Liquid – Wikipedia

One of many 4 elementary states of matter

A liquid is an almost incompressible fluid that conforms to the form of its container however retains a (practically) fixed quantity unbiased of strain. As such, it is likely one of the 4 elementary states of matter (the others being stable, gasoline, and plasma), and is the one state with a particular quantity however no mounted form. A liquid is made up of tiny vibrating particles of matter, reminiscent of atoms, held collectively by intermolecular bonds. Like a gasoline, a liquid is ready to circulation and take the form of a container. Most liquids resist compression, though others will be compressed. In contrast to a gasoline, a liquid doesn’t disperse to fill each area of a container, and maintains a reasonably fixed density. A particular property of the liquid state is floor stress, resulting in wetting phenomena. Water is, by far, the commonest liquid on Earth.

The density of a liquid is often near that of a stable, and far greater than in a gasoline. Subsequently, liquid and stable are each termed condensed matter. Alternatively, as liquids and gases share the flexibility to circulation, they’re each known as fluids. Though liquid water is considerable on Earth, this state of matter is definitely the least widespread within the recognized universe, as a result of liquids require a comparatively slender temperature/strain vary to exist. Most recognized matter within the universe is in gaseous type (with traces of detectable stable matter) as interstellar clouds or in plasma from inside stars.


Thermal picture of a sink stuffed with sizzling water with chilly water being added, exhibiting how the recent and the chilly water circulation into one another.

Liquid is likely one of the 4 major states of matter, with the others being stable, gasoline and plasma. A liquid is a fluid. In contrast to a stable, the molecules in a liquid have a a lot higher freedom to maneuver. The forces that bind the molecules collectively in a stable are solely non permanent in a liquid, permitting a liquid to circulation whereas a stable stays inflexible.

A liquid, like a gasoline, shows the properties of a fluid. A liquid can circulation, assume the form of a container, and, if positioned in a sealed container, will distribute utilized strain evenly to each floor within the container. If liquid is positioned in a bag, it may be squeezed into any form. In contrast to a gasoline, a liquid is sort of incompressible, which means that it occupies practically a continuing quantity over a variety of pressures; it doesn’t typically increase to fill accessible area in a container however varieties its personal floor, and it could not at all times combine readily with one other liquid. These properties make a liquid appropriate for purposes reminiscent of hydraulics.

Liquid particles are sure firmly however not rigidly. They can transfer round each other freely, leading to a restricted diploma of particle mobility. Because the temperature will increase, the elevated vibrations of the molecules causes distances between the molecules to extend. When a liquid reaches its boiling level, the cohesive forces that bind the molecules carefully collectively break, and the liquid modifications to its gaseous state (except superheating happens). If the temperature is decreased, the distances between the molecules grow to be smaller. When the liquid reaches its freezing level the molecules will often lock into a really particular order, known as crystallizing, and the bonds between them grow to be extra inflexible, altering the liquid into its stable state (except supercooling happens).


Solely two components are liquid at commonplace circumstances for temperature and strain: mercury and bromine. 4 extra components have melting factors barely above room temperature: francium, caesium, gallium and rubidium.[1] Steel alloys which might be liquid at room temperature embrace NaK, a sodium-potassium steel alloy, galinstan, a fusible alloy liquid, and a few amalgams (alloys involving mercury).

Pure substances which might be liquid below regular circumstances embrace water, ethanol and lots of different natural solvents. Liquid water is of important significance in chemistry and biology; it’s believed to be a necessity for the existence of life.

Inorganic liquids embrace water, magma, inorganic nonaqueous solvents and lots of acids.

Essential on a regular basis liquids embrace aqueous options like family bleach, different mixtures of various substances reminiscent of mineral oil and gasoline, emulsions like French dressing or mayonnaise, suspensions like blood, and colloids like paint and milk.

Many gases will be liquefied by cooling, producing liquids reminiscent of liquid oxygen, liquid nitrogen, liquid hydrogen and liquid helium. Not all gases will be liquified at atmospheric strain, nevertheless. Carbon dioxide, for instance, can solely be liquified at pressures above 5.1 atm.[2]

Some supplies can’t be categorised throughout the classical three states of matter; they possess solid-like and liquid-like properties. Examples embrace liquid crystals, utilized in LCD shows, and organic membranes.


A lava lamp incorporates two immiscible liquids (a molten wax and a watery answer) which add motion because of convection. Along with the highest floor, surfaces additionally type between the liquids, requiring a stress breaker to recombine the wax droplets on the backside.

Liquids have a wide range of makes use of, as lubricants, solvents, and coolants. In hydraulic programs, liquid is used to transmit energy.

In tribology, liquids are studied for his or her properties as lubricants. Lubricants reminiscent of oil are chosen for viscosity and circulation traits which might be appropriate all through the working temperature vary of the element. Oils are sometimes utilized in engines, gear bins, metalworking, and hydraulic programs for his or her good lubrication properties.[3]

Many liquids are used as solvents, to dissolve different liquids or solids. Options are present in all kinds of purposes, together with paints, sealants, and adhesives. Naphtha and acetone are used continuously in business to scrub oil, grease, and tar from elements and equipment. Physique fluids are water based mostly options.

Surfactants are generally present in soaps and detergents. Solvents like alcohol are sometimes used as antimicrobials. They’re present in cosmetics, inks, and liquid dye lasers. They’re used within the meals business, in processes such because the extraction of vegetable oil.[4]

Liquids are likely to have higher thermal conductivity than gases, and the flexibility to circulation makes a liquid appropriate for eradicating extra warmth from mechanical elements. The warmth will be eliminated by channeling the liquid via a warmth exchanger, reminiscent of a radiator, or the warmth will be eliminated with the liquid throughout evaporation.[5] Water or glycol coolants are used to maintain engines from overheating.[6] The coolants utilized in nuclear reactors embrace water or liquid metals, reminiscent of sodium or bismuth.[7]Liquid propellant movies are used to chill the thrust chambers of rockets.[8] In machining, water and oils are used to take away the surplus warmth generated, which might rapidly spoil each the work piece and the tooling. Throughout perspiration, sweat removes warmth from the human physique by evaporating. Within the heating, air flow, and air-conditioning business (HVAC), liquids reminiscent of water are used to switch warmth from one space to a different.[9]

Equally, liquids are sometimes utilized in cooking for his or her higher heat-transfer properties. Along with higher conductivity, as a result of hotter fluids increase and rise whereas cooler areas contract and sink, liquids with low kinematic viscosity are likely to switch warmth via convection at a reasonably fixed temperature, making a liquid appropriate for blanching, boiling, or frying. Even greater charges of warmth switch will be achieved by condensing a gasoline right into a liquid. On the liquid’s boiling level, all the warmth vitality is used to trigger the section change from a liquid to a gasoline, with out an accompanying enhance in temperature, and is saved as chemical potential vitality. When the gasoline condenses again right into a liquid this extra heat-energy is launched at a continuing temperature. This phenomenon is utilized in processes reminiscent of steaming. Since liquids usually have completely different boiling factors, mixtures or options of liquids or gases can sometimes be separated by distillation, utilizing warmth, chilly, vacuum, strain, or different means. Distillation will be present in the whole lot from the manufacturing of alcoholic drinks, to grease refineries, to the cryogenic distillation of gases reminiscent of argon, oxygen, nitrogen, neon, or xenon by liquefaction (cooling them beneath their particular person boiling factors).[10]

Liquid is the first element of hydraulic programs, which make the most of Pascal’s regulation to offer fluid energy. Gadgets reminiscent of pumps and waterwheels have been used to alter liquid movement into mechanical work since historic instances. Oils are pressured via hydraulic pumps, which transmit this power to hydraulic cylinders. Hydraulics will be discovered in lots of purposes, reminiscent of automotive brakes and transmissions, heavy gear, and airplane management programs. Numerous hydraulic presses are used extensively in restore and manufacturing, for lifting, urgent, clamping and forming.[11]

Liquids are typically utilized in measuring gadgets. A thermometer usually makes use of the thermal enlargement of liquids, reminiscent of mercury, mixed with their means to circulation to point temperature. A manometer makes use of the load of the liquid to point air strain.[12]

Mechanical properties


Portions of liquids are measured in models of quantity. These embrace the SI unit cubic metre (m3) and its divisions, particularly the cubic decimeter, extra generally known as the litre (1 dm3 = 1 L = 0.001 m3), and the cubic centimetre, additionally known as millilitre (1 cm3 = 1 mL = 0.001 L = 10−6 m3).[13]

The amount of a amount of liquid is mounted by its temperature and strain. Liquids typically increase when heated, and contract when cooled. Water between 0 °C and 4 °C is a notable exception.[14]

Alternatively, liquids have little compressibility. Water, for instance, will compress by solely 46.Four elements per million for each unit enhance in atmospheric strain (bar).[15] At round 4000 bar (400 megapascals or 58,000 psi) of strain at room temperature water experiences solely an 11% lower in quantity.[16] Incompressibility makes liquids appropriate for transmitting hydraulic energy, as a result of a change in strain at one level in a liquid is transmitted undiminished to each different a part of the liquid and little or no vitality is misplaced within the type of compression.[17]

Nonetheless, the negligible compressibility does result in different phenomena. The banging of pipes, known as water hammer, happens when a valve is instantly closed, creating an enormous pressure-spike on the valve that travels backward via the system at slightly below the pace of sound. One other phenomenon brought on by liquid’s incompressibility is cavitation. As a result of liquids have little elasticity they will actually be pulled aside in areas of excessive turbulence or dramatic change in course, such because the trailing fringe of a ship propeller or a pointy nook in a pipe. A liquid in an space of low strain (vacuum) vaporizes and varieties bubbles, which then collapse as they enter excessive strain areas. This causes liquid to fill the cavities left by the bubbles with great localized power, eroding any adjoining stable floor.[18]

Stress and buoyancy

In a gravitational area, liquids exert strain on the edges of a container in addition to on something throughout the liquid itself. This strain is transmitted in all instructions and will increase with depth. If a liquid is at relaxation in a uniform gravitational area, the strain

p{displaystyle p}

at depth

z{displaystyle z}

is given by[19]

the place:

For a physique of water open to the air,

p0{displaystyle p_{0}}

can be the atmospheric strain.

Static liquids in uniform gravitational fields additionally exhibit the phenomenon of buoyancy, the place objects immersed within the liquid expertise a web power because of the strain variation with depth. The magnitude of the power is the same as the load of the liquid displaced by the item, and the course of the power will depend on the common density of the immersed object. If the density is smaller than that of the liquid, the buoyant power factors upward and the item floats, whereas if the density is bigger, the buoyant power factors downward and the item sinks. This is named Archimedes’ precept.[20]


Until the quantity of a liquid precisely matches the quantity of its container, a number of surfaces are noticed. The presence of a floor introduces new phenomena which aren’t current in a bulk liquid. It’s because a molecule at a floor possesses bonds with different liquid molecules solely on the internal aspect of the floor, which suggests a web power pulling floor molecules inward. Equivalently, this power will be described when it comes to vitality: there’s a mounted quantity of vitality related to forming a floor of a given space. This amount is a fabric property known as the floor stress, in models of vitality per unit space (SI models: J/m2). Liquids with sturdy intermolecular forces are likely to have giant floor tensions.[21]

A sensible implication of floor stress is that liquids have a tendency to reduce their floor space, forming spherical drops and bubbles except different constraints are current. Floor stress is accountable for a spread of different phenomena as nicely, together with floor waves, capillary motion, wetting, and ripples. In liquids below nanoscale confinement, floor results can play a dominating position since – in contrast with a macroscopic pattern of liquid – a a lot higher fraction of molecules are positioned close to a floor.

The floor stress of a liquid straight impacts its wettability. Most typical liquids have tensions ranging within the tens of mJ/m2, so droplets of oil, water, or glue can simply merge and cling to different surfaces, whereas liquid metals reminiscent of mercury might have tensions ranging within the tons of of mJ/m2, thus droplets don’t mix simply and surfaces might solely moist below particular circumstances.

The floor tensions of widespread liquids occupy a comparatively slender vary of values, which contrasts strongly with the big variation seen in different mechanical properties, reminiscent of viscosity.[22]


A simulation of viscosity. The fluid on the left has a decrease viscosity and Newtonian habits whereas the liquid on the appropriate has greater viscosity and non-Newtonian habits.

An vital bodily property characterizing the circulation of liquids is viscosity. Intuitively, viscosity describes the resistance of a liquid to circulation.

Extra technically, viscosity measures the resistance of a liquid to deformation at a given fee, reminiscent of when it’s being sheared at finite velocity.[23] A selected instance is a liquid flowing via a
pipe: on this case the liquid undergoes shear deformation because it flows extra slowly close to the partitions of the pipe
than close to the middle. In consequence, it reveals viscous resistance to circulation. With the intention to preserve circulation, an exterior power have to be utilized, reminiscent of a strain distinction between the ends of the pipe.

The viscosity of liquids decreases with rising temperature.[24][25]

Exact management of
viscosity is vital in lots of purposes, notably the lubrication business.
One solution to obtain such management is by mixing two or extra liquids of differing viscosities in exact ratios.[26]
As well as, numerous components exist which might modulate the temperature-dependence of the
viscosity of lubricating oils. This functionality is vital since equipment usually function over a spread of
temperatures (see additionally viscosity index).[27]

The viscous habits of a liquid will be both Newtonian or non-Newtonian. A Newtonian liquid reveals a linear pressure/stress curve, which means its viscosity is unbiased of time, shear fee, or shear-rate historical past. Examples of Newtonian liquids embrace water, glycerin, motor oil, honey, or mercury. A non-Newtonian liquid is one the place the viscosity is just not unbiased of those components and both thickens (will increase in viscosity) or thins (decreases in viscosity) below shear. Examples of non-Newtonian liquids embrace ketchup, mayonnaise, hair gels, play dough, or starch options.[28]

Elasticity below confinement

Confined liquids might exhibit completely different mechanical properties in comparison with bulk liquids. For instance,
liquids below sub-millimeter confinement (e.g. within the hole between inflexible partitions) exhibit a solid-like mechanical response and possess a surprisingly giant low-frequency elastic shear modulus, which scales with the inverse cubic energy of the confinement size.[29]

Sound propagation

The pace of sound in a liquid is given by

c=Ok/ρ{displaystyle c={sqrt {Ok/rho }}}

the place

Ok{displaystyle Ok}

is the majority modulus of the liquid and

ρ{displaystyle rho }

the density. For instance, water has a bulk modulus of about 2.2 GPa and a density of 1000 kg/m3, which provides c = 1.5 km/s.[30]


Section transitions

At a temperature beneath the boiling level, any matter in liquid type will evaporate till the condensation of gasoline above attain an equilibrium. At this level the gasoline will condense on the identical fee because the liquid evaporates. Thus, a liquid can not exist completely if the evaporated liquid is regularly eliminated. A liquid at its boiling level will evaporate extra rapidly than the gasoline can condense on the present strain. A liquid at or above its boiling level will usually boil, although superheating can stop this in sure circumstances.

At a temperature beneath the freezing level, a liquid will are likely to crystallize, altering to its stable type. In contrast to the transition to gasoline, there isn’t a equilibrium at this transition below fixed strain, so except supercooling happens, the liquid will ultimately fully crystallize. Notice that that is solely true below fixed strain, so e.g. water and ice in a closed, sturdy container may attain an equilibrium the place each phases coexist. For the alternative transition from stable to liquid, see melting.

Liquids in area

The section diagram explains why liquids don’t exist in area or some other vacuum. Because the strain is zero (besides on surfaces or interiors of planets and moons) water and different liquids uncovered to area will both instantly boil or freeze relying on the temperature. In areas of area close to the earth, water will freeze if the solar is just not shining straight on it and vapourize (elegant) as quickly as it’s in daylight. If water exists as ice on the moon, it could solely exist in shadowed holes the place the solar by no means shines and the place the encircling rock does not warmth it up an excessive amount of. Sooner or later close to the orbit of Saturn, the sunshine from the solar is just too faint to elegant ice to water vapour. That is evident from the longevity of the ice that composes Saturn’s rings.


Liquids can type options with gases, solids, and different liquids.

Two liquids are mentioned to be miscible if they will type an answer in any proportion; in any other case they’re immiscible. For instance, water and ethanol (ingesting alcohol) are miscible whereas water and gasoline are immiscible.[31] In some instances a combination of in any other case immiscible liquids will be stabilized to type an emulsion, the place one liquid is dispersed all through the opposite as microscopic droplets. Often this requires the presence of a surfactant in an effort to stabilize the droplets. A well-recognized instance of an emulsion is mayonnaise, which consists of a combination of water and oil that’s stabilized by lecithin, a substance present in egg yolks.[32]

Microscopic description

The molecules which compose liquids are disordered and strongly interacting,
which makes liquids troublesome to explain rigorously on the molecular stage. This stands
in distinction with the opposite two widespread phases of matter, gases and solids.
Though gases are disordered, they’re sufficiently dilute that
many-body interactions will be ignored, and molecular interactions can as a substitute be modeled
when it comes to well-defined binary collision occasions. Conversely, though solids are dense and strongly
interacting, their common construction on the molecular stage (e.g. a crystalline lattice) permits for
important theoretical simplifications. For these causes, the microscopic concept of liquids
is much less developed than that of gases and solids.[33]

Static construction issue

Construction of a classical monatomic liquid. Atoms have many nearest neighbors involved, but no long-range order is current.

In a liquid, atoms don’t type a crystalline lattice, nor do they present some other type of long-range order. That is evidenced by the absence of Bragg peaks in X-ray and neutron diffraction. Beneath regular circumstances, the diffraction sample has round symmetry, expressing the isotropy of the liquid. In radial course, the diffraction depth easily oscillates. That is often described by the static construction issue S(q), with wavenumber q=(4π/λ)sinθ given by the wavelength λ of the probe (photon or neutron) and the Bragg angle θ. The oscillations of S(q) specific the close to order of the liquid, i.e. the correlations between an atom and some shells of nearest, second nearest, … neighbors.

A extra intuitive description of those correlations is given by the radial distribution perform g(r), which is mainly the Fourier rework of S(q). It represents a spatial common of a temporal snapshot of pair correlations within the liquid.

Sound dispersion and structural leisure

The above expression for the sound velocity

c=Ok/ρ{displaystyle c={sqrt {Ok/rho }}}

incorporates the majority modulus Ok. If Ok is frequency unbiased then the liquid behaves as a linear medium, in order that sound propagates with out dissipation and with out mode coupling. In actuality, any liquid exhibits some dispersion: with rising frequency, Ok crosses over from the low-frequency, liquid-like restrict

Ok0{displaystyle K_{0}}

to the high-frequency, solid-like restrict

Ok{displaystyle K_{infty }}

. In regular liquids, most of this cross over takes place at frequencies between GHz and THz, typically known as hypersound.

At sub-GHz frequencies, a standard liquid can not maintain shear waves: the zero-frequency restrict of the shear modulus is

G0=0{displaystyle G_{0}=0}

. That is typically seen because the defining property of a liquid.[34][35]
Nonetheless, simply as the majority modulus Ok, the shear modulus G is frequency dependent,
and at hypersound frequencies it exhibits an identical cross over from the liquid-like restrict

G0{displaystyle G_{0}}

to a solid-like, non-zero restrict

G{displaystyle G_{infty }}


Based on the Kramers-Kronig relation, the dispersion within the sound velocity (given by the actual a part of Ok or G) goes together with a most within the sound attenuation (dissipation, given by the imaginary a part of Ok or G). Based on linear response concept, the Fourier rework of Ok or G describes how the system returns to equilibrium after an exterior perturbation; for that reason, the dispersion step within the GHz..THz area can be known as structural leisure. Based on the fluctuation-dissipation theorem, leisure in the direction of equilibrium is intimately related to fluctuations in equilibrium. The density fluctuations related to sound waves will be experimentally noticed by Brillouin scattering.

On supercooling a liquid in the direction of the glass transition, the crossover from liquid-like to solid-like response strikes from GHz to MHz, kHz, Hz, …; equivalently, the attribute time of structural leisure will increase from ns to μs, ms, s, … That is the microscopic clarification for the above-mentioned viscoelastic behaviour of glass-forming liquids.

Results of affiliation

The mechanisms of atomic/molecular diffusion (or particle displacement) in solids are carefully associated to the mechanisms of viscous circulation and solidification in liquid supplies. Descriptions of viscosity when it comes to molecular “free area” throughout the liquid[36]
have been modified as wanted in an effort to account for liquids whose molecules are recognized to be “related” within the liquid state at atypical temperatures. When numerous molecules mix collectively to type an related molecule, they enclose inside a semi-rigid system a specific amount of area which earlier than was accessible as free area for cellular molecules. Thus, enhance in viscosity upon cooling because of the tendency of most substances to grow to be related on cooling.[37]

Comparable arguments could possibly be used to explain the consequences of strain on viscosity, the place it could be assumed that the viscosity is mainly a perform of the quantity for liquids with a finite compressibility. An rising viscosity with rise of strain is subsequently anticipated. As well as, if the quantity is expanded by warmth however lowered once more by strain, the viscosity stays the identical.

The native tendency to orientation of molecules in small teams lends the liquid (as referred to beforehand) a sure diploma of affiliation. This affiliation ends in a substantial “inner strain” inside a liquid, which is due virtually totally to these molecules which, on account of their non permanent low velocities (following the Maxwell distribution) have coalesced with different molecules. The inner strain between a number of such molecules may correspond to that between a bunch of molecules within the stable type.


  1. ^ Theodore Grey, The Parts: A Visible Exploration of Each Identified Atom within the Universe New York: Workman Publishing, 2009 p. 127 ISBN 1-57912-814-9
  2. ^ Silberberg, Martin S. (2009), Chemistry: The Molecular Nature of Matter and Change, McGraw-Hill Increased Schooling, pp. 448–449, ISBN 978-0-07-304859-8
  3. ^ Theo Mang, Wilfried Dressel ’’Lubricants and lubrication’’, Wiley-VCH 2007 ISBN 3-527-31497-0
  4. ^ George Wypych ’’Handbook of solvents’’ William Andrew Publishing 2001 pp. 847–881 ISBN 1-895198-24-0
  5. ^ N. B. Vargaftik ’’Handbook of thermal conductivity of liquids and gases’’ CRC Press 1994 ISBN 0-8493-9345-0
  6. ^ Jack Erjavec ’’Automotive expertise: a programs method’’ Delmar Studying 2000 p. 309 ISBN 1-4018-4831-1
  7. ^ Gerald Wendt ’’The prospects of nuclear energy and expertise’’ D. Van Nostrand Firm 1957 p. 266
  8. ^ ’’Fashionable engineering for design of liquid-propellant rocket engines’’ by Dieter Ok. Huzel, David H. Huang – American Institute of Aeronautics and Astronautics 1992 p. 99 ISBN 1-56347-013-6
  9. ^ Thomas E Mull ’’HVAC ideas and purposes handbook’’ McGraw-Hill 1997 ISBN 0-07-044451-X
  10. ^ Unit Operations in Meals Processing by R. L. Earle — Pergamon Press 1983 Web page 56–62, 138–141
  11. ^ R. Keith Mobley Fluid energy dynamics Butterworth-Heinemann 2000 p. vii ISBN 0-7506-7174-2
  12. ^ Bela G. Liptak ’’Instrument engineers’ handbook: course of management’’ CRC Press 1999 p. 807 ISBN 0-8493-1081-4
  13. ^ Knight, Randall D. (2008), Physics for Scientists and Engineers: A Strategic Method (With Fashionable Physics), Addison-Wesley, p. 443, ISBN 978-0-8053-2736-6
  14. ^ Silberberg, Martin S. (2009), Chemistry: The Molecular Nature of Matter and Change, McGraw-Hill Increased Schooling, p. 461, ISBN 978-0-07-304859-8
  15. ^ “Compressibility of Liquids”. Archived from the unique on 7 December 2017. Retrieved Eight Could 2018.
  16. ^ Clever Power Subject Manufacturing: Interdisciplinary Course of Improvements By Wenwu Zhang — CRC Press 2011 Web page 144
  17. ^ Knight (2008) p. 454
  18. ^ Fluid Mechanics and Hydraulic Machines by S. C. Gupta — Dorling-Kindersley 2006 Web page 85
  19. ^ Knight (2008) p. 448
  20. ^ Knight (2008) pp. 455-459
  21. ^ Silberberg, Martin S. (2009), Chemistry: The Molecular Nature of Matter and Change, McGraw-Hill Increased Schooling, p. 457, ISBN 978-0-07-304859-8
  22. ^ Edward Yu. Bormashenko (5 November 2018). Wetting of Actual Surfaces. De Gruyter. pp. 3–5. ISBN 978-3-11-058314-4.
  23. ^ Landau, L.D.; Lifshitz, E.M. (1987), Fluid Mechanics (2nd ed.), Pergamon Press, pp. 44–45, ISBN 978-0-08-033933-7
  24. ^
  25. ^ Krausser, J.; Samwer, Ok.; Zaccone, A. (2015). “Interatomic repulsion softness straight controls the fragility of supercooled metallic melts”. Proceedings of the Nationwide Academy of Sciences of the USA. 112 (45): 13762. arXiv:1510.08117. Bibcode:2015PNAS..11213762Ok. doi:10.1073/pnas.1503741112. PMID 26504208.
  26. ^ Zhmud, Boris (2014), “Viscosity Mixing Equations” (PDF), Lube-Tech, 93
  27. ^ “Viscosity Index”. UK: Anton Paar. Retrieved 29 August 2018.[permanent dead link]
  28. ^ Honey in Conventional and Fashionable Medication by Laid Boukraa — CRC Press 2014 Web page 22–24
  29. ^ Zaccone, A.; Trachenko, Ok. (2020). “Explaining the low-frequency shear elasticity of confined liquids”. Proceedings of the Nationwide Academy of Sciences of the USA. 117 (33): 19653–19655. arXiv:2007.11916. doi:10.1073/pnas.2010787117. PMID 32747540.
  30. ^ Taylor, John R. (2005), Classical Mechanics, College Science Books, pp. 727–729, ISBN 978-1-891389-22-1
  31. ^ Silberberg, pp. 188 and 502
  32. ^ Miodownik, Mark (2019), Liquid guidelines: The Pleasant and Harmful Substances that Movement By Our Lives, Houghton Mifflin Harcourt, p. 124, ISBN 978-0-544-85019-4
  33. ^ Fisher, I.Z. (1964), Statistical Idea of Liquids, The College of Chicago Press, pp. 1–11
  34. ^ Born, Max (1940). “On the soundness of crystal lattices”. Mathematical Proceedings. Cambridge Philosophical Society. 36 (2): 160–172. Bibcode:1940PCPS…36..160B. doi:10.1017/S0305004100017138.
  35. ^ Born, Max (1939). “Thermodynamics of Crystals and Melting”. Journal of Chemical Physics. 7 (8): 591–604. Bibcode:1939JChPh…7..591B. doi:10.1063/1.1750497. Archived from the unique on 2016-05-15.
  36. ^
    D.B. Macleod (1923). “On a relation between the viscosity of a liquid and its coefficient of enlargement”. Trans. Faraday Soc. 19: 6. doi:10.1039/tf9231900006.
  37. ^
    G.W. Stewart (1930). “The Cybotactic (Molecular Group) Situation in Liquids; the Affiliation of Molecules”. Phys. Rev. 35 (7): 726. Bibcode:1930PhRv…35..726S. doi:10.1103/PhysRev.35.726.


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