple functional forms to experimental data. For example, the

1922: 1419: 1326: 1236: 1216: 1192: 1183:

at a fairly constant temperature, making a liquid suitable for

1147: 1135: 1127: 1026:, and hydraulic systems for their good lubrication properties. 893: 6079: 5400:"Bernal's road to random packing and the structure of liquids" 3378:

use equations that model the dynamics of individual molecules.

2076:

can vary with pressure. The red line shows the boundary where

2060: 1849: 6748: 6734: 4451: 3515:

Thermodynamic potentials are functions that characterize the

2729:

For a liquid to behave classically at the macroscopic level,

2202: 1910: 1773: 1769: 1248: 1232: 1043: 925: 874: 768: 702: 694: 301: 48: 6414:

Introduction to theoretical and computational fluid dynamics

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An equivalent representation of these correlations is the

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Like all known forms of matter, liquids are fundamentally

1014:

and flow characteristics that are suitable throughout the

6744: 5680:. New York, NY: Cambridge University Press. p. 130. 5279: 4858:(2nd ed.), John Wiley & Sons, Inc., p. 21, 3942:(6). Springer Science and Business Media LLC: 1009–1013. 3793: 1325:

Liquid metals have several properties that are useful in

1081: 852: 706: 437: 5133: 5131: 2072:

can vary with pressure, and the blue line shows how the

1295:. Hydraulics can be found in many applications, such as 1018:

range of the component. Oils are often used in engines,

827:. Four more elements have melting points slightly above 6637: 6263: 5552:"Liquids: Condensed, disordered, and sometimes complex" 4590:

Publications of the Astronomical Society of the Pacific

4402: 3053:

At sub-GHz frequencies, a normal liquid cannot sustain

2992:

crosses over from the low-frequency, liquid-like limit

1381:

The free surface of a rotating liquid forms a circular

1042:

are found in a wide variety of applications, including

5711: 4799: 4346:"Stretchable and Soft Electronics using Liquid Metals" 3984: 1255:(cooling them below their individual boiling points). 6082:

The lattice Boltzmann method: principles and practice

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Handbook of thermal conductivity of liquids and gases

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The surface tension of a liquid directly affects its

1682: 1654: 1627: 1597: 1545: 1522: 1502: 83: 6276:(42). American Chemical Society (ACS): 15449–15472. 6192: 5240:(24). American Chemical Society (ACS): 13308–13361. 4853: 4778:

Chemistry: The Molecular Nature of Matter and Change

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Chemistry: The Molecular Nature of Matter and Change

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Chemistry: The Molecular Nature of Matter and Change

3978: 1122:, or the heat can be removed with the liquid during 6237:. Engineering online library. Springer. p. 1. 5929: 4408: 4293:. Oxford: Pergamon Press. pp. 56–62, 138–141. 2920:The expression for the sound velocity of a liquid, 1358:Liquids are sometimes used in measuring devices. A 6357: 6328: 5743: 5741: 5602: 4090:, McGraw-Hill Higher Education, pp. 448–449, 3774: 3625: 3601: 3573: 3549: 3492: 3472: 3452: 3350: 3339: 3306: 3271: 3242: 3219: 3199: 3147: 3038: 3011: 2953: 2899: 2876: 2821: 2785: 2741: 2709: 2689: 2665: 2642: 2477: 2447: 2417: 2397: 2369: 2288: 2150:(drinking alcohol) are miscible whereas water and 2013: 1989: 1969: 1718:than that of the liquid, the buoyant force points 1695: 1661: 1634: 1611: 1577: 1528: 1508: 851:). An example is the sodium-potassium metal alloy 118: 6495: 5671: 5669: 5137: 4748:by S. C. Gupta -- Dorling-Kindersley 2006 Page 85 2749:must be small compared with the average distance 2229:, which persists over a few molecular diameters. 1722:and the object floats, whereas if the density is 7203: 6322: 5876: 4834:(2nd ed.), Pergamon Press, pp. 44–45, 817:standard conditions for temperature and pressure 6331:Journal of Physical and Chemical Reference Data 6270:Industrial & Engineering Chemistry Research 6120: 5997:(2). Cambridge Philosophical Society: 160–172. 5936:Proceedings of the National Academy of Sciences 5816:Proceedings of the National Academy of Sciences 5738: 5556:Proceedings of the National Academy of Sciences 5360: 5358: 5356: 5320: 5275: 5273: 5271: 4793: 4511:Instrument engineers' handbook: process control 3725: 1935:Speed of sound § Speed of sound in liquids 1893:The viscous behavior of a liquid can be either 1418:Quantities of liquids are measured in units of 6405: 6368:, Princeton University Press, pp. 467–476 6366:The Princeton Companion to Applied Mathematics 5885:(3). Springer Science and Business Media LLC. 5666: 5626:Hansen, Jean-Pierre; McDonald, Ian R. (2013). 5625: 4945:, University Science Books, pp. 727–729, 4829: 3200:{\displaystyle q=(4\pi /\lambda )\sin \theta } 1768:, in units of energy per unit area (SI units: 1397:). A common choice for the liquid is mercury. 1146:films are used to cool the thrust chambers of 6700: 6568: 6381:Computational fluid dynamics: an introduction 6075: 6073: 6071: 5455: 5453: 5451: 5225: 4931:by Laid Boukraa -- CRC Press 2014 Page 22--24 4780:, McGraw-Hill Higher Education, p. 457, 4675:, McGraw-Hill Higher Education, p. 461, 4583: 4238:The prospects of nuclear power and technology 2225:as in a crystalline lattice, they do possess 2025:and a density of 1000 kg/m, which gives 1287:since ancient times. Oils are forced through 667: 6438: 6199:(2nd ed.). John Wiley & Sons, Inc. 5803: 5543: 5367:Introduction to modern statistical mechanics 5353: 5268: 5192: 5059: 4103: 4028: 3933: 2877:{\displaystyle \tau \gg {\frac {h}{k_{B}T}}} 2324: 1283:have been used to change liquid motion into 6714: 6631: 6562: 6126: 5707: 5705: 5326: 4586:"Image Quality of Liquid‐Mirror Telescopes" 4577: 4524: 4178:William Andrew Publishing 2001 pp. 847–881 4037:Annual Review of Astronomy and Astrophysics 3884: 3504: 2425:is the average distance between molecules. 2096:can prevent this in certain circumstances. 1939:The speed of sound in a liquid is given by 119:{\displaystyle J=-D{\frac {d\varphi }{dx}}} 6707: 6693: 6411: 6153: 6112:: CS1 maint: location missing publisher ( 6068: 5780:: CS1 maint: location missing publisher ( 5747: 5658:: CS1 maint: location missing publisher ( 5500: 5492:: CS1 maint: location missing publisher ( 5464:. Oxford, United Kingdom. pp. 48–52. 5448: 5391: 5312:: CS1 maint: location missing publisher ( 5046:, Houghton Mifflin Harcourt, p. 124, 4775: 4718: 4670: 4454:"Gallium Liquid Metal: The Devil's Elixir" 4337: 4085: 3927: 3407:is sometimes approximated by the function 3405:temperature-dependence of liquid viscosity 2822:{\displaystyle {\frac {\Lambda }{a}}\ll 1} 2697:is the molecule's mass. Typical values of 2177: 1374:uses the weight of the liquid to indicate 1160:heating, ventilation, and air-conditioning 1076:. Solvents like alcohol are often used as 674: 660: 6647: 6582: 6537: 6372: 6297: 6257: 5973: 5955: 5890: 5853: 5835: 5585: 5567: 5423: 5151: 5079: 5038: 4964: 4871: 4727:By Wenwu Zhang -- CRC Press 2011 Page 144 4609: 4544: 4477: 4369: 4282: 4217:Automotive technology: a systems approach 4127: 4109: 4034: 3393: 3227:of the probe (photon or neutron) and the 1658: 1646:of the liquid, assumed uniform with depth 1631: 1608: 1574: 1414:Cavitation in water from a boat propeller 6489: 6444: 6224: 6034:"Thermodynamics of Crystals and Melting" 5702: 5549: 5410:(31–33). Informa UK Limited: 3940–3969. 5364: 5198: 5065: 4929:Honey in Traditional and Modern Medicine 3090: 3019:to the high-frequency, solid-like limit 2357:Table 1: Thermal de Broglie wavelengths 2212: 2059: 1848: 1751: 1476: 1409: 1400: 1307:, and airplane control systems. Various 1134:include water or liquid metals, such as 981: 750: 38: 6363: 4539:. American Astronomical Society: L201. 4270:HVAC principles and applications manual 3365:and time scales over which they apply. 3102: 2208: 2139:with gases, solids, and other liquids. 1730:and the object sinks. This is known as 1437:On the other hand, liquids have little 1038:, to dissolve other liquids or solids. 763:, with the others being solid, gas and 14: 7204: 5923: 5794: 5675: 5506: 5459: 5397: 5098:10.1146/annurev-physchem-052516-044941 5004: 4940: 4746:Fluid Mechanics and Hydraulic Machines 4640: 4343: 4057:10.1146/annurev.astro.43.051804.102202 3936:Analytical and Bioanalytical Chemistry 3794:Ab initio (quantum) molecular dynamics 2191: 939:by cooling, producing liquids such as 6688: 6416:. New York: Oxford University Press. 5932:"Quantum nature of the hydrogen bond" 5369:. New York: Oxford University Press. 5007:"Does water freeze or boil in space?" 4877: 4830:Landau, L.D.; Lifshitz, E.M. (1987), 4288: 2786:{\displaystyle a\approx \rho ^{-1/3}} 2299: 2245: 1676:For a body of water open to the air, 699:the four fundamental states of matter 6230: 6031: 5988: 5748:Marx, Dominik; Hutter, Jürg (2012). 5327:Gallo, Paola; Rovere, Mauro (2021). 4967:Introduction to Liquid State Physics 4706:from the original on 7 December 2017 4584:Hickson, Paul; Racine, Réne (2007). 4479:10.1146/annurev-matsci-080819-125403 3095:Radial distribution function of the 2984:. In reality, all liquids show some 2915: 2037: 1928: 6162:The properties of gases and liquids 5716:. Oxford: Oxford University Press. 5068:Annual Review of Physical Chemistry 4458:Annual Review of Materials Research 4240:D. Van Nostrand Company 1957 p. 266 3694:. Conceptually, it is based on the 2954:{\displaystyle c={\sqrt {K/\rho }}} 2115: 1970:{\displaystyle c={\sqrt {K/\rho }}} 1263:Liquid is the primary component of 888:Important everyday liquids include 24: 4327:Butterworth-Heinemann 2000 p. vii 4291:Unit operations in food processing 3618: 3594: 3566: 3519:of a substance. An example is the 3057:: the zero-frequency limit of the 3031: 2805: 2736: 2704: 2571: 2464: 2442: 2384: 2364: 25: 7233: 5799:, The University of Chicago Press 4344:Dickey, Michael D. (2017-04-18). 4112:"Introduction to liquid crystals" 4110:Andrienko, Denis (October 2018). 3800:Car–Parrinello molecular dynamics 3609:. Thus, a single correlation for 3453:{\displaystyle \eta (T)=Ae^{B/T}} 2032: 1578:{\displaystyle p=p_{0}+\rho gz\,} 1267:systems, which take advantage of 873:Inorganic liquids include water, 55:, which is the natural result of 6767: 6453:(8). IOP Publishing: 1703–1759. 5678:Statistical physics of particles 5462:Water: a very short introduction 4965:March, N.H.; Tosi, M.P. (2002), 4906:. UK: Anton Paar. Archived from 4596:(854). IOP Publishing: 456–465. 3893:Journal of Materials Chemistry A 3712:multiparticle collision dynamics 3637: 2184:Structure of liquids and glasses 1353: 1321:Liquid metal § Applications 1314: 1072:are commonly found in soaps and 900:of different substances such as 6571:The Journal of Chemical Physics 6213:from the original on 2020-03-02 6186: 6131:. Cham, Switzerland: Springer. 6025: 5982: 5788: 5203:. Singapore: World Scientific. 5032: 5023: 4998: 4969:, World Scientific, p. 7, 4958: 4934: 4922: 4896: 4847: 4823: 4769: 4760: 4751: 4739: 4730: 4688: 4664: 4634: 4502: 4315: 4262: 4243: 4230: 4208: 4188: 3704:smoothed-particle hydrodynamics 3357:Computational materials science 3351:Prediction of liquid properties 2343:classical statistical mechanics 1445:(bar). At around 4000 bar (400 1385:and can therefore be used as a 1291:, which transmit this force to 1206: 1080:. They are found in cosmetics, 977: 746: 6577:(15). AIP Publishing: 150901. 6447:Reports on Progress in Physics 5550:Chandler, David (2009-09-08). 5398:Finney, John L. (2013-02-22). 5140:Reports on Progress in Physics 4880:"Viscosity Blending Equations" 4776:Silberberg, Martin S. (2009), 4671:Silberberg, Martin S. (2009), 4464:(1). Annual Reviews: 381–408. 4166: 4144: 4086:Silberberg, Martin S. (2009), 4079: 3868: 3775:{\displaystyle F=m{\ddot {x}}} 3717: 3658:partial differential equations 3626:{\displaystyle {\mathcal {F}}} 3602:{\displaystyle {\mathcal {F}}} 3574:{\displaystyle {\mathcal {F}}} 3544: 3532: 3423: 3417: 3388: 3334: 3328: 3301: 3295: 3266: 3260: 3185: 3168: 3142: 3136: 1619:is the pressure at the surface 1468:. Because liquids have little 1179:tend to transfer heat through 995: 13: 1: 7156:Macroscopic quantum phenomena 5797:Statistical Theory of Liquids 5162:10.1088/0034-4885/79/1/016502 5146:(1). IOP Publishing: 016502. 4700:hyperphysics.phy-astr.gsu.edu 3862: 3708:dissipative particle dynamics 3672: 2988:: with increasing frequency, 2793:between molecules. That is, 2289:{\displaystyle k_{\text{B}}T} 2221:While liquids do not exhibit 1258: 879:inorganic nonaqueous solvents 761:four primary states of matter 43:The formation of a spherical 7166:Order and disorder (physics) 6337:(1). AIP Publishing: 63–96. 5425:10.1080/14786435.2013.770179 5074:(1). Annual Reviews: 19–38. 5005:Siegel, Ethan (2014-12-11). 4809:. De Gruyter. pp. 3–5. 4696:"Compressibility of Liquids" 4411:Advanced Intelligent Systems 4220:Delmar Learning 2000 p. 309 4150:Theo Mang, Wilfried Dressel 4129:10.1016/j.molliq.2018.01.175 4116:Journal of Molecular Liquids 4014:10.1016/j.chemer.2007.09.002 3726:Classical molecular dynamics 3648:Computational fluid dynamics 3284:radial distribution function 2124: 1825:of a liquid is disturbed by 1455:transmitting hydraulic power 1110:Liquids tend to have better 1029: 863:(alloys involving mercury). 7: 6658:10.1007/978-3-540-87706-6_1 6508:(2241). The Royal Society. 6127:Steinhauser, M. O. (2022). 6038:Journal of Chemical Physics 5246:10.1021/acs.chemrev.5b00308 5029:Silberberg, pp. 188 and 502 4641:Knight, Randall D. (2008), 3808: 3076:, the Fourier transform of 3039:{\displaystyle K_{\infty }} 2142:Two liquids are said to be 2088:At a temperature below the 1737: 1726:, the buoyant force points 1344:wearable healthcare devices 1066:are water-based solutions. 806: 10: 7238: 6467:10.1088/0034-4885/68/8/r01 5714:Theory of molecular fluids 4647:, Addison-Wesley, p. 4153:Lubricants and lubrication 3797: 3729: 3676: 3641: 3508: 3354: 3314:, which is related to the 2478:{\displaystyle \Lambda /a} 2398:{\displaystyle \Lambda /a} 2205:are a notable exception). 2181: 2128: 2041: 1932: 1860: 1741: 1671:gravitational acceleration 1480: 1318: 1170:Liquids are often used in 1165: 1099: 1095: 999: 29: 7118: 7072: 6944: 6858: 6832: 6776: 6765: 6727: 6164:. New York: McGraw-Hill. 6011:10.1017/S0305004100017138 4766:Knight (2008) pp. 455-459 4533:The Astrophysical Journal 3948:10.1007/s00216-005-0069-7 3660:, which can be linear or 3097:Lennard-Jones model fluid 2325:Role of quantum mechanics 2242:breaking, and reforming. 1405: 1034:Many liquids are used as 7191:Thermo-dielectric effect 7090:Enthalpy of vaporization 6784:Bose–Einstein condensate 6282:10.1021/acs.iecr.2c01427 5991:Mathematical Proceedings 5879:Nature Reviews Chemistry 5365:Chandler, David (1987). 5329:Physics of liquid matter 5199:Ben-Naim, Arieh (2009). 4941:Taylor, John R. (2005), 4806:Wetting of Real Surfaces 3987:"Water and astrobiology" 3688:lattice Boltzmann method 3505:Thermodynamic potentials 3220:{\displaystyle \lambda } 3207:given by the wavelength 2742:{\displaystyle \Lambda } 2710:{\displaystyle \Lambda } 2448:{\displaystyle \Lambda } 2370:{\displaystyle \Lambda } 1391:liquid-mirror telescopes 178:Clausius–Duhem (entropy) 128:Fick's laws of diffusion 7085:Enthalpy of sublimation 6412:Pozrikidis, C. (2011). 5957:10.1073/pnas.1016653108 5901:10.1038/s41570-017-0109 5837:10.1073/pnas.1308560110 5676:Kardar, Mehran (2007). 5569:10.1073/pnas.0908029106 5515:(7). Wiley: 1369–1375. 4049:2005ARA&A..43...31C 3243:{\displaystyle \theta } 3125:static structure factor 2351:Lennard-Jones potential 2339:Newton's laws of motion 2264:microcanonical ensemble 2178:Microscopic description 2170:, a substance found in 1844: 1635:{\displaystyle \rho \,} 1612:{\displaystyle p_{0}\,} 1335:electrical conductivity 972:liquid-crystal displays 336:Navier–Stokes equations 274:Material failure theory 32:Liquid (disambiguation) 7100:Latent internal energy 6850:Color-glass condensate 6522:10.1098/rspa.2019.0801 5521:10.1002/cphc.200400663 5460:Finney, J. L. (2015). 5404:Philosophical Magazine 4801:Edward Yu. Bormashenko 4514:CRC Press 1999 p. 807 4423:10.1002/aisy.202000275 4371:10.1002/adma.201606425 4356:(27). Wiley: 1606425. 3776: 3627: 3603: 3575: 3551: 3550:{\displaystyle G(p,T)} 3494: 3474: 3454: 3394:Empirical correlations 3341: 3308: 3273: 3250:. The oscillations of 3244: 3221: 3201: 3149: 3099: 3074:linear response theory 3040: 3013: 2955: 2901: 2878: 2823: 2787: 2743: 2711: 2691: 2667: 2666:{\displaystyle \hbar } 2644: 2479: 2449: 2419: 2399: 2371: 2290: 2218: 2085: 2015: 1991: 1971: 1858: 1760: 1697: 1663: 1636: 1613: 1579: 1530: 1510: 1415: 1229:cryogenic distillation 1006:Liquids are useful as 992: 771:. Unlike a solid, the 756: 120: 60: 6910:Magnetically ordered 5795:Fisher, I.Z. (1964), 4878:Zhmud, Boris (2014), 4417:(7). Wiley: 2000275. 4289:Earle, R. L. (1983). 3784:intermolecular forces 3777: 3628: 3604: 3576: 3552: 3495: 3475: 3455: 3342: 3309: 3274: 3245: 3222: 3202: 3150: 3094: 3041: 3014: 3012:{\displaystyle K_{0}} 2956: 2902: 2900:{\displaystyle \tau } 2879: 2824: 2788: 2744: 2712: 2692: 2668: 2645: 2559:de Broglie wavelength 2480: 2450: 2420: 2400: 2372: 2291: 2262:at fixed energy (see 2216: 2063: 2016: 2014:{\displaystyle \rho } 1992: 1972: 1852: 1805:nanoscale confinement 1755: 1732:Archimedes' principle 1698: 1696:{\displaystyle p_{0}} 1664: 1637: 1614: 1580: 1531: 1511: 1477:Pressure and buoyancy 1413: 1401:Mechanical properties 1389:. These are known as 1333:, particularly their 1016:operating temperature 985: 759:Liquid is one of the 754: 331:Bernoulli's principle 324:Archimedes' principle 121: 42: 6789:Fermionic condensate 6383:. Berlin: Springer. 4757:Knight (2008) p. 448 4736:Knight (2008) p. 454 4324:Fluid power dynamics 4175:Handbook of solvents 3748: 3613: 3589: 3561: 3526: 3484: 3464: 3411: 3340:{\displaystyle S(q)} 3322: 3307:{\displaystyle g(r)} 3289: 3272:{\displaystyle S(q)} 3254: 3234: 3211: 3159: 3148:{\displaystyle S(q)} 3130: 3103:Experimental methods 3065:, the shear modulus 3023: 2996: 2927: 2891: 2843: 2800: 2753: 2733: 2701: 2681: 2657: 2568: 2536:Carbon tetrachloride 2461: 2439: 2409: 2381: 2361: 2270: 2209:Short-range ordering 2131:Solution (chemistry) 2005: 1981: 1943: 1705:atmospheric pressure 1680: 1652: 1625: 1595: 1543: 1520: 1500: 1443:atmospheric pressure 1422:. These include the 1366:of liquids, such as 1215:, using heat, cold, 1112:thermal conductivity 729:intermolecular bonds 423:Cohesion (chemistry) 245:Infinitesimal strain 81: 30:For other uses, see 7004:Chemical ionization 6896:Programmable matter 6886:Quantum spin liquid 6754:Supercritical fluid 6593:2017JChPh.146o0901E 6514:2020RSPSA.47690801L 6459:2005RPPh...68.1703M 6196:Transport Phenomena 6050:1939JChPh...7..591B 6003:1940PCPS...36..160B 5948:2011PNAS..108.6369L 5828:2013PNAS..11015591C 5822:(39): 15591–15596. 5562:(36): 15111–15112. 5416:2013PMag...93.3940F 5090:2017ARPC...68...19C 5011:Starts With A Bang! 4975:2002ilsp.book.....M 4943:Classical Mechanics 4856:Transport Phenomena 4803:(5 November 2018). 4602:2007PASP..119..456H 4555:1994ApJ...436L.201H 4470:2021AnRMS..51..381T 4362:2017AdM....2906425D 4006:2007ChEG...67..253M 3856:Supercritical fluid 3742:Newton's second law 3736:Molecular mechanics 3376:Microscopic methods 3370:Macroscopic methods 3117:neutron diffraction 2426: 2335:classical mechanics 2307:perturbation theory 2223:long-range ordering 2199:crystalline lattice 2192:General description 1803:. In liquids under 1662:{\displaystyle g\,} 1489:gravitational field 1293:hydraulic cylinders 1221:alcoholic beverages 1177:kinematic viscosity 737:interstellar clouds 341:Poiseuille equation 72:Continuum mechanics 66:Part of a series on 7151:Leidenfrost effect 7080:Enthalpy of fusion 6845:Quark–gluon plasma 6032:Born, Max (1939). 5331:. Cham: Springer. 4350:Advanced Materials 3905:10.1039/d2ta06882f 3772: 3732:Molecular dynamics 3696:Boltzmann equation 3686:An example is the 3679:Mesoscopic physics 3623: 3599: 3571: 3547: 3490: 3470: 3450: 3382:Mesoscopic methods 3337: 3304: 3269: 3240: 3217: 3197: 3155:, with wavenumber 3145: 3100: 3036: 3009: 2951: 2897: 2874: 2819: 2783: 2739: 2707: 2687: 2663: 2640: 2475: 2445: 2415: 2395: 2367: 2356: 2331:quantum mechanical 2300:No small parameter 2286: 2246:Energy and entropy 2219: 2086: 2011: 2001:of the liquid and 1987: 1967: 1859: 1761: 1693: 1659: 1632: 1609: 1575: 1526: 1506: 1416: 1275:. Devices such as 993: 935:Many gases can be 757: 701:(the others being 547:Magnetorheological 542:Electrorheological 279:Fracture mechanics 116: 61: 7199: 7198: 7181:Superheated vapor 7176:Superconductivity 7146:Equation of state 6994:Flash evaporation 6946:Phase transitions 6931:String-net liquid 6824:Photonic molecule 6794:Degenerate matter 6667:978-3-540-87705-9 6601:10.1063/1.4979514 6423:978-0-19-990912-4 6390:978-3-540-85056-4 6244:978-3-540-67311-8 6231:Span, R. (2000). 6206:978-0-470-11539-8 6138:978-3-030-98954-5 6091:978-3-319-44649-3 6058:10.1063/1.1750497 5942:(16): 6369–6373. 5759:978-0-521-89863-8 5687:978-0-521-87342-0 5637:978-0-12-387033-9 5471:978-0-19-870872-8 5338:978-3-030-68349-8 5210:978-981-283-761-5 5053:978-0-544-85019-4 4992:978-981-3102-53-8 4952:978-1-891389-22-1 4904:"Viscosity Index" 4865:978-0-470-11539-8 4841:978-0-08-033933-7 4816:978-3-11-058314-4 4787:978-0-07-304859-8 4682:978-0-07-304859-8 4658:978-0-8053-2736-6 4272:McGraw-Hill 1997 4156:, Wiley-VCH 2007 4097:978-0-07-304859-8 3826:Liquid dielectric 3769: 3521:Gibbs free energy 3517:equilibrium state 3511:Equation of state 3493:{\displaystyle B} 3473:{\displaystyle A} 3316:Fourier transform 2949: 2916:Dynamic phenomena 2872: 2811: 2720:zero-point motion 2690:{\displaystyle m} 2620: 2613: 2555: 2554: 2418:{\displaystyle a} 2280: 2227:short-range order 2135:Liquids can form 2038:Phase transitions 2029:= 1.5 km/s. 1990:{\displaystyle K} 1965: 1929:Sound propagation 1839:surface roughness 1529:{\displaystyle z} 1509:{\displaystyle p} 1364:thermal expansion 1309:hydraulic presses 1297:automotive brakes 1231:of gases such as 1144:Liquid propellant 1106:Immersion cooling 890:aqueous solutions 684: 683: 559: 558: 493: 492: 262:Contact mechanics 185: 184: 114: 16:(Redirected from 7229: 7217:Phases of matter 7136:Compressed fluid 6771: 6716:States of matter 6709: 6702: 6695: 6686: 6685: 6680: 6679: 6651: 6635: 6629: 6628: 6586: 6566: 6560: 6559: 6541: 6493: 6487: 6486: 6442: 6436: 6435: 6409: 6403: 6402: 6376: 6370: 6369: 6361: 6355: 6354: 6343:10.1063/1.556015 6326: 6320: 6319: 6301: 6261: 6255: 6254: 6252: 6251: 6228: 6222: 6221: 6219: 6218: 6190: 6184: 6183: 6157: 6151: 6150: 6124: 6118: 6117: 6111: 6103: 6077: 6066: 6065: 6060:. Archived from 6029: 6023: 6022: 5986: 5980: 5979: 5977: 5959: 5927: 5921: 5920: 5894: 5874: 5868: 5867: 5857: 5839: 5807: 5801: 5800: 5792: 5786: 5785: 5779: 5771: 5745: 5736: 5735: 5709: 5700: 5699: 5673: 5664: 5663: 5657: 5649: 5623: 5600: 5599: 5589: 5571: 5547: 5541: 5540: 5504: 5498: 5497: 5491: 5483: 5457: 5446: 5445: 5427: 5395: 5389: 5388: 5362: 5351: 5350: 5324: 5318: 5317: 5311: 5303: 5277: 5266: 5265: 5234:Chemical Reviews 5229: 5223: 5222: 5196: 5190: 5189: 5155: 5135: 5126: 5125: 5083: 5063: 5057: 5056: 5036: 5030: 5027: 5021: 5020: 5018: 5017: 5002: 4996: 4995: 4962: 4956: 4955: 4938: 4932: 4926: 4920: 4919: 4917: 4915: 4910:on March 9, 2020 4900: 4894: 4893: 4884: 4875: 4869: 4868: 4851: 4845: 4844: 4827: 4821: 4820: 4797: 4791: 4790: 4773: 4767: 4764: 4758: 4755: 4749: 4743: 4737: 4734: 4728: 4722: 4716: 4715: 4713: 4711: 4692: 4686: 4685: 4668: 4662: 4661: 4638: 4632: 4631: 4613: 4581: 4575: 4574: 4548: 4546:astro-ph/9406057 4528: 4522: 4506: 4500: 4499: 4481: 4449: 4443: 4442: 4406: 4400: 4399: 4373: 4341: 4335: 4321:R. Keith Mobley 4319: 4313: 4312: 4286: 4280: 4266: 4260: 4247: 4241: 4234: 4228: 4212: 4206: 4194:N. B. Vargaftik 4192: 4186: 4170: 4164: 4148: 4142: 4141: 4131: 4107: 4101: 4100: 4083: 4077: 4076: 4032: 4026: 4025: 3991: 3982: 3976: 3975: 3931: 3925: 3924: 3888: 3882: 3872: 3836:Liquid breathing 3781: 3779: 3778: 3773: 3771: 3770: 3762: 3632: 3630: 3629: 3624: 3622: 3621: 3608: 3606: 3605: 3600: 3598: 3597: 3580: 3578: 3577: 3572: 3570: 3569: 3556: 3554: 3553: 3548: 3499: 3497: 3496: 3491: 3479: 3477: 3476: 3471: 3459: 3457: 3456: 3451: 3449: 3448: 3444: 3346: 3344: 3343: 3338: 3313: 3311: 3310: 3305: 3278: 3276: 3275: 3270: 3249: 3247: 3246: 3241: 3226: 3224: 3223: 3218: 3206: 3204: 3203: 3198: 3181: 3154: 3152: 3151: 3146: 3045: 3043: 3042: 3037: 3035: 3034: 3018: 3016: 3015: 3010: 3008: 3007: 2960: 2958: 2957: 2952: 2950: 2945: 2937: 2906: 2904: 2903: 2898: 2883: 2881: 2880: 2875: 2873: 2871: 2867: 2866: 2853: 2828: 2826: 2825: 2820: 2812: 2804: 2792: 2790: 2789: 2784: 2782: 2781: 2777: 2748: 2746: 2745: 2740: 2716: 2714: 2713: 2708: 2696: 2694: 2693: 2688: 2672: 2670: 2669: 2664: 2649: 2647: 2646: 2641: 2639: 2638: 2634: 2625: 2621: 2619: 2615: 2614: 2611: 2601: 2600: 2599: 2583: 2484: 2482: 2481: 2476: 2471: 2454: 2452: 2451: 2446: 2433:Temperature (K) 2427: 2424: 2422: 2421: 2416: 2405:is small, where 2404: 2402: 2401: 2396: 2391: 2376: 2374: 2373: 2368: 2355: 2315:virial expansion 2295: 2293: 2292: 2287: 2282: 2281: 2278: 2116:Liquids in space 2020: 2018: 2017: 2012: 1996: 1994: 1993: 1988: 1976: 1974: 1973: 1968: 1966: 1961: 1953: 1853:A simulation of 1793:capillary action 1702: 1700: 1699: 1694: 1692: 1691: 1668: 1666: 1665: 1660: 1641: 1639: 1638: 1633: 1618: 1616: 1615: 1610: 1607: 1606: 1584: 1582: 1581: 1576: 1561: 1560: 1535: 1533: 1532: 1527: 1515: 1513: 1512: 1507: 1491:, liquids exert 1395:zenith telescope 1197:potential energy 1132:nuclear reactors 920:like blood, and 849:eutectic mixture 829:room temperature 767:. A liquid is a 739:) or plasma (as 722:condensed matter 676: 669: 662: 508: 507: 473:Gay-Lussac's law 463:Combined gas law 413:Capillary action 298: 297: 141: 140: 125: 123: 122: 117: 115: 113: 105: 97: 63: 62: 21: 7237: 7236: 7232: 7231: 7230: 7228: 7227: 7226: 7202: 7201: 7200: 7195: 7126:Baryonic matter 7114: 7068: 7039:Saturated fluid 6979:Crystallization 6940: 6914:Antiferromagnet 6854: 6828: 6772: 6763: 6723: 6713: 6683: 6668: 6636: 6632: 6567: 6563: 6494: 6490: 6443: 6439: 6424: 6410: 6406: 6391: 6377: 6373: 6362: 6358: 6327: 6323: 6262: 6258: 6249: 6247: 6245: 6229: 6225: 6216: 6214: 6207: 6191: 6187: 6172: 6158: 6154: 6139: 6125: 6121: 6105: 6104: 6092: 6084:. Switzerland. 6078: 6069: 6030: 6026: 5987: 5983: 5928: 5924: 5875: 5871: 5808: 5804: 5793: 5789: 5773: 5772: 5760: 5746: 5739: 5724: 5710: 5703: 5688: 5674: 5667: 5651: 5650: 5638: 5624: 5603: 5548: 5544: 5505: 5501: 5485: 5484: 5472: 5458: 5449: 5396: 5392: 5377: 5363: 5354: 5339: 5325: 5321: 5305: 5304: 5292: 5278: 5269: 5230: 5226: 5211: 5197: 5193: 5136: 5129: 5064: 5060: 5054: 5040:Miodownik, Mark 5037: 5033: 5028: 5024: 5015: 5013: 5003: 4999: 4993: 4963: 4959: 4953: 4939: 4935: 4927: 4923: 4913: 4911: 4902: 4901: 4897: 4882: 4876: 4872: 4866: 4852: 4848: 4842: 4832:Fluid Mechanics 4828: 4824: 4817: 4798: 4794: 4788: 4774: 4770: 4765: 4761: 4756: 4752: 4744: 4740: 4735: 4731: 4723: 4719: 4709: 4707: 4694: 4693: 4689: 4683: 4669: 4665: 4659: 4639: 4635: 4582: 4578: 4529: 4525: 4508:Bela G. Liptak 4507: 4503: 4450: 4446: 4407: 4403: 4342: 4338: 4320: 4316: 4301: 4287: 4283: 4267: 4263: 4248: 4244: 4235: 4231: 4213: 4209: 4198:CRC Press 1994 4193: 4189: 4171: 4167: 4149: 4145: 4108: 4104: 4098: 4084: 4080: 4033: 4029: 3989: 3983: 3979: 3932: 3928: 3889: 3885: 3873: 3869: 3865: 3860: 3841:Liquid resistor 3811: 3802: 3796: 3761: 3760: 3749: 3746: 3745: 3738: 3730:Main articles: 3728: 3720: 3681: 3675: 3650: 3642:Main articles: 3640: 3617: 3616: 3614: 3611: 3610: 3593: 3592: 3590: 3587: 3586: 3565: 3564: 3562: 3559: 3558: 3527: 3524: 3523: 3513: 3507: 3485: 3482: 3481: 3465: 3462: 3461: 3440: 3436: 3432: 3412: 3409: 3408: 3396: 3391: 3359: 3353: 3323: 3320: 3319: 3290: 3287: 3286: 3255: 3252: 3251: 3235: 3232: 3231: 3212: 3209: 3208: 3177: 3160: 3157: 3156: 3131: 3128: 3127: 3105: 3030: 3026: 3024: 3021: 3020: 3003: 2999: 2997: 2994: 2993: 2941: 2936: 2928: 2925: 2924: 2918: 2892: 2889: 2888: 2862: 2858: 2857: 2852: 2844: 2841: 2840: 2803: 2801: 2798: 2797: 2773: 2766: 2762: 2754: 2751: 2750: 2734: 2731: 2730: 2726:are important. 2702: 2699: 2698: 2682: 2679: 2678: 2675:Planck constant 2658: 2655: 2654: 2630: 2626: 2610: 2606: 2602: 2595: 2591: 2584: 2582: 2578: 2577: 2569: 2566: 2565: 2541: 2492: 2467: 2462: 2459: 2458: 2440: 2437: 2436: 2410: 2407: 2406: 2387: 2382: 2379: 2378: 2362: 2359: 2358: 2347:classical limit 2327: 2319:lattice defects 2302: 2277: 2273: 2271: 2268: 2267: 2252:entropic forces 2248: 2239:hydrogen-bonded 2211: 2194: 2186: 2180: 2133: 2127: 2118: 2058: 2042:Main articles: 2040: 2035: 2006: 2003: 2002: 1982: 1979: 1978: 1957: 1952: 1944: 1941: 1940: 1937: 1931: 1888:viscosity index 1869: 1863:Fluid mechanics 1861:Main articles: 1847: 1766:surface tension 1750: 1748:Surface science 1744:Surface tension 1742:Main articles: 1740: 1687: 1683: 1681: 1678: 1677: 1653: 1650: 1649: 1626: 1623: 1622: 1602: 1598: 1596: 1593: 1592: 1556: 1552: 1544: 1541: 1540: 1521: 1518: 1517: 1501: 1498: 1497: 1485: 1479: 1439:compressibility 1408: 1403: 1362:often uses the 1356: 1323: 1317: 1305:heavy equipment 1289:hydraulic pumps 1285:mechanical work 1261: 1209: 1168: 1108: 1098: 1032: 1004: 998: 980: 968:liquid crystals 949:liquid hydrogen 945:liquid nitrogen 892:like household 809: 749: 680: 651: 650: 649: 569: 561: 560: 514:Viscoelasticity 505: 495: 494: 482: 432: 428:Surface tension 392: 295: 293:Fluid mechanics 285: 284: 283: 197: 195:Solid mechanics 187: 186: 138: 130: 106: 98: 96: 82: 79: 78: 57:surface tension 35: 28: 27:State of matter 23: 22: 15: 12: 11: 5: 7235: 7225: 7224: 7219: 7214: 7197: 7196: 7194: 7193: 7188: 7183: 7178: 7173: 7168: 7163: 7158: 7153: 7148: 7143: 7138: 7133: 7128: 7122: 7120: 7116: 7115: 7113: 7112: 7107: 7105:Trouton's rule 7102: 7097: 7092: 7087: 7082: 7076: 7074: 7070: 7069: 7067: 7066: 7061: 7056: 7051: 7046: 7041: 7036: 7031: 7026: 7021: 7016: 7011: 7006: 7001: 6996: 6991: 6986: 6981: 6976: 6974:Critical point 6971: 6966: 6961: 6956: 6950: 6948: 6942: 6941: 6939: 6938: 6933: 6928: 6927: 6926: 6921: 6916: 6908: 6903: 6898: 6893: 6888: 6883: 6878: 6876:Liquid crystal 6873: 6868: 6862: 6860: 6856: 6855: 6853: 6852: 6847: 6842: 6836: 6834: 6830: 6829: 6827: 6826: 6821: 6816: 6811: 6809:Strange matter 6806: 6804:Rydberg matter 6801: 6796: 6791: 6786: 6780: 6778: 6774: 6773: 6766: 6764: 6762: 6761: 6756: 6751: 6742: 6737: 6731: 6729: 6725: 6724: 6712: 6711: 6704: 6697: 6689: 6682: 6681: 6666: 6630: 6561: 6488: 6437: 6422: 6404: 6389: 6371: 6356: 6321: 6256: 6243: 6223: 6205: 6185: 6170: 6152: 6137: 6119: 6090: 6067: 6064:on 2016-05-15. 6044:(8): 591–604. 6024: 5981: 5922: 5869: 5802: 5787: 5758: 5737: 5722: 5701: 5686: 5665: 5636: 5601: 5542: 5499: 5470: 5447: 5390: 5375: 5352: 5337: 5319: 5290: 5267: 5224: 5209: 5191: 5127: 5058: 5052: 5031: 5022: 4997: 4991: 4957: 4951: 4933: 4921: 4895: 4870: 4864: 4846: 4840: 4822: 4815: 4792: 4786: 4768: 4759: 4750: 4738: 4729: 4717: 4687: 4681: 4663: 4657: 4633: 4611:10.1086/517619 4576: 4563:10.1086/187667 4523: 4501: 4444: 4401: 4336: 4314: 4299: 4281: 4268:Thomas E Mull 4261: 4242: 4229: 4207: 4187: 4172:George Wypych 4165: 4143: 4102: 4096: 4078: 4027: 4000:(4): 253–282. 3977: 3926: 3883: 3866: 3864: 3861: 3859: 3858: 3853: 3848: 3843: 3838: 3833: 3831:Liquid marbles 3828: 3823: 3818: 3812: 3810: 3807: 3795: 3792: 3768: 3765: 3759: 3756: 3753: 3727: 3724: 3719: 3716: 3674: 3671: 3644:Fluid dynamics 3639: 3636: 3620: 3596: 3568: 3546: 3543: 3540: 3537: 3534: 3531: 3506: 3503: 3489: 3469: 3447: 3443: 3439: 3435: 3431: 3428: 3425: 3422: 3419: 3416: 3395: 3392: 3390: 3387: 3386: 3385: 3379: 3373: 3352: 3349: 3336: 3333: 3330: 3327: 3303: 3300: 3297: 3294: 3268: 3265: 3262: 3259: 3239: 3216: 3196: 3193: 3190: 3187: 3184: 3180: 3176: 3173: 3170: 3167: 3164: 3144: 3141: 3138: 3135: 3104: 3101: 3033: 3029: 3006: 3002: 2963: 2962: 2948: 2944: 2940: 2935: 2932: 2917: 2914: 2896: 2885: 2884: 2870: 2865: 2861: 2856: 2851: 2848: 2834:molecular mass 2830: 2829: 2818: 2815: 2810: 2807: 2780: 2776: 2772: 2769: 2765: 2761: 2758: 2738: 2706: 2686: 2662: 2651: 2650: 2637: 2633: 2629: 2624: 2618: 2609: 2605: 2598: 2594: 2590: 2587: 2581: 2576: 2573: 2553: 2552: 2549: 2546: 2543: 2539: 2532: 2531: 2528: 2525: 2522: 2518: 2517: 2514: 2511: 2508: 2504: 2503: 2500: 2497: 2494: 2490: 2486: 2485: 2474: 2470: 2466: 2456: 2444: 2434: 2431: 2414: 2394: 2390: 2386: 2366: 2326: 2323: 2301: 2298: 2285: 2276: 2247: 2244: 2210: 2207: 2193: 2190: 2179: 2176: 2129:Main article: 2126: 2123: 2117: 2114: 2070:freezing point 2039: 2036: 2034: 2033:Thermodynamics 2031: 2010: 1986: 1964: 1960: 1956: 1951: 1948: 1933:Main article: 1930: 1927: 1867:Fluid dynamics 1846: 1843: 1739: 1736: 1690: 1686: 1674: 1673: 1657: 1647: 1630: 1620: 1605: 1601: 1586: 1585: 1573: 1570: 1567: 1564: 1559: 1555: 1551: 1548: 1525: 1505: 1481:Main article: 1478: 1475: 1407: 1404: 1402: 1399: 1355: 1352: 1316: 1313: 1260: 1257: 1225:oil refineries 1208: 1205: 1167: 1164: 1116:heat exchanger 1097: 1094: 1078:antimicrobials 1031: 1028: 997: 994: 979: 976: 957:Carbon dioxide 904:and gasoline, 815:are liquid at 808: 805: 797:freezing point 748: 745: 692:incompressible 682: 681: 679: 678: 671: 664: 656: 653: 652: 648: 647: 642: 637: 632: 627: 622: 617: 612: 607: 602: 597: 592: 587: 582: 577: 571: 570: 567: 566: 563: 562: 557: 556: 555: 554: 549: 544: 536: 535: 529: 528: 527: 526: 521: 516: 506: 501: 500: 497: 496: 491: 490: 484: 483: 481: 480: 475: 470: 465: 460: 455: 450: 444: 441: 440: 434: 433: 431: 430: 425: 420: 418:Chromatography 415: 410: 404: 401: 400: 394: 393: 391: 390: 371: 370: 369: 350: 338: 333: 321: 308: 305: 304: 296: 291: 290: 287: 286: 282: 281: 276: 271: 270: 269: 259: 254: 249: 248: 247: 242: 232: 227: 222: 217: 216: 215: 205: 199: 198: 193: 192: 189: 188: 183: 182: 181: 180: 172: 171: 167: 166: 165: 164: 159: 154: 146: 145: 139: 136: 135: 132: 131: 126: 112: 109: 104: 101: 95: 92: 89: 86: 75: 74: 68: 67: 51:minimizes the 26: 9: 6: 4: 3: 2: 7234: 7223: 7220: 7218: 7215: 7213: 7210: 7209: 7207: 7192: 7189: 7187: 7184: 7182: 7179: 7177: 7174: 7172: 7169: 7167: 7164: 7162: 7161:Mpemba effect 7159: 7157: 7154: 7152: 7149: 7147: 7144: 7142: 7141:Cooling curve 7139: 7137: 7134: 7132: 7129: 7127: 7124: 7123: 7121: 7117: 7111: 7108: 7106: 7103: 7101: 7098: 7096: 7093: 7091: 7088: 7086: 7083: 7081: 7078: 7077: 7075: 7071: 7065: 7064:Vitrification 7062: 7060: 7057: 7055: 7052: 7050: 7047: 7045: 7042: 7040: 7037: 7035: 7032: 7030: 7029:Recombination 7027: 7025: 7024:Melting point 7022: 7020: 7017: 7015: 7012: 7010: 7007: 7005: 7002: 7000: 6997: 6995: 6992: 6990: 6987: 6985: 6982: 6980: 6977: 6975: 6972: 6970: 6969:Critical line 6967: 6965: 6962: 6960: 6959:Boiling point 6957: 6955: 6952: 6951: 6949: 6947: 6943: 6937: 6934: 6932: 6929: 6925: 6922: 6920: 6917: 6915: 6912: 6911: 6909: 6907: 6904: 6902: 6899: 6897: 6894: 6892: 6891:Exotic matter 6889: 6887: 6884: 6882: 6879: 6877: 6874: 6872: 6869: 6867: 6864: 6863: 6861: 6857: 6851: 6848: 6846: 6843: 6841: 6838: 6837: 6835: 6831: 6825: 6822: 6820: 6817: 6815: 6812: 6810: 6807: 6805: 6802: 6800: 6797: 6795: 6792: 6790: 6787: 6785: 6782: 6781: 6779: 6775: 6770: 6760: 6757: 6755: 6752: 6750: 6746: 6743: 6741: 6738: 6736: 6733: 6732: 6730: 6726: 6721: 6717: 6710: 6705: 6703: 6698: 6696: 6691: 6690: 6687: 6677: 6673: 6669: 6663: 6659: 6655: 6650: 6645: 6641: 6634: 6626: 6622: 6618: 6614: 6610: 6606: 6602: 6598: 6594: 6590: 6585: 6580: 6576: 6572: 6565: 6557: 6553: 6549: 6545: 6540: 6535: 6531: 6527: 6523: 6519: 6515: 6511: 6507: 6503: 6499: 6492: 6484: 6480: 6476: 6472: 6468: 6464: 6460: 6456: 6452: 6448: 6441: 6433: 6429: 6425: 6419: 6415: 6408: 6400: 6396: 6392: 6386: 6382: 6375: 6367: 6360: 6352: 6348: 6344: 6340: 6336: 6332: 6325: 6317: 6313: 6309: 6305: 6300: 6295: 6291: 6287: 6283: 6279: 6275: 6271: 6267: 6260: 6246: 6240: 6236: 6235: 6227: 6212: 6208: 6202: 6198: 6197: 6189: 6181: 6177: 6173: 6171:0-07-011682-2 6167: 6163: 6156: 6148: 6144: 6140: 6134: 6130: 6123: 6115: 6109: 6101: 6097: 6093: 6087: 6083: 6076: 6074: 6072: 6063: 6059: 6055: 6051: 6047: 6043: 6039: 6035: 6028: 6020: 6016: 6012: 6008: 6004: 6000: 5996: 5992: 5985: 5976: 5971: 5967: 5963: 5958: 5953: 5949: 5945: 5941: 5937: 5933: 5926: 5918: 5914: 5910: 5906: 5902: 5898: 5893: 5888: 5884: 5880: 5873: 5865: 5861: 5856: 5851: 5847: 5843: 5838: 5833: 5829: 5825: 5821: 5817: 5813: 5806: 5798: 5791: 5783: 5777: 5769: 5765: 5761: 5755: 5752:. Cambridge. 5751: 5744: 5742: 5733: 5729: 5725: 5723:0-19-855602-0 5719: 5715: 5708: 5706: 5697: 5693: 5689: 5683: 5679: 5672: 5670: 5661: 5655: 5647: 5643: 5639: 5633: 5630:. Amsterdam. 5629: 5622: 5620: 5618: 5616: 5614: 5612: 5610: 5608: 5606: 5597: 5593: 5588: 5583: 5579: 5575: 5570: 5565: 5561: 5557: 5553: 5546: 5538: 5534: 5530: 5526: 5522: 5518: 5514: 5510: 5503: 5495: 5489: 5481: 5477: 5473: 5467: 5463: 5456: 5454: 5452: 5443: 5439: 5435: 5431: 5426: 5421: 5417: 5413: 5409: 5405: 5401: 5394: 5386: 5382: 5378: 5376:0-19-504276-X 5372: 5368: 5361: 5359: 5357: 5348: 5344: 5340: 5334: 5330: 5323: 5315: 5309: 5301: 5297: 5293: 5291:0-19-855611-X 5287: 5283: 5276: 5274: 5272: 5263: 5259: 5255: 5251: 5247: 5243: 5239: 5235: 5228: 5220: 5216: 5212: 5206: 5202: 5195: 5187: 5183: 5179: 5175: 5171: 5167: 5163: 5159: 5154: 5149: 5145: 5141: 5134: 5132: 5123: 5119: 5115: 5111: 5107: 5103: 5099: 5095: 5091: 5087: 5082: 5077: 5073: 5069: 5062: 5055: 5049: 5045: 5041: 5035: 5026: 5012: 5008: 5001: 4994: 4988: 4984: 4980: 4976: 4972: 4968: 4961: 4954: 4948: 4944: 4937: 4930: 4925: 4909: 4905: 4899: 4892: 4888: 4881: 4874: 4867: 4861: 4857: 4850: 4843: 4837: 4833: 4826: 4818: 4812: 4808: 4807: 4802: 4796: 4789: 4783: 4779: 4772: 4763: 4754: 4747: 4742: 4733: 4726: 4721: 4705: 4701: 4697: 4691: 4684: 4678: 4674: 4667: 4660: 4654: 4650: 4646: 4645: 4637: 4629: 4625: 4621: 4617: 4612: 4607: 4603: 4599: 4595: 4591: 4587: 4580: 4572: 4568: 4564: 4560: 4556: 4552: 4547: 4542: 4538: 4534: 4527: 4521: 4520:0-8493-1081-4 4517: 4513: 4512: 4505: 4497: 4493: 4489: 4485: 4480: 4475: 4471: 4467: 4463: 4459: 4455: 4448: 4440: 4436: 4432: 4428: 4424: 4420: 4416: 4412: 4405: 4397: 4393: 4389: 4385: 4381: 4377: 4372: 4367: 4363: 4359: 4355: 4351: 4347: 4340: 4334: 4333:0-7506-7174-2 4330: 4326: 4325: 4318: 4310: 4306: 4302: 4300:0-08-025537-X 4296: 4292: 4285: 4279: 4278:0-07-044451-X 4275: 4271: 4265: 4259: 4258:1-56347-013-6 4255: 4251: 4246: 4239: 4236:Gerald Wendt 4233: 4227: 4226:1-4018-4831-1 4223: 4219: 4218: 4214:Jack Erjavec 4211: 4205: 4204:0-8493-9345-0 4201: 4197: 4191: 4185: 4184:1-895198-24-0 4181: 4177: 4176: 4169: 4163: 4162:3-527-31497-0 4159: 4155: 4154: 4147: 4139: 4135: 4130: 4125: 4121: 4117: 4113: 4106: 4099: 4093: 4089: 4082: 4074: 4070: 4066: 4062: 4058: 4054: 4050: 4046: 4042: 4038: 4031: 4023: 4019: 4015: 4011: 4007: 4003: 3999: 3995: 3988: 3981: 3973: 3969: 3965: 3961: 3957: 3953: 3949: 3945: 3941: 3937: 3930: 3922: 3918: 3914: 3910: 3906: 3902: 3898: 3894: 3887: 3881: 3880:1-57912-814-9 3877: 3871: 3867: 3857: 3854: 3852: 3851:Fluidized bed 3849: 3847: 3846:Microfluidics 3844: 3842: 3839: 3837: 3834: 3832: 3829: 3827: 3824: 3822: 3819: 3817: 3814: 3813: 3806: 3801: 3791: 3789: 3785: 3766: 3763: 3757: 3754: 3751: 3743: 3737: 3733: 3723: 3715: 3713: 3709: 3705: 3700: 3697: 3693: 3689: 3684: 3680: 3670: 3667: 3663: 3659: 3655: 3649: 3645: 3638:Hydrodynamics 3635: 3584: 3541: 3538: 3535: 3529: 3522: 3518: 3512: 3502: 3501:experiments. 3487: 3467: 3445: 3441: 3437: 3433: 3429: 3426: 3420: 3414: 3406: 3402: 3383: 3380: 3377: 3374: 3371: 3368: 3367: 3366: 3364: 3363:length scales 3358: 3348: 3331: 3325: 3317: 3298: 3292: 3285: 3280: 3263: 3257: 3237: 3230: 3214: 3194: 3191: 3188: 3182: 3178: 3174: 3171: 3165: 3162: 3139: 3133: 3126: 3122: 3118: 3114: 3110: 3098: 3093: 3089: 3087: 3083: 3079: 3075: 3072:According to 3070: 3068: 3064: 3060: 3059:shear modulus 3056: 3051: 3049: 3027: 3004: 3000: 2991: 2987: 2983: 2982:mode coupling 2979: 2975: 2971: 2968: 2965:contains the 2946: 2942: 2938: 2933: 2930: 2923: 2922: 2921: 2913: 2909: 2894: 2868: 2863: 2859: 2854: 2849: 2846: 2839: 2838: 2837: 2835: 2816: 2813: 2808: 2796: 2795: 2794: 2778: 2774: 2770: 2767: 2763: 2759: 2756: 2727: 2725: 2721: 2684: 2676: 2660: 2635: 2631: 2627: 2622: 2616: 2607: 2603: 2596: 2592: 2588: 2585: 2579: 2574: 2564: 2563: 2562: 2560: 2550: 2547: 2544: 2537: 2534: 2533: 2529: 2526: 2523: 2520: 2519: 2515: 2512: 2509: 2506: 2505: 2501: 2498: 2495: 2488: 2487: 2472: 2468: 2457: 2435: 2432: 2429: 2428: 2412: 2392: 2388: 2354: 2352: 2348: 2344: 2340: 2336: 2332: 2322: 2320: 2316: 2312: 2308: 2297: 2283: 2274: 2265: 2261: 2255: 2253: 2243: 2240: 2237:important in 2234: 2230: 2228: 2224: 2215: 2206: 2204: 2200: 2189: 2185: 2175: 2173: 2169: 2165: 2161: 2157: 2153: 2149: 2145: 2140: 2138: 2132: 2122: 2113: 2111: 2106: 2102: 2097: 2095: 2091: 2090:boiling point 2083: 2079: 2075: 2074:boiling point 2071: 2067: 2066:phase diagram 2062: 2057: 2056:Melting point 2053: 2049: 2048:Boiling point 2045: 2030: 2028: 2024: 2008: 2000: 1984: 1962: 1958: 1954: 1949: 1946: 1936: 1926: 1924: 1920: 1916: 1912: 1908: 1904: 1900: 1899:non-Newtonian 1896: 1891: 1889: 1883: 1880: 1876: 1874: 1868: 1864: 1856: 1851: 1842: 1840: 1836: 1832: 1828: 1824: 1819: 1815: 1813: 1808: 1806: 1802: 1798: 1794: 1790: 1789:surface waves 1786: 1782: 1777: 1775: 1771: 1767: 1758: 1757:Surface waves 1754: 1749: 1745: 1735: 1733: 1729: 1725: 1721: 1717: 1713: 1708: 1706: 1703:would be the 1688: 1684: 1672: 1655: 1648: 1645: 1628: 1621: 1603: 1599: 1591: 1590: 1589: 1571: 1568: 1565: 1562: 1557: 1553: 1549: 1546: 1539: 1538: 1537: 1536:is given by 1523: 1503: 1494: 1490: 1484: 1483:Fluid statics 1474: 1471: 1467: 1463: 1458: 1456: 1452: 1448: 1444: 1440: 1435: 1433: 1428: 1425: 1421: 1412: 1398: 1396: 1392: 1388: 1384: 1379: 1377: 1373: 1369: 1365: 1361: 1354:Miscellaneous 1351: 1349: 1345: 1341: 1336: 1332: 1328: 1322: 1315:Liquid metals 1312: 1310: 1306: 1302: 1301:transmissions 1298: 1294: 1290: 1286: 1282: 1278: 1274: 1270: 1266: 1256: 1254: 1250: 1246: 1242: 1238: 1234: 1230: 1226: 1222: 1218: 1214: 1204: 1202: 1198: 1194: 1190: 1186: 1182: 1178: 1173: 1163: 1161: 1157: 1153: 1149: 1145: 1141: 1137: 1133: 1129: 1125: 1121: 1117: 1113: 1107: 1103: 1102:Water cooling 1093: 1091: 1090:vegetable oil 1087: 1084:, and liquid 1083: 1079: 1075: 1071: 1067: 1065: 1061: 1057: 1053: 1049: 1045: 1041: 1037: 1027: 1025: 1021: 1017: 1013: 1009: 1003: 989: 984: 975: 973: 969: 964: 962: 958: 954: 953:liquid helium 950: 946: 942: 941:liquid oxygen 938: 933: 931: 927: 923: 919: 915: 911: 907: 903: 899: 895: 891: 886: 884: 880: 876: 871: 869: 864: 862: 858: 854: 850: 846: 842: 838: 834: 830: 826: 822: 818: 814: 804: 802: 798: 794: 790: 789:boiling point 784: 782: 776: 774: 770: 766: 762: 753: 744: 742: 738: 732: 730: 725: 723: 719: 714: 712: 708: 704: 700: 696: 693: 689: 677: 672: 670: 665: 663: 658: 657: 655: 654: 646: 643: 641: 638: 636: 633: 631: 628: 626: 623: 621: 618: 616: 613: 611: 608: 606: 603: 601: 598: 596: 593: 591: 588: 586: 583: 581: 578: 576: 573: 572: 565: 564: 553: 550: 548: 545: 543: 540: 539: 538: 537: 534: 531: 530: 525: 522: 520: 517: 515: 512: 511: 510: 509: 504: 499: 498: 489: 486: 485: 479: 476: 474: 471: 469: 466: 464: 461: 459: 458:Charles's law 456: 454: 451: 449: 446: 445: 443: 442: 439: 436: 435: 429: 426: 424: 421: 419: 416: 414: 411: 409: 406: 405: 403: 402: 399: 396: 395: 389: 386: 382: 379: 375: 372: 367: 366:non-Newtonian 364: 360: 356: 355: 354: 351: 349: 346: 342: 339: 337: 334: 332: 329: 325: 322: 320: 317: 313: 310: 309: 307: 306: 303: 300: 299: 294: 289: 288: 280: 277: 275: 272: 268: 265: 264: 263: 260: 258: 255: 253: 252:Compatibility 250: 246: 243: 241: 240:Finite strain 238: 237: 236: 233: 231: 228: 226: 223: 221: 218: 214: 211: 210: 209: 206: 204: 201: 200: 196: 191: 190: 179: 176: 175: 174: 173: 169: 168: 163: 160: 158: 155: 153: 150: 149: 148: 147: 144:Conservations 143: 142: 134: 133: 129: 110: 107: 102: 99: 93: 90: 87: 84: 77: 76: 73: 70: 69: 65: 64: 58: 54: 50: 46: 41: 37: 33: 19: 7186:Superheating 7059:Vaporization 7054:Triple point 7049:Supercooling 7014:Lambda point 6964:Condensation 6881:Time crystal 6859:Other states 6799:Quantum Hall 6739: 6639: 6633: 6574: 6570: 6564: 6505: 6501: 6491: 6450: 6446: 6440: 6413: 6407: 6380: 6374: 6365: 6359: 6334: 6330: 6324: 6273: 6269: 6259: 6248:. Retrieved 6233: 6226: 6215:. Retrieved 6195: 6188: 6161: 6155: 6128: 6122: 6081: 6062:the original 6041: 6037: 6027: 5994: 5990: 5984: 5939: 5935: 5925: 5882: 5878: 5872: 5819: 5815: 5805: 5796: 5790: 5749: 5713: 5677: 5627: 5559: 5555: 5545: 5512: 5509:ChemPhysChem 5508: 5502: 5461: 5407: 5403: 5393: 5366: 5328: 5322: 5281: 5237: 5233: 5227: 5200: 5194: 5143: 5139: 5071: 5067: 5061: 5043: 5034: 5025: 5014:. Retrieved 5010: 5000: 4983:10.1142/4717 4966: 4960: 4942: 4936: 4928: 4924: 4912:. Retrieved 4908:the original 4898: 4890: 4886: 4873: 4855: 4849: 4831: 4825: 4805: 4795: 4777: 4771: 4762: 4753: 4745: 4741: 4732: 4724: 4720: 4708:. Retrieved 4699: 4690: 4672: 4666: 4643: 4636: 4593: 4589: 4579: 4536: 4532: 4526: 4510: 4504: 4461: 4457: 4447: 4414: 4410: 4404: 4353: 4349: 4339: 4323: 4317: 4290: 4284: 4269: 4264: 4249: 4245: 4237: 4232: 4216: 4210: 4195: 4190: 4174: 4168: 4152: 4146: 4119: 4115: 4105: 4087: 4081: 4043:(1): 31–74. 4040: 4036: 4030: 3997: 3994:Geochemistry 3993: 3980: 3939: 3935: 3929: 3896: 3892: 3886: 3870: 3821:Heavy liquid 3816:Ionic liquid 3803: 3787: 3739: 3721: 3701: 3685: 3682: 3651: 3514: 3397: 3381: 3375: 3369: 3360: 3281: 3106: 3081: 3077: 3071: 3066: 3062: 3052: 2989: 2973: 2969: 2967:bulk modulus 2964: 2919: 2910: 2886: 2831: 2728: 2652: 2556: 2328: 2303: 2256: 2249: 2235: 2231: 2220: 2195: 2187: 2141: 2134: 2119: 2105:supercooling 2098: 2094:superheating 2087: 2026: 1999:bulk modulus 1938: 1892: 1884: 1881: 1877: 1870: 1823:free surface 1820: 1816: 1809: 1778: 1762: 1727: 1723: 1719: 1715: 1709: 1675: 1587: 1486: 1462:water hammer 1459: 1436: 1429: 1417: 1380: 1376:air pressure 1357: 1324: 1269:Pascal's law 1262: 1253:liquefaction 1213:distillation 1210: 1207:Distillation 1169: 1156:perspiration 1118:, such as a 1109: 1068: 1033: 1024:metalworking 1005: 978:Applications 965: 934: 887: 872: 865: 810: 801:supercooling 793:superheating 785: 777: 758: 747:Introduction 733: 726: 715: 690:is a nearly 687: 685: 533:Smart fluids 478:Graham's law 397: 384: 377: 362: 348:Pascal's law 344: 327: 315: 170:Inequalities 53:surface area 36: 18:Liquid state 7095:Latent heat 7044:Sublimation 6989:Evaporation 6924:Ferromagnet 6919:Ferrimagnet 6901:Dark matter 6833:High energy 4122:: 520–541. 3718:Microscopic 3666:homogeneous 3583:derivatives 3389:Macroscopic 3229:Bragg angle 3109:Bragg peaks 3055:shear waves 2978:dissipation 2489:Hydrogen (H 2101:crystallize 2078:sublimation 1925:solutions. 1812:wettability 1447:megapascals 1360:thermometer 1340:soft robots 1281:waterwheels 1273:fluid power 1271:to provide 1126:. Water or 1124:evaporation 1070:Surfactants 1064:Body fluids 996:Lubrication 918:suspensions 910:vinaigrette 902:mineral oil 552:Ferrofluids 453:Boyle's law 225:Hooke's law 203:Deformation 59:in liquids. 7206:Categories 7110:Volatility 7073:Quantities 7034:Regelation 7009:Ionization 6984:Deposition 6936:Superglass 6906:Antimatter 6840:QCD matter 6819:Supersolid 6814:Superfluid 6777:Low energy 6584:1612.04574 6250:2023-04-01 6217:2019-09-18 6147:1337924123 5892:1803.01037 5347:1259588062 5284:. Oxford. 5153:1512.06592 5081:1609.04837 5016:2022-02-10 3863:References 3798:See also: 3692:collisions 3677:See also: 3673:Mesoscopic 3509:See also: 3355:See also: 3086:relaxation 3048:hypersound 2986:dispersion 2182:See also: 2164:mayonnaise 2160:surfactant 2084:can occur. 2082:deposition 2064:A typical 1470:elasticity 1466:cavitation 1449:or 58,000 1383:paraboloid 1319:See also: 1259:Hydraulics 1181:convection 1100:See also: 1086:dye lasers 1074:detergents 1020:gear boxes 1008:lubricants 1000:See also: 914:mayonnaise 781:hydraulics 605:Gay-Lussac 568:Scientists 468:Fick's law 448:Atmosphere 267:frictional 220:Plasticity 208:Elasticity 47:of liquid 7222:Viscosity 6649:0808.2157 6609:0021-9606 6556:221538477 6530:1364-5021 6475:0034-4885 6432:812917029 6399:656397653 6351:0047-2689 6316:249968848 6290:0888-5885 6108:cite book 6100:963198053 6019:104272002 5966:0027-8424 5909:2397-3358 5846:0027-8424 5776:cite book 5768:869135580 5696:148639922 5654:cite book 5646:855895733 5578:0027-8424 5529:1439-4235 5488:cite book 5480:914537747 5434:1478-6435 5308:cite book 5254:0009-2665 5219:696342117 5170:0034-4885 5106:0066-426X 4914:29 August 4887:Lube-Tech 4628:120735632 4620:0004-6280 4571:0004-637X 4496:236566966 4488:1531-7331 4439:235568215 4431:2640-4567 4396:205276487 4380:0935-9648 4138:0167-7322 4073:0066-4146 4065:1545-4282 4022:0009-2819 3956:1618-2642 3921:252979251 3913:2050-7488 3767:¨ 3662:nonlinear 3415:η 3238:θ 3215:λ 3195:θ 3192:⁡ 3183:λ 3175:π 3032:∞ 2947:ρ 2895:τ 2850:≫ 2847:τ 2814:≪ 2806:Λ 2768:− 2764:ρ 2760:≈ 2737:Λ 2724:tunneling 2705:Λ 2661:ℏ 2593:ℏ 2589:π 2572:Λ 2465:Λ 2443:Λ 2385:Λ 2365:Λ 2311:ideal gas 2172:egg yolks 2137:solutions 2125:Solutions 2009:ρ 1963:ρ 1907:motor oil 1895:Newtonian 1873:viscosity 1855:viscosity 1629:ρ 1566:ρ 1516:at depth 1387:telescope 1372:manometer 1331:actuation 1265:hydraulic 1227:, to the 1185:blanching 1152:machining 1052:adhesives 1040:Solutions 1030:Solvation 1012:viscosity 1002:Tribology 988:lava lamp 970:(used in 937:liquefied 906:emulsions 881:and many 857:galinstan 811:Only two 803:occurs). 773:molecules 645:Truesdell 575:Bernoulli 524:Rheometer 519:Rheometry 359:Newtonian 353:Viscosity 103:φ 91:− 7171:Spinodal 7119:Concepts 6999:Freezing 6617:28433024 6548:33071565 6308:36329835 6211:Archived 6180:44712950 5864:24014589 5732:10145548 5596:19805248 5537:15991270 5442:55689631 5385:13946448 5262:26624528 5186:42203015 5178:26696098 5122:37248336 5114:28375691 5042:(2019), 4704:Archived 4388:28417536 3972:22732411 3964:16228199 3809:See also 3460:, where 3121:isotropy 2718:such as 2521:Krypton 2168:lecithin 2156:emulsion 2152:gasoline 2144:miscible 1903:glycerin 1831:flatness 1759:in water 1738:Surfaces 1728:downward 1712:buoyancy 1493:pressure 1432:pressure 1241:nitrogen 1201:steaming 1120:radiator 1048:sealants 1036:solvents 922:colloids 898:mixtures 896:, other 861:amalgams 845:rubidium 833:francium 813:elements 807:Examples 503:Rheology 408:Adhesion 388:Pressure 374:Buoyancy 319:Dynamics 157:Momentum 7212:Liquids 7131:Binodal 7019:Melting 6954:Boiling 6871:Crystal 6866:Colloid 6676:8433369 6589:Bibcode 6539:7544338 6510:Bibcode 6483:5987481 6455:Bibcode 6299:9619405 6046:Bibcode 5999:Bibcode 5975:3081025 5944:Bibcode 5917:4938804 5855:3785726 5824:Bibcode 5587:2741213 5412:Bibcode 5300:8139179 5086:Bibcode 4971:Bibcode 4598:Bibcode 4551:Bibcode 4466:Bibcode 4358:Bibcode 4309:8451210 4045:Bibcode 4002:Bibcode 3401:fitting 2673:is the 2430:Liquid 2260:entropy 2203:glasses 2148:ethanol 2110:melting 2052:Melting 2044:Boiling 1997:is the 1919:custard 1915:ketchup 1827:gravity 1801:ripples 1797:wetting 1785:bubbles 1716:smaller 1669:is the 1644:density 1642:is the 1588:where: 1368:mercury 1348:gallium 1327:sensing 1189:boiling 1172:cooking 1166:Cooking 1148:rockets 1140:bismuth 1096:Cooling 1060:acetone 1056:Naphtha 991:bottom. 868:ethanol 841:gallium 837:caesium 825:bromine 821:mercury 718:density 590:Charles 398:Liquids 312:Statics 257:Bending 45:droplet 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