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[[Податотека:09. Вискозност на течности.ogg|мини|десно|280п|Опит кој го прикажува поведението на вискозна течност, видливо со помош на сина боја ставена во неа. Течноста тече бавно бидејќи пружа [[отпор]] на изобличувањето при нејзиното испуштање од цевката.<small>Извел: проф. [[Оливер Зајков]]. Институт за физика, [[ПМФ]], Скопје</small>]]
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{{Infobox Physical quantity
| bgcolour = {default}
| name = Viscosity
| image = [[File:Viscosities.gif|Viscosities|400px]]
| caption = A simulation of substances with different viscosities. The substance on the left has lower viscosity than the substance on the right
| unit = [[Pascal (unit)|Pa]]·[[Second|s]] = ([[newton (unit)|N]]·[[second|s]])/[[metre|m]]<sup>2</sup> = [[kilogram|kg]]/([[second|s]]·[[metre|m]])
| symbols = [[Eta (letter)|η]], [[Mu (letter)|μ]]
| derivations = μ = [[Shear modulus|G]]·[[time|t]]
}}
The '''viscosity''' of a [[fluid]] is a measure of its [[drag (physics)|resistance]] to gradual deformation by [[shear stress]] or [[tensile stress]].<ref>http://www.merriam-webster.com/dictionary/viscosity</ref> For liquids, it corresponds to the informal concept of "thickness"; for example, [[honey]] has a much higher viscosity than [[water]].<ref>
{{cite book
| author = Symon, Keith
| title = Mechanics
| edition = Third
| publisher = Addison-Wesley
| date = 1971
| isbn = 0-201-07392-7
}}
</ref>
Viscosity is a property arising from collisions between neighboring particles in a fluid that are moving at different [[velocity|velocities]]. When the fluid is forced through a tube, the particles which compose the fluid generally move more quickly near the tube's axis and more slowly near its walls; therefore some [[stress (physics)|stress]] (such as a [[pressure]] difference between the two ends of the tube) is needed to overcome the friction between particle layers to keep the fluid moving. For a given velocity pattern, the stress required is proportional to the fluid's viscosity.
A fluid that has no resistance to shear stress is known as an ''ideal'' or ''inviscid'' fluid. Zero viscosity is observed only at [[cryogenics|very low temperatures]] in [[Superfluidity|superfluids]]. Otherwise, all fluids have positive viscosity, and are technically said to be viscous or viscid. In common parlance, however, a liquid is said to be ''viscous'' if its viscosity is substantially greater than that of water, and may be described as ''mobile'' if the viscosity is noticeably less than water. A fluid with a relatively high viscosity, such as [[pitch (resin)|pitch]], may appear to be a [[solid]].
==Etymology==
The word "viscosity" is derived from the [[Latin]] "{{lang|la|viscum}}", meaning [[mistletoe]] and also a viscous [[glue]] made from mistletoe berries.<ref name=":0">{{cite web|url=http://www.etymonline.com/index.php?term=viscous |title=The Online Etymology Dictionary |publisher=Etymonline.com |accessdate=2010-09-14}}</ref>
==Definition==
=== Dynamic (shear) viscosity {{anchor|Dynamic viscosity}} ===
[[File:Laminar shear.svg|thumb|right|320px|Laminar shear of fluid between two plates. Friction between the fluid and the moving boundaries causes the fluid to shear. The force required for this action is a measure of the fluid's viscosity.]]
[[File:Laminar shear flow.svg|thumb|right|320px|In a general parallel flow (such as could occur in a straight pipe), the shear stress is proportional to the gradient of the velocity]]
The dynamic (shear) viscosity of a fluid expresses its resistance to shearing flows, where adjacent layers move parallel to each other with different speeds. It can be defined through the idealized situation known as a [[Couette flow]], where a layer of fluid is trapped between two horizontal plates, one fixed and one moving horizontally at constant speed <math>u</math>. This fluid has to be homogeneous in the layer and at different shear stresses. (The plates are assumed to be very large, so that one need not consider what happens near their edges.)
If the speed of the top plate is small enough, the fluid particles will move [[parallel (geometry)|parallel]] to it, and their speed will vary [[linear function|linearly]] from zero at the bottom to <math>u</math> at the top. Each layer of fluid will move faster than the one just below it, and friction between them will give rise to a [[force (physics)|force]] resisting their relative motion. In particular, the fluid will apply on the top plate a force in the direction opposite to its motion, and an equal but opposite one to the bottom plate. An external force is therefore required in order to keep the top plate moving at constant speed.
The magnitude <math>F</math> of this force is found to be proportional to the speed <math>u</math> and the area <math>A</math> of each plate, and inversely proportional to their separation <math>y</math>:
:<math> F=\mu A \frac{u}{y}.</math>
The proportionality factor ''μ'' in this formula is the viscosity (specifically, the ''dynamic viscosity'') of the fluid.
The ratio <math>u/y</math> is called the ''rate of shear deformation'' or ''[[shear velocity]]'', and is the [[derivative]] of the fluid speed in the direction [[perpendicular]] to the plates. [[Isaac Newton]] expressed the viscous forces by the [[differential equation]]
:<math>\tau=\mu \frac{\partial u}{\partial y},</math>
where <math>\tau = F/A</math> and <math>{\partial u}/{\partial y}</math> is the local shear velocity. This formula assumes that the flow is moving along parallel lines and the <math>y</math> axis, perpendicular to the flow, points in the direction of maximum shear velocity. This equation can be used where the velocity does not vary linearly with <math>y</math>, such as in fluid flowing through a pipe.
Use of the [[mu (letter)|Greek letter mu]] (''μ'') for the dynamic stress viscosity is common among mechanical and chemical engineers, as well as physicists.<ref>Streeter, Victor Lyle; Wylie, E. Benjamin and Bedford, Keith W. (1998) ''Fluid Mechanics'', McGraw-Hill, ISBN 0-07-062537-9</ref><ref>Holman, J. P. (2002) ''Heat Transfer'', McGraw-Hill, ISBN 0-07-122621-4</ref><ref>Incropera, Frank P. and DeWitt, David P. (2007) ''Fundamentals of Heat and Mass Transfer'', Wiley, ISBN 0-471-45728-0</ref> However, the [[eta (letter)|Greek letter eta]] (''η'') is also used by chemists, physicists, and the [[IUPAC]].<ref>{{cite book|chapter=dynamic viscosity, η|doi=10.1351/goldbook|title=IUPAC Compendium of Chemical Terminology|date=1997|publisher=Blackwell Scientific Publications|place= Oxford |editor1-last=Nič|editor1-first=Miloslav|editor2-last=Jirát|editor2-first=Jiří|editor3-last=Košata|editor3-first=Bedřich|editor4-last=Jenkins|editor4-first=Aubrey|isbn=0-9678550-9-8}}</ref>
=== Kinematic viscosity ===
The kinematic viscosity (also called "momentum diffusivity") is the ratio of the dynamic viscosity ''μ'' to the [[density]] of the fluid ''ρ''. It is usually denoted by the [[Nu (letter)|Greek letter nu]] (<math>\nu</math>).
: <math>\nu = \frac{\mu}{\rho}</math>
It is a convenient concept when analyzing the [[Reynolds number]], which expresses the ratio of the [[inertia]]l forces to the viscous forces:
: <math>Re = \frac{\rho u L}{\mu} = \frac{uL}{\nu} \;,</math>
where <math>L</math> is a typical length scale in the system.
=== Bulk viscosity ===
When a [[compressible fluid]] is compressed or expanded evenly, without shear, it may still exhibit a form of internal friction that resists its flow. These forces are related to the rate of compression or expansion by a factor called the [[volume viscosity]], bulk viscosity or second viscosity.
The bulk viscosity is important only when the fluid is being rapidly compressed or expanded, such as in [[sound]] and [[shock wave]]s. Bulk viscosity explains the loss of energy in those waves, as described by [[Stokes' law (sound attenuation)|Stokes' law of sound attenuation]].
===Viscosity tensor===
{{Main|Viscous stress tensor}}
In general, the [[stress (mechanics)|stresses]] within a flow can be attributed partly to the [[deformation (mechanics)|deformation]] of the material from some rest state ([[Elasticity (physics)|elastic]] stress), and partly to the [[strain rate|rate of change of the deformation]] over time (viscous stress). In a fluid, by definition, the elastic stress includes only the [[hydrostatic pressure]].
In very general terms, the fluid's viscosity is the relation between the strain rate and the viscous stress. In the [[Newtonian fluid]] model, the relationship is by definition a linear map, described by a viscosity tensor that, multiplied by the [[strain rate tensor]] (which is the [[gradient]] of the flow's velocity), gives the viscous stress tensor.
The viscosity tensor has nine independent [[degrees of freedom]] in general. For [[isotropic]] Newtonian fluids, these can be reduced to two independent parameters. The most usual decomposition yields the stress viscosity ''μ'' and the bulk viscosity ''σ''.
==Newtonian and non-Newtonian fluids==
[[File:Viscous regimes chart.png|thumb|right|320px|Viscosity, the slope of each line, varies among materials]]
Newton's law of viscosity is a [[constitutive equation]] (like [[Hooke's law]], [[Fick's law]], [[Ohm's law]]): it is not a fundamental law of nature but an approximation that holds in some materials and fails in others.
A fluid that behaves according to Newton's law, with a viscosity ''μ'' that is independent of the stress, is said to be [[Newtonian fluid|Newtonian]]. [[Gas]]es, [[water]], and many common liquids can be considered Newtonian in ordinary conditions and contexts. There are many [[non-Newtonian fluid]]s that significantly deviate from that law in some way or other. For example:
*[[Shear thickening]] liquids, whose viscosity increases with the rate of shear strain.
*[[Shear thinning]] liquids, whose viscosity decreases with the rate of shear strain.
*[[Thixotropic]] liquids, that become less viscous over time when shaken, agitated, or otherwise stressed.
*[[Rheopectic]] liquids, that become more viscous over time when shaken, agitated, or otherwise stressed.
*[[Bingham plastic]]s that behave as a solid at low stresses but flow as a viscous fluid at high stresses.
Shear thinning liquids are very commonly, but misleadingly, described as thixotropic.
Even for a Newtonian fluid, the viscosity usually depends on its composition and temperature. For gases and other [[compressible fluid]]s, it depends on temperature and varies very slowly with pressure.
The viscosity of some fluids may depend on other factors. A [[magnetorheological fluid]], for example, becomes thicker when subjected to a [[magnetic field]], possibly to the point of behaving like a solid.
==Viscosity in solids==
The viscous forces that arise during fluid flow must not be confused with the [[Elasticity (physics)|elastic]] forces that arise in a solid in response to shear, compression or extension stresses. While in the latter the stress is proportional to the ''amount'' of shear deformation, in a fluid it is proportional to the ''rate'' of deformation over time. (For this reason, [[James Clerk Maxwell|Maxwell]] used the term ''fugitive elasticity'' for fluid viscosity.)
However, many liquids (including water) will briefly react like elastic solids when subjected to sudden stress. Conversely, many "solids" (even [[granite]]) will flow like liquids, albeit very slowly, even under arbitrarily small stress.<ref>{{cite journal
|last = Kumagai
|first = Naoichi
|author2=Sadao Sasajima |author3=Hidebumi Ito
|title = Long-term Creep of Rocks: Results with Large Specimens Obtained in about 20 Years and Those with Small Specimens in about 3 Years
|journal = Journal of the Society of Materials Science (Japan)
|volume = 27
|issue = 293
|pages = 157–161
|publisher = Japan Energy Society
|url = http://translate.google.com/translate?hl=en&sl=ja&u=http://ci.nii.ac.jp/naid/110002299397/&sa=X&oi=translate&resnum=4&ct=result&prev=/search%3Fq%3DIto%2BHidebumi%26hl%3Den
|date = 15 February 1978
|accessdate = 2008-06-16}}</ref> Such materials are therefore best described as possessing both elasticity (reaction to deformation) and viscosity (reaction to rate of deformation); that is, being [[viscoelasticity|viscoelastic]].
Indeed, some authors have claimed that [[amorphous solid]]s, such as [[glass]] and many [[polymers]], are actually liquids with a very high viscosity (e.g.~greater than 10<sup>12</sup> Pa·s).
<!--<ref>[http://web.umr.edu/~brow/PDF_viscosity.pdf The Properties of Glass ], page 6, retrieved on August 1, 2007</ref>--><ref name=r1>{{cite web|url=http://physics.info/viscosity/|work=The Physics Hypertextbook| last=Elert|first=Glenn|title=Viscosity}}</ref> However, other authors dispute this hypothesis, claiming instead that there is some threshold for the stress, below which most solids will not flow at all,<ref>{{cite web|last = Gibbs
|first = Philip
|title = Is Glass a Liquid or a Solid?
|url = http://math.ucr.edu/home/baez/physics/General/Glass/glass.html
|accessdate = 2007-07-31}}</ref> and that alleged instances of glass flow in window panes of old buildings are due to the crude manufacturing process of older eras rather than to the viscosity of glass.<ref>{{cite journal|doi=10.1021/ed066p994|url=http://dwb.unl.edu/Teacher/NSF/C01/C01Links/www.ualberta.ca/~bderksen/windowpane.html|title=Antique windowpanes and the flow of supercooled liquids|date=1989|last1=Plumb|first1=Robert C.|journal=Journal of Chemical Education|volume=66|issue=12|pages=994|bibcode = 1989JChEd..66..994P }}</ref>
Viscoelastic solids may exhibit both shear viscosity and bulk viscosity. The [[extensional viscosity]] is a [[linear combination]] of the shear and bulk viscosities that describes the reaction of a solid elastic material to elongation. It is widely used for characterizing polymers.
In [[geology]], earth materials that exhibit viscous deformation at least three orders of magnitude greater than their elastic deformation are sometimes called [[rheid]]s.<ref>{{cite journal|doi=10.1016/0022-3093(88)90086-5|title=Viscoelasticity in silica gel|date=1988|last1=Scherer|first1=George W.|last2=Pardenek|first2=Sandra A.|last3=Swiatek|first3=Rose M.|journal=Journal of Non-Crystalline Solids|volume=107|pages=14|bibcode = 1988JNCS..107...14S }}</ref>
==See also==
{{Columns-list|2|
* [[Dashpot]]
* [[Deborah number]]
* [[Dilatant]]
* [[Herschel–Bulkley fluid]]
* [[Hyperviscosity syndrome]]
* [[Intrinsic viscosity]]
* [[Inviscid flow]]
* [[Morton number]]
* [[Relative viscosity]]
* [[Reyn]]
* [[Reynolds number]]
* [[Trouton's ratio]]
* [[Two-dimensional point vortex gas]]
* [[Viscoelasticity]]
* [[Viscoplasticity]]
* [[Viscosity index]]
* [[Joback method]] (estimation of the liquid viscosity from molecular structure)
* [[Microviscosity]]
* [[Rheology]]
* [[Superfluid helium-4]]
* [[Stokes flow]]
}}
==References==
{{reflist|30em}}
==Further reading==
* Hatschek, Emil (1928). ''The Viscosity of Liquids''. New York: [[Van Nostrand]]. {{oclc|53438464}}.
*{{cite book
| author = Massey, B. S.
|author2=Ward-Smith, A. J.
| title = Mechanics of Fluids
| edition = Ninth
| publisher= Spon Press
| location = London; New York
| date = 2011 |url=http://science.fire.ustc.edu.cn/download/job.php?job=download&id=141&did=0
| oclc = 690084654
| isbn = 978-0-415-60259-4}}
==External links==
{{Wiktionary}}
{{NSRW Poster|Viscosity of Liquids}}
*[http://webbook.nist.gov/chemistry/fluid/ Fluid properties] High accuracy calculation of viscosity and other physical properties of frequent used pure liquids and gases.
*[http://www.enggcyclopedia.com/calculators/physical-properties/gas-viscosity/ Gas viscosity calculator as function of temperature]
*[http://www.enggcyclopedia.com/calculators/physical-properties/air-viscosity-calculator/ Air viscosity calculator as function of temperature and pressure]
*[http://www.engineersedge.com/fluid_flow/fluid_data.htm Fluid Characteristics Chart] A table of viscosities and vapor pressures for various fluids
*[http://web.ics.purdue.edu/~alexeenk/GDT/index.html Gas Dynamics Toolbox] Calculate coefficient of viscosity for mixtures of gases
*[http://glassproperties.com/viscosity/ViscosityMeasurement.htm Glass Viscosity Measurement] Viscosity measurement, viscosity units and fixpoints, glass viscosity calculation
*[http://www.diracdelta.co.uk/science/source/k/i/kinematic%20viscosity/source.html Kinematic Viscosity] conversion between kinematic and dynamic viscosity.
*[http://www.thermexcel.com/english/tables/eau_atm.htm Physical Characteristics of Water] A table of water viscosity as a function of temperature
*[http://www.iop.org/EJ/abstract/0953-8984/12/46/305 Vogel–Tammann–Fulcher Equation Parameters]
*[http://ddbonline.ddbst.de/VogelCalculation/VogelCalculationCGI.exe Calculation of temperature-dependent dynamic viscosities for some common components]
*[http://www.epa.gov/EPA-AIR/2005/July/Day-13/a11534d.htm "Test Procedures for Testing Highway and Nonroad Engines and Omnibus Technical Amendments"]. [[United States Environmental Protection Agency]]
*[http://www.astro.uu.se/~bf/course/numhd_course/2_5_2Artificial_viscosity.html Artificial viscosity]
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