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polymers.Volume viscosity is essential for Acoustics influids, see Stokes' law (sound attenuation)Newton's theoryIn general, in any flow, layers move at differentvelocities and thefluid's viscosity arises from the shear stress between the layersthat ultimately opposes any applied force.Isaac Newtonpostulated that, for straight, paralleland uniform flow, the shear stress, τ, between layers isproportional to the velocity gradient, ∂u/∂y, in thedirection perpendicular to thelayers.Here, the constant η is known as the coefficientof viscosity, the viscosity, the dynamic viscosity, or theNewtonian viscosity. Many fluids, such as water and most gases, satisfy Newton's criterionand are known as Newtonianfluids. Non-Newtonianfluids exhibit a more complicated relationship between shearstress and velocity gradient than simple linearity.The relationship between the shear stress and thevelocity gradient can also be obtained by considering two platesclosely spaced apart at a distance y, and separated by a homogeneous substance.Assuming that the plates are very large, with a large area A, suchthat edge effects may be ignored, and that the lower plate isfixed, let a force F be applied to the upper plate. If this forcecauses the substance between the plates to undergo shear flow (asopposed to just shearing elastically until the shear stress in the substance balancesthe applied force), the substance is called a fluid. The appliedforce is proportional to the area and velocity of the plate andinversely proportional to the distance between the plates.Combining these three relations results in the equation F =η(Au/y), where η is the proportionality factor called the absoluteviscosity (with units Pa·s = kg/(m·s) or slugs/(ft·s)). Theabsolute viscosity is also known as the dynamic viscosity, and isoften shortened to simply viscosity. The equation can be expressedin terms of shear stress; τ = F/A = η(u/y). The rate of sheardeformation is u/y and can be also written as a shear velocity,du/dy. Hence, through this method, the relation between the shearstress and the velocity gradient can be obtained.JamesClerk Maxwell called viscosity fugitive elasticity because ofthe analogy that elastic deformation opposes shear stress insolids, while in viscousfluids, shear stress isopposed by rate of deformation.Viscosity measurementDynamic viscosity is measured with various typesof viscometer. Closetemperature control of the fluid is essential to accuratemeasurements, particularly in materials like lubricants, whoseviscosity can double with a change of only 5 °C. For some fluids,it is a constant over a wide range of shear rates. These areNewtonianfluids.The fluids without a constant viscosity arecalled Non-Newtonianfluids. Their viscosity cannot be described by a single number.Non-Newtonian fluids exhibit a variety of different correlationsbetween shear stress and shear rate.One of the most common instruments for measuringkinematic viscosity is the glass capillary viscometer.In paint industries, viscosity is commonlymeasured with a Zahn cup, inwhich the efflux timeis determined and given to customers. The efflux time can also beconverted to kinematic viscosities (cSt) through the conversionequations.Also used in paint, a Stormer viscometer usesload-based rotation in order to determine viscosity. The viscosityis reported in Krebs units (KU), which are unique to Stormerviscometers.Vibrating viscometers can also be used to measureviscosity. These models use vibration rather than rotation tomeasure viscosity.Extensional viscosity can be measured withvarious rheometersthat apply extensionalstressVolumeviscosity can be measured with acousticrheometer.Units of measureViscosity (dynamic/absolute viscosity)Dynamic viscosity and absolute viscosity aresynonymous. The IUPAC symbol forviscosity is the Greek symbol eta (), and dynamic viscosity is alsocommonly referred to using the Greek symbol mu (). The SI physicalunit of dynamic viscosity is the pascal-second(Pa·s), which is identical to kg·m−1·s−1. If a fluid with a viscosity of one Pa·sis placed between two plates, and one plate is pushed sideways witha shearstress of one pascal, itmoves a distance equal to the thickness of the layer between theplates in one second.The name poiseuille (Pl) was proposedfor this unit (after Jean Louis Marie Poiseuille who formulated Poiseuille'slaw of viscous flow), but not accepted internationally. Caremust be taken in not confusing the poiseuille with the poise named after the sameperson.The cgsphysicalunit for dynamic viscosity is the poise (P), named afterJean Louis Marie Poiseuille. It is more commonly expressed,particularly in ASTM standards, ascentipoise (cP). The centipoise is commonly used because water hasa viscosity of 1.0020 cP (at 20 °C; the closeness to one is aconvenient coincidence).In many situations, we are concerned with theratio of the viscous force to the inertial force, the lattercharacterised by the fluiddensity ρ. This ratio ischaracterised by the kinematic viscosity (\nu ), defined asfollows:where \mu is the (dynamic or absolute) viscosity(in centipoise cP), and \rho is the density (in grams/cm^3), and\nu is the kinematic viscosity (in centistokes cSt ).Kinematic viscosity (Greek symbol: ) has SI unitsPa.s/(kg/m3) = m2·s−1. The cgs physical unit for kinematicviscosity is the stokes (abbreviated S or St), named after GeorgeGabriel Stokes. It is sometimes expressed in terms ofcentistokes (cS or cSt). In U.S. usage, stoke is sometimes used asthe singular form.1 stokes = 100 centistokes = 1 cm2·s−1 = 0.0001 m2·s−1.1 centistokes = 1 mm2·s-1 = 10-6m2·s−1Saybolt Universal ViscosityAt one time the petroleum industry relied onmeasuring kinematic viscosity by means of the Saybolt viscometer,and expressing kinematic viscosity in units of Saybolt UniversalSeconds (SUS). Kinematic viscosity in centistoke can be convertedfrom SUS according to the arithmetic and the reference tabelprovided in ASTM D 2161. It canalso be converted in computerized method, or vice versa.Relation to Mean Free Path of Diffusing ParticlesInrelation to diffusion, the kinematic viscosity provides a betterunderstanding of the behavior of mass transport of a dilutespecies. Viscosity is related to shear stress and the rate of shearin a fluid, which illustrates its dependence on the mean free path,\lambda , of the diffusing particles.From fluidmechanics, shearstress, \tau , is the rate of change of velocity with distanceperpendicular to the direction of movement.Interpreting shear stress as the time rate ofchange of momentum,p,per unit area (rate of momentum flux) of an arbitrary controlsurface gives\frac = \dot = \rho \bar A \; \; \Rightarrow \; \; \tau =\underbrace_ \cdot \frac \; \; \Rightarrow \; \; \nu = \frac = 2\bar \lambdawhere\dot is the rate of change of mass\rho is the density of the fluid\bar is the average molecular speed\mu is the dynamic viscosity.Dynamic versus kinematic viscosityConversion betweenkinematic and dynamic viscosity is given by \nu \rho = \mu.For example,if \nu = 0.0001 m2·s-1 and \rho = 1000 kg m-3 then \mu = \nu\rho = 0.1 kg·m−1·s−1 = 0.1 Pa·sif \nu = 1 St (= 1 cm2·s−1) and \rho = 1 g cm-3 then \mu = \nu\rho = 1 g·cm−1·s−1 = 1 PA plot of the kinematic viscosity of air as afunction of absolute temperature is available on theInternet.Example: viscosity of waterBecause of its density of \rho= 1 g/cm3 (varies slightly with temperature), and its dynamicviscosity is near 1 mPa·s (see #Viscosityof water section), the viscosity values of water are, to roughprecision, all powers of ten:Dynamic viscosity:= 1 mPa·s = 10-3 Pa·s = 1 cP = 10-2 poiseKinematic viscosity:= 1 cSt = 10-2 stokes = 1 mm²/sMolecular originsThe viscosity of a system is determinedby how molecules constituting the system interact. There are nosimple but correct expressions for the viscosity of a fluid. Thesimplest exact expressions are the Green-Kuborelations for the linear shear viscosity or the Transient Time Correlation Function expressions derived byEvans and Morriss in 1985. Although these expressions are eachexact in order to calculate the viscosity of a dense fluid, usingthese relations requires the use of moleculardynamics computer simulation.GasesViscosity in gases arises principally from themolecular diffusion that transports momentum between layers offlow. The kinetic theory of gases allows accurate prediction of thebehavior of gaseous viscosity.Within the regime where the theory is applicable:Viscosity is independent of pressure andViscosity increases as temperature increases.JamesClerk Maxwell published a famous paper in 1866 using thekinetic theory of gases to study gaseous viscosity. (Reference:J.C. Maxwell, "On the viscosity or internal friction of air andother gases", Philosophical Transactions of the Royal Society ofLondon, vol. 156 (1866), pp. 249-268.)Effect of temperature on the viscosity of a gasSutherland'sformula can be used to derive the dynamic viscosity of anidealgas as a function of the temperature:= viscosity in (Pa·s) at input temperature T_0 = reference viscosity in (Pa·s) at reference temperature T_0T = input temperature in kelvinT_0 = reference temperature in kelvinC = Sutherland's constant for the gaseous material inquestionValid for temperatures between 0 T 555 Kwith an error due to pressure less than 10% below 3.45 MPaSutherland's constant and reference temperaturefor some gases (also see: )Viscosity of a dilute gasThe Chapman-Enskogequation may be used to estimate viscosity for a dilute gas.This equation is based on semi-theorethical assumption by Chapmanand Enskoq. The equation requires three empirically determinedparameters: the collision diameter (σ), the maximum energy ofattraction divided by the Boltzmannconstant (є/к) and the collision integral (ω(T*)).= the collision diameter (Å)/ = the maximum energy of attraction divided by the Boltzmannconstant (K)_ = the collision integralLiquidsIn liquids, the additional forces betweenmolecules become important. This leads to an additionalcontribution to the shear stress though the exact mechanics of thisare still controversial. Thus, in liquids:Viscosity tends to fall as temperature increases (for example,water viscosity goes from 1.79 cP to 0.28 cP in the temperaturerange from 0°C to 100°C); see temperature dependence of liquid viscosity for moredetails.The dynamic viscosities of liquids are typicallyseveral orders of magnitude higher than dynamic viscosities ofgases.Viscosity of blends of liquidsThe viscosity of the blendof two or more liquids can be estimated using the Refutas equation.The calculation is carried out in three steps.The first step is to calculate the ViscosityBlending Number (VBN) (also called the Viscosity Blending Index) ofeach component of the blend:(1) \mbox = 14.534 \times ln[ln(v + 0.8)] + 10.975\,where v is the kinematic viscosity in centistokes(cSt). It is important that the kinematic viscosity of eachcomponent of the blend be obtained at the same temperature.The next step is to calculate the VBN of theblend, using this equation:(2) \mbox_\mbox = [x_A \times \mbox_A] + [x_B \times \mbox_B] +... + [x_N \times \mbox_N]\,where x_X is the massfraction of each component of the blend.Once the viscosity blending number of a blend hasbeen calculated using equation (2), the final step is to determinethe kinematic viscosity of the blend by solving equation (1) forViscosity of selected substancesThe viscosity of air andwater are by far the two most important materials for aviationaerodynamics and shipping fluid dynamics. Temperature plays themain role in determining viscosity.Viscosity of airThe viscosity of air depends mostly on thetemperature. At 15.0 °C, the viscosity of air is 1.78 10 5 kg/(m·s) or 1.78 10 4 P. Onecan get the viscosity of air as a function of temperature from theGasViscosity CalculatorViscosity of waterThe viscosity of water is 8.90 10−4 Pa·s or 8.90 10−3 dyn·s/cm2 or 0.890cP at about 25 °C. As a function of temperature T (K): μ(Pa·s) = A 10B/(T−C) where A=2.414 10−5 Pa·s ; B =247.8 K ; and C = 140 K.Viscosity of water at different temperatures islisted below.Viscosity of various materialsSome dynamic viscosities of Newtonian fluids arelisted below:Gases (at 0 °C): Liquids (at 25°C):Fluids with variablecompositions, such as honey, can have a wide range ofviscosities.A more complete table can be found at Transwiki,including the following:These materials are highly non-Newtonian.Viscosity of solidsOn the basis that all solids flow to a smallextent in response to shear stresssome researchers have contended that substances known as amorphoussolids, such as glassand many polymers, maybe considered to have viscosity. This has led some to the view thatsolids are simply liquids with a very highviscosity, typically greater than 1012 Pa·s. This position is oftenadopted by supporters of the widely held misconception thatglass flow can be observed in old buildings. This distortion ismore likely the result of glass making process rather than theviscosity of glass.However, others argue that solids are, in general, elasticfor small stresses while fluids are not. Even if solids flow at higher stresses,they are characterized by their low-stress behavior. Viscosity maybe an appropriate characteristic for solids in a plasticregime. The situation becomes somewhat confused as the termviscosity is sometimes used for solid materials, for exampleMaxwellmaterials, to describe the relationship between stress and therate of change of strain, rather than rate of shear.These distinctions may be largely resolved byconsidering the constitutive equations of the material in question,which take into account both its viscous and elastic behaviors.Materials for which both their viscosity and their elasticity areimportant in a particular range of deformation and deformation rateare called viscoelastic. Ingeology, earth materialsthat exhibit viscous deformation at least three times greater thantheir elastic deformation are sometimes called rheids.Viscosity of amorphous materialsViscous flow in amorphousmaterials (e.g. in glasses and melts) is a thermallyactivated process:\eta = A \cdot e^where Q is activation energy, T is temperature, Ris the molar gas constant and A is approximately a constant.The viscous flow in amorphous materials ischaracterized by a deviation from the Arrhenius-typebehavior: Q changes from a high value Q_H at low temperatures (inthe glassy state) to a low value Q_L at high temperatures (in theliquid state). Depending on this change, amorphous materials areclassified as eitherThe fragility of amorphous materials isnumerically characterized by the Doremus’ fragility ratio:R_D = Q_H/Q_Land strong material have R_D whereas fragilematerials have R_D \ge 2The viscosity of amorphous materials is quiteexactly described by a two-exponential equation:\eta = A_1 \cdot T \cdot [1 + A_2 \cdot e^] \cdot[1 + C \cdot e^]with constants A_1 , A_2 , B, C and D related tothermodynamic parameters of joining bonds of an amorphousmaterial.Not very far from the glass transition temperature, T_g, this equation can beapproximated by a Vogel-Tammann-Fulcher (VTF) equation or a Kohlrausch-type stretched-exponential law.If the temperature is significantly lower thanthe glass transition temperature, T , then the two-exponentialequation simplifies to an Arrhenius type equation:\eta = A_LT \cdot e^with:Q_H = H_d + H_mwhere H_d is the enthalpyof formation of broken bonds (termed configurons) and H_m is theenthalpy of theirmotion. When the temperature is less than the glass transitiontemperature, T , the activation energy of viscosity is high becausethe amorphous materials are in the glassy state and most of theirjoining bonds are intact.If the temperature is highly above the glasstransition temperature, T T_g, the two-exponential equationalso simplifies to an Arrhenius type equation:\eta = A_HT\cdot e^with:Q_L = H_mWhen the temperature is higher than the glasstransition temperature, T T_g, the activation energy ofviscosity is low because amorphous materials are melt and have mostof their joining bonds broken which facilitates flow.Volume (bulk) viscosityThe negative-one-third of thetraceof the stresstensor is oftenidentified with the thermodynamic pressure,-T_a^a = p,which only depends upon the equilibrium statepotentials like temperature and density (equationof state). In general, the trace of the stress tensor is thesum of thermodynamic pressure contribution plus anothercontribution which is proportional to the divergence of thevelocity field. This constant of proportionality is called thevolumeviscosity.Eddy viscosityIn the study of turbulence in fluids, a common practicalstrategy for calculation is to ignore the small-scale vortices (oreddies) in the motion and to calculate a large-scale motion with aneddy viscosity that characterizes the transport and dissipation ofenergy in thesmaller-scale flow (see largeeddy simulation). Values of eddy viscosity used in modelingocean circulation may befrom 5x104 to 106 Pa·s depending upon the resolution of thenumerical grid.FluidityThe reciprocal of viscosity isfluidity, usually symbolized by \phi = 1/\eta or F=1/\eta,depending on the convention used, measured in reciprocal poise(cm·s·g-1), sometimes called the rhe.Fluidity is seldom used in engineering practice.The concept of fluidity can be used to determinethe viscosity of an idealsolution. For two components a and b, the fluidity when a and bare mixed iswhere \chi_a and \chi_b is the mole fraction ofcomponent a and b respectively, and \eta_a and \eta_b are thecomponents pure viscosities.The linear viscous stress tensor(See Hooke's lawand straintensor for an analogous development for linearly elasticmaterials.)Viscous forces in a fluid are a function of therate at which the fluid velocity is changing over distance. Thevelocity at any point \mathbf is specified by the velocity field\mathbf(\mathbf). The velocity at a small distance d\mathbf frompoint \mathbf may be written as a Taylorseries:This is just the Jacobianof the velocity field. Viscous forces are the result of relativemotion between elements of the fluid, and so are expressible as afunction of the velocity field. In other words, the forces at\mathbf are a function of \mathbf(\mathbf) and all derivatives of\mathbf(\mathbf) at that point. In the case of linear viscosity,the viscous force will be a function of the Jacobian tensor alone. For almost allpractical situations, the linear approximation is sufficient.If we represent x, y, and z by indices 1, 2, and3 respectively, the i,j component of the Jacobian may be written as\partial_i v_j where \partial_i is shorthand for \partial /\partialx_i. Note that when the first and higher derivative terms are zero,the velocity of all fluid elements is parallel, and there are noviscous forces.Any matrix may be written as the sum of anantisymmetricmatrix and a symmetricmatrix, and this decomposition is independent of coordinatesystem, and so has physical significance. The velocity field may beapproximated as:v_i(\mathbf+d\mathbf) = v_i(\mathbf)+\frac\left(\partial_iv_j-\partial_j v_i\right)dr_i + \frac\left(\partial_iv_j+\partial_j v_i\right)dr_iwhere Einsteinnotation is now being used in which repeated indices in aproduct are implicitly summed. The second term from the right isthe asymmetric part of the first derivative term, and it representsa rigid rotation of the fluid about \mathbf with angular velocity\omega where:\omega=\frac12 \mathbf\times \mathbf=\frac\begin\partial_2v_3-\partial_3 v_2\\ \partial_3 v_1-\partial_1 v_3\\ \partial_1v_2-\partial_2 v_1 \endFor such a rigid rotation, there is no change inthe relative positions of the fluid elements, and so there is noviscous force associated with this term. The remaining symmetricterm is responsible for the viscous forces in the fluid. Assumingthe fluid is isotropic(i.e. its properties are the same in all directions), then the mostgeneral way that the symmetric term (the rate-of-strain tensor) canbe broken down in a coordinate-independent (and thereforephysically real) way is as the sum of a constant tensor (therate-of-expansion tensor) and a traceless symmetric tensor (therate-of-shear tensor):\frac\left(\partial_i v_j+\partial_j v_i\right) =\underbrace_ + \underbrace_where \delta_ is the unittensor. The most general linear relationship between the stresstensor \mathbf and the rate-of-strain tensor is then a linearcombination of these two tensors:\sigma_ = \zeta\partial_k v_k \delta_+\eta\left(\partial_iv_j+\partial_j v_i-\frac\partial_k v_k \delta_\right)where \zeta is the coefficient of bulk viscosity(or "second viscosity") and \eta is the coefficient of (shear)viscosity.The forces in the fluid are due to the velocitiesof the individual molecules. The velocity of a molecule may bethought of as the sum of the fluid velocity and the thermalvelocity. The viscous stress tensor described above gives the forcedue to the fluid velocity only. The force on an area element in thefluid due to the thermal velocities of the molecules is just thehydrostatic pressure.This pressure term (-p\delta_) must be added to the viscous stresstensor to obtain the total stress tensor for the fluid.The infinitesimal force dF_i on an infinitesimalarea dA_i is then given by the usual relationship:SAE-ISO-AGMAcomparison chartSAE J300 Motor Oil Viscosity ChartSAE J306 Automotive Gear Oil Viscosity ChartGas DynamicsToolbox Calculate coefficient of viscosity for mixtures ofgasesPhysicalCharacteristics of Water A table of water viscosity as afunction of temperatureGlassViscosity Measurement Viscosity measurement, viscosity unitsand fixpoints, glass viscosity calculationdiracdelta.co.uk conversion between kinematic and dynamicviscosity.Vogel-Tammann-FulcherEquation ParametersDispersion TechnologyTheeffects of viscosity in a car engineviscosity in Arabic: لزوجةviscosity in Bulgarian: Вискозитетviscosity in Bengali: সান্দ্রতাviscosity in Bosnian: Viskoznostviscosity in Catalan: Viscositatviscosity in Czech: Viskozitaviscosity in Danish: Viskositetviscosity in German: Viskositätviscosity in Modern Greek (1453-):Ρευστότηταviscosity in Esperanto: Viskozecoviscosity in Spanish: Viscosidadviscosity in Estonian: Viskoossusviscosity in Basque: Biskositatezinematikoviscosity in Persian: گرانرویviscosity in Finnish: Viskositeettiviscosity in French: Viscositéviscosity in Hebrew: צמיגותviscosity in Croatian: Viskoznostviscosity in Hungarian: Viszkozitásviscosity in Indonesian: Viskositasviscosity in Icelandic: Seigjaviscosity in Italian: Viscositàviscosity in Japanese: 粘度viscosity in Luxembourgish: Viskositéitviscosity in Lithuanian: Klampumasviscosity in Latvian: Viskozitāteviscosity in Malay (macrolanguage):Kelikatanviscosity in Dutch: Viscositeitviscosity in Norwegian Nynorsk: Viskositetviscosity in Norwegian: Viskositetviscosity in Polish: Lepkośćviscosity in Portuguese: Viscosidadeviscosity in Romanian: Viscozitateviscosity in Russian: Вязкостьviscosity in Slovak: Viskozitaviscosity in Slovenian: Viskoznostviscosity in Swedish: Viskositetviscosity in Tamil: பிசுக்குமைviscosity in Turkish: Viskoziteviscosity in Ukrainian: В'язкістьviscosity in Vietnamese: Độ nhớtviscosity in Chinese: 粘性Synonyms, Antonyms and RelatedWordsadhesiveness, bullheadedness, clabbering, clamminess, closeness, clotting, coagulation, cohesiveness, colloidality, compactness, congestedness, congestion, consistence, consistency, crowdedness, curdling, denseness, density, doughiness, firmness, gelatinity, gelatinousness, gluelikeness, gluiness, glutinosity, glutinousness, gumlikeness, gumminess, hardness, heaviness, impenetrability,impermeability,imporosity, incompressibility,incrassation,inspissation,jammedness, jellification, jellylikeness, lentor, mucilaginousness,obstinacy, pastiness, persistence, persistency, relativedensity, retention,ropiness, slabbiness, sliminess, snugness, solidity, solidness, specific gravity,spissitude,stick-to-itiveness, stickiness, stodginess, stringiness, stubbornness, syrupiness, tackiness, tenaciousness, tenacity, thickening, thickness, tightness, toughness, treacliness, viscidity, viscousness

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