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70-828: TCX Technology is the brand name for a hydrocarbon -based ethanol production process developed and marketed by Celanese Corporation . Celanese researchers developed the TCX Technology in its Clear Lake City, Texas plant under the direction of its CEO to create a fuel that helps countries reduce their need to import oil and gas. Celanese launched the TCX Technology in November 2010 and plans to invest $ 700 million to build one-to-two plants in China and one in Texas that will produce TCX-based ethanol. Celanese expects to produce approximately 300 million gallons of TCX ethanol by 2016. In

140-579: A hydrocarbon is an organic compound consisting entirely of hydrogen and carbon . Hydrocarbons are examples of group 14 hydrides . Hydrocarbons are generally colourless and hydrophobic ; their odor is usually faint, and may be similar to that of gasoline or lighter fluid . They occur in a diverse range of molecular structures and phases: they can be gases (such as methane and propane ), liquids (such as hexane and benzene ), low melting solids (such as paraffin wax and naphthalene ) or polymers (such as polyethylene and polystyrene ). In

210-435: A magnetic field , possibly to the point of behaving like a solid. The viscous forces that arise during fluid flow are distinct from the elastic forces that occur 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 used

280-414: A common thermoplastic material. Addition reactions apply to alkenes and alkynes. It is because they add reagents that they are called unsaturated. In this reaction a variety of reagents add "across" the pi-bond(s). Chlorine, hydrogen chloride, water , and hydrogen are illustrative reagents. Polymerization is a form of addition. Alkenes and some alkynes also undergo polymerization by opening of

350-436: A constant viscosity ( non-Newtonian fluids ) cannot be described by a single number. Non-Newtonian fluids exhibit a variety of different correlations between shear stress and shear rate. One of the most common instruments for measuring kinematic viscosity is the glass capillary viscometer. In coating industries, viscosity may be measured with a cup in which the efflux time is measured. There are several sorts of cup—such as

420-504: A cost of $ 1.50 to $ 1.75 per gallon. TCX can function as a fuel additive to operate vehicles and in industrial-grade applications to manufacture paints, coatings, inks and pharmaceuticals. It is intended for use in countries or regions wanting to lessen dependence on imported energy and with easy access to plentiful hydrocarbons. These include China, Middle East, Southeast Asia, South America, United States and other developing and growing countries. Hydrocarbon In organic chemistry ,

490-426: A double bond between carbon atoms are sometimes referred to as 'olefins'. The predominant use of hydrocarbons is as a combustible fuel source. Methane is the predominant component of natural gas. C through C alkanes, alkenes, cycloalkanes, and aromatic hydrocarbons are the main components of gasoline , naphtha , jet fuel , and specialized industrial solvent mixtures. With the progressive addition of carbon units,

560-506: A fluid, just as thermal conductivity characterizes heat transport, and (mass) diffusivity characterizes mass transport. This perspective is implicit in Newton's law of viscosity, τ = μ ( ∂ u / ∂ y ) {\displaystyle \tau =\mu (\partial u/\partial y)} , because the shear stress τ {\displaystyle \tau } has units equivalent to

630-415: A momentum flux , i.e., momentum per unit time per unit area. Thus, τ {\displaystyle \tau } can be interpreted as specifying the flow of momentum in the y {\displaystyle y} direction from one fluid layer to the next. Per Newton's law of viscosity, this momentum flow occurs across a velocity gradient, and the magnitude of the corresponding momentum flux

700-529: A single C–C bond it is alkane metathesis , for a double C–C bond it is alkene metathesis (olefin metathesis), and for a triple C–C bond it is alkyne metathesis . The vast majority of hydrocarbons found on Earth occur in crude oil , petroleum, coal , and natural gas. Since thousands of years they have been exploited and used for a vast range of purposes. Petroleum ( lit.   ' rock oil ' ) and coal are generally thought to be products of decomposition of organic matter. Coal, in contrast to petroleum,

770-416: A specific fluid state. To standardize comparisons among experiments and theoretical models, viscosity data is sometimes extrapolated to ideal limiting cases, such as the zero shear limit, or (for gases) the zero density limit. Transport theory provides an alternative interpretation of viscosity in terms of momentum transport: viscosity is the material property which characterizes momentum transport within

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840-468: A two neutral radical atoms ( homolytic fission ). all the way to CCl 4 ( carbon tetrachloride ) all the way to C 2 Cl 6 ( hexachloroethane ) Aromatic compounds, almost uniquely for hydrocarbons, undergo substitution reactions. The chemical process practiced on the largest scale is the reaction of benzene and ethene to give ethylbenzene : The resulting ethylbenzene is dehydrogenated to styrene and then polymerized to manufacture polystyrene ,

910-664: Is 1 cP divided by 1000 kg/m^3, close to the density of water. The kinematic viscosity of water at 20 °C is about 1 cSt. The most frequently used systems of US customary, or Imperial , units are the British Gravitational (BG) and English Engineering (EE). In the BG system, dynamic viscosity has units of pound -seconds per square foot (lb·s/ft ), and in the EE system it has units of pound-force -seconds per square foot (lbf·s/ft ). The pound and pound-force are equivalent;

980-457: 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 rheids . Viscosity is measured with various types of viscometers and rheometers . Close temperature control of

1050-462: Is a calculation derived from tests performed on drilling fluid used in oil or gas well development. These calculations and tests help engineers develop and maintain the properties of the drilling fluid to the specifications required. Nanoviscosity (viscosity sensed by nanoprobes) can be measured by fluorescence correlation spectroscopy . The SI unit of dynamic viscosity is the newton -second per square meter (N·s/m ), also frequently expressed in

1120-550: Is a viscosity tensor that maps the velocity gradient tensor ∂ v k / ∂ r ℓ {\displaystyle \partial v_{k}/\partial r_{\ell }} onto the viscous stress tensor τ i j {\displaystyle \tau _{ij}} . Since the indices in this expression can vary from 1 to 3, there are 81 "viscosity coefficients" μ i j k l {\displaystyle \mu _{ijkl}} in total. However, assuming that

1190-696: Is also potential to harvest hydrocarbons from plants like Euphorbia lathyris and E. tirucalli as an alternative and renewable energy source for vehicles that use diesel. Furthermore, endophytic bacteria from plants that naturally produce hydrocarbons have been used in hydrocarbon degradation in attempts to deplete hydrocarbon concentration in polluted soils. Saturated hydrocarbons are notable for their inertness. Unsaturated hydrocarbons (alkanes, alkenes and aromatic compounds) react more readily, by means of substitution, addition, polymerization. At higher temperatures they undergo dehydrogenation, oxidation and combustion. The cracking of saturated hydrocarbons

1260-400: Is called autoxidation , begins with the formation of hydroperoxides (ROOH). Combustion of hydrocarbons is currently the main source of the world's energy for electric power generation , heating (such as home heating), and transportation. Often this energy is used directly as heat such as in home heaters, which use either petroleum or natural gas . The hydrocarbon is burnt and the heat

1330-532: Is called the rate of shear deformation or shear velocity , and is the derivative of the fluid speed in the direction parallel to the normal vector of the plates (see illustrations to the right). If the velocity does not vary linearly with y {\displaystyle y} , then the appropriate generalization is: where τ = F / A {\displaystyle \tau =F/A} , and ∂ u / ∂ y {\displaystyle \partial u/\partial y}

1400-457: Is derived from the Latin viscum (" mistletoe "). Viscum also referred to a viscous glue derived from mistletoe berries. In materials science and engineering , there is often interest in understanding the forces or stresses involved in the deformation of a material. For instance, if the material were a simple spring, the answer would be given by Hooke's law , which says that

1470-448: Is determined by the viscosity. The analogy with heat and mass transfer can be made explicit. Just as heat flows from high temperature to low temperature and mass flows from high density to low density, momentum flows from high velocity to low velocity. These behaviors are all described by compact expressions, called constitutive relations , whose one-dimensional forms are given here: where ρ {\displaystyle \rho }

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1540-540: Is equal to the SI millipascal second (mPa·s). The SI unit of kinematic viscosity is square meter per second (m /s), whereas the CGS unit for kinematic viscosity is the stokes (St, or cm ·s = 0.0001 m ·s ), named after Sir George Gabriel Stokes . In U.S. usage, stoke is sometimes used as the singular form. The submultiple centistokes (cSt) is often used instead, 1 cSt = 1 mm ·s  = 10  m ·s . 1 cSt

1610-482: Is estimated at more than 58 million metric tons, which will increase to 60 million tons in 2022. Hydrocarbons are also prevalent in nature. Some eusocial arthropods, such as the Brazilian stingless bee, Schwarziana quadripunctata , use unique cuticular hydrocarbon "scents" in order to determine kin from non-kin. This hydrocarbon composition varies between age, sex, nest location, and hierarchal position. There

1680-576: Is in terms of the standard (scalar) viscosity μ {\displaystyle \mu } and the bulk viscosity κ {\displaystyle \kappa } such that α = κ − 2 3 μ {\displaystyle \alpha =\kappa -{\tfrac {2}{3}}\mu } and β = γ = μ {\displaystyle \beta =\gamma =\mu } . In vector notation this appears as: where δ {\displaystyle \mathbf {\delta } }

1750-658: Is not a fundamental law of nature, but rather a constitutive equation (like Hooke's law , Fick's law , and Ohm's law ) which serves to define the viscosity μ {\displaystyle \mu } . Its form is motivated by experiments which show that for a wide range of fluids, μ {\displaystyle \mu } is independent of strain rate. Such fluids are called Newtonian . Gases , water , and many common liquids can be considered Newtonian in ordinary conditions and contexts. However, there are many non-Newtonian fluids that significantly deviate from this behavior. For example: Trouton 's ratio

1820-415: Is possible. Hydrocarbons are generally of low toxicity, hence the widespread use of gasoline and related volatile products. Aromatic compounds such as benzene and toluene are narcotic and chronic toxins, and benzene in particular is known to be carcinogenic . Certain rare polycyclic aromatic compounds are carcinogenic. Hydrocarbons are highly flammable . Viscosities Viscosity quantifies

1890-463: Is richer in carbon and poorer in hydrogen. Natural gas is the product of methanogenesis . A seemingly limitless variety of compounds comprise petroleum, hence the necessity of refineries. These hydrocarbons consist of saturated hydrocarbons, aromatic hydrocarbons, or combinations of the two. Missing in petroleum are alkenes and alkynes. Their production requires refineries. Petroleum-derived hydrocarbons are mainly consumed for fuel, but they are also

1960-588: Is the dynamic viscosity of the fluid, often simply referred to as the viscosity . It is denoted by the Greek letter mu ( μ ). The dynamic viscosity has the dimensions ( m a s s / l e n g t h ) / t i m e {\displaystyle \mathrm {(mass/length)/time} } , therefore resulting in the SI units and the derived units : The aforementioned ratio u / y {\displaystyle u/y}

2030-408: Is the density, J {\displaystyle \mathbf {J} } and q {\displaystyle \mathbf {q} } are the mass and heat fluxes, and D {\displaystyle D} and k t {\displaystyle k_{t}} are the mass diffusivity and thermal conductivity. The fact that mass, momentum, and energy (heat) transport are among

2100-425: Is the local shear velocity. This expression is referred to as Newton's law of viscosity . In shearing flows with planar symmetry, it is what defines μ {\displaystyle \mu } . It is a special case of the general definition of viscosity (see below), which can be expressed in coordinate-free form. Use of the Greek letter mu ( μ {\displaystyle \mu } ) for

2170-616: Is the main industrial route to alkenes and alkyne . These reactions require heterogeneous catalysts and temperatures >500 °C. Widely practice conversions of hydrocarbons involves their reaction with oxygen. In the presence of excess oxygen, hydrocarbons combust. With, however, careful conditions, which have been optimized for many years, partial oxidation results. Useful compounds can obtained in this way: maleic acid from butane , terephthalic acid from xylenes , acetone together with phenol from cumene (isopropylbenzene), and cyclohexanone from cyclohexane]]. The process, which

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2240-398: Is the paucity of enzymes that act on them. Nonetheless, the area has received regular attention. Bacteria in the gabbroic layer of the ocean's crust can degrade hydrocarbons; but the extreme environment makes research difficult. Other bacteria such as Lutibacterium anuloederans can also degrade hydrocarbons. Mycoremediation or breaking down of hydrocarbon by mycelium and mushrooms

2310-611: Is the ratio of extensional viscosity to shear viscosity . For a Newtonian fluid, the Trouton ratio is 3. Shear-thinning liquids are very commonly, but misleadingly, described as thixotropic. Viscosity may also depend on the fluid's physical state (temperature and pressure) and other, external , factors. For gases and other compressible fluids , 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

2380-554: Is the unit tensor. This equation can be thought of as a generalized form of Newton's law of viscosity. The bulk viscosity (also called volume viscosity) expresses a type of internal friction that resists the shearless compression or expansion of a fluid. Knowledge of κ {\displaystyle \kappa } is frequently not necessary in fluid dynamics problems. For example, an incompressible fluid satisfies ∇ ⋅ v = 0 {\displaystyle \nabla \cdot \mathbf {v} =0} and so

2450-597: Is used to heat water, which is then circulated. A similar principle is used to create electrical energy in power plants . Both saturated and unsaturated hydrocarbons undergo this process. Common properties of hydrocarbons are the facts that they produce steam, carbon dioxide and heat during combustion and that oxygen is required for combustion to take place. The simplest hydrocarbon, methane , burns as follows: In inadequate supply of air, carbon black and water vapour are formed: And finally, for any linear alkane of n carbon atoms, Partial oxidation characterizes

2520-541: The Solar System . Lakes of liquid methane and ethane have been found on Titan , Saturn 's largest moon, as confirmed by the Cassini–Huygens space probe. Hydrocarbons are also abundant in nebulae forming polycyclic aromatic hydrocarbon compounds. Burning hydrocarbons as fuel, which produces carbon dioxide and water , is a major contributor to anthropogenic global warming . Hydrocarbons are introduced into

2590-589: The Zahn cup and the Ford viscosity cup —with the usage of each type varying mainly according to the industry. Also used in coatings, a Stormer viscometer employs load-based rotation to determine viscosity. The viscosity is reported in Krebs units (KU), which are unique to Stormer viscometers. Vibrating viscometers can also be used to measure viscosity. Resonant, or vibrational viscometers work by creating shear waves within

2660-425: The density of the fluid ( ρ ). It is usually denoted by the Greek letter nu ( ν ): and has the dimensions ( l e n g t h ) 2 / t i m e {\displaystyle \mathrm {(length)^{2}/time} } , therefore resulting in the SI units and the derived units : In very general terms, the viscous stresses in a fluid are defined as those resulting from

2730-454: The fossil fuel industries, hydrocarbon refers to naturally occurring petroleum , natural gas and coal , or their hydrocarbon derivatives and purified forms. Combustion of hydrocarbons is the main source of the world's energy. Petroleum is the dominant raw-material source for organic commodity chemicals such as solvents and polymers. Most anthropogenic (human-generated) emissions of greenhouse gases are either carbon dioxide released by

2800-431: The shear viscosity . However, at least one author discourages the use of this terminology, noting that μ {\displaystyle \mu } can appear in non-shearing flows in addition to shearing flows. In fluid dynamics, it is sometimes more appropriate to work in terms of kinematic viscosity (sometimes also called the momentum diffusivity ), defined as the ratio of the dynamic viscosity ( μ ) over

2870-491: The BG and EE systems. Nonstandard units include the reyn (lbf·s/in ), a British unit of dynamic viscosity. In the automotive industry the viscosity index is used to describe the change of viscosity with temperature. The reciprocal of viscosity is fluidity , usually symbolized by ϕ = 1 / μ {\displaystyle \phi =1/\mu } or F = 1 / μ {\displaystyle F=1/\mu } , depending on

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2940-468: The Couette flow, a fluid is trapped between two infinitely large plates, one fixed and one in parallel motion at constant speed u {\displaystyle u} (see illustration to the right). If the speed of the top plate is low enough (to avoid turbulence), then in steady state the fluid particles move parallel to it, and their speed varies from 0 {\displaystyle 0} at

3010-501: The TCX process, natural gas or other hydrocarbons are first converted to acetic acid . Thereafter, acetic acid is hydrogenated (presumably obtained by methane reforming ) to give ethanol; a supported platinum-tin catalyst for this purpose was patented by Celanese. Starting from coal, it is gasified . Impurities such as mercury and cadmium are removed, before further reaction. Celanese claims to be able to produce hydrocarbon-based ethanol for

3080-425: The bottom to u {\displaystyle u} at the top. Each layer of fluid moves faster than the one just below it, and friction between them gives rise to a force resisting their relative motion. In particular, the fluid applies on the top plate a force in the direction opposite to its motion, and an equal but opposite force on the bottom plate. An external force is therefore required in order to keep

3150-495: The burning of fossil fuels , or methane released from the handling of natural gas or from agriculture. As defined by the International Union of Pure and Applied Chemistry 's nomenclature of organic chemistry , hydrocarbons are classified as follows: The term 'aliphatic' refers to non-aromatic hydrocarbons. Saturated aliphatic hydrocarbons are sometimes referred to as 'paraffins'. Aliphatic hydrocarbons containing

3220-602: The convention used, measured in reciprocal poise (P , or cm · s · g ), sometimes called the rhe . Fluidity is seldom used in engineering practice. At one time the petroleum industry relied on measuring kinematic viscosity by means of the Saybolt viscometer , and expressing kinematic viscosity in units of Saybolt universal seconds (SUS). Other abbreviations such as SSU ( Saybolt seconds universal ) or SUV ( Saybolt universal viscosity ) are sometimes used. Kinematic viscosity in centistokes can be converted from SUS according to

3290-465: The dynamic viscosity (sometimes also called the absolute viscosity ) is common among mechanical and chemical engineers , as well as mathematicians and physicists. However, the Greek letter eta ( η {\displaystyle \eta } ) is also used by chemists, physicists, and the IUPAC . The viscosity μ {\displaystyle \mu } is sometimes also called

3360-524: The environment through their extensive use as fuels and chemicals as well as through leaks or accidental spills during exploration, production, refining, or transport of fossil fuels. Anthropogenic hydrocarbon contamination of soil is a serious global issue due to contaminant persistence and the negative impact on human health. When soil is contaminated by hydrocarbons, it can have a significant impact on its microbiological, chemical, and physical properties. This can serve to prevent, slow down or even accelerate

3430-457: The equivalent forms pascal - second (Pa·s), kilogram per meter per second (kg·m ·s ) and poiseuille (Pl). The CGS unit is the poise (P, or g·cm ·s = 0.1 Pa·s), named after Jean Léonard Marie Poiseuille . It is commonly expressed, particularly in ASTM standards, as centipoise (cP). The centipoise is convenient because the viscosity of water at 20 °C is about 1 cP, and one centipoise

3500-409: The fluid do not depend on the distance the fluid has been sheared; rather, they depend on how quickly the shearing occurs. Viscosity is the material property which relates the viscous stresses in a material to the rate of change of a deformation (the strain rate). Although it applies to general flows, it is easy to visualize and define in a simple shearing flow, such as a planar Couette flow . In

3570-459: The fluid is essential to obtain accurate measurements, particularly in materials like lubricants, whose viscosity can double with a change of only 5 °C. A rheometer is used for fluids that cannot be defined by a single value of viscosity and therefore require more parameters to be set and measured than is the case for a viscometer. For some fluids, the viscosity is constant over a wide range of shear rates ( Newtonian fluids ). The fluids without

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3640-426: The force experienced by a spring is proportional to the distance displaced from equilibrium. Stresses which can be attributed to the deformation of a material from some rest state are called elastic stresses. In other materials, stresses are present which can be attributed to the deformation rate over time . These are called viscous stresses. For instance, in a fluid such as water the stresses which arise from shearing

3710-405: The friction between the layers of the fluid which are in relative motion. For a tube with a constant rate of flow, the strength of the compensating force is proportional to the fluid's viscosity. In general, viscosity depends on a fluid's state, such as its temperature, pressure, and rate of deformation. However, the dependence on some of these properties is negligible in certain cases. For example,

3780-495: The growth of vegetation depending on the exact changes that occur. Crude oil and natural gas are the two largest sources of hydrocarbon contamination of soil. Bioremediation of hydrocarbon from soil or water contaminated is a formidable challenge because of the chemical inertness that characterize hydrocarbons (hence they survived millions of years in the source rock). Nonetheless, many strategies have been devised, bioremediation being prominent. The basic problem with bioremediation

3850-409: The internal frictional force between adjacent layers of fluid that are in relative motion. For instance, when a viscous fluid is forced through a tube, it flows more quickly near the tube's center line than near its walls. Experiments show that some stress (such as a pressure difference between the two ends of the tube) is needed to sustain the flow. This is because a force is required to overcome

3920-529: The liquid. In this method, the sensor is submerged in the fluid and is made to resonate at a specific frequency. As the surface of the sensor shears through the liquid, energy is lost due to its viscosity. This dissipated energy is then measured and converted into a viscosity reading. A higher viscosity causes a greater loss of energy. Extensional viscosity can be measured with various rheometers that apply extensional stress . Volume viscosity can be measured with an acoustic rheometer . Apparent viscosity

3990-435: The most relevant processes in continuum mechanics is not a coincidence: these are among the few physical quantities that are conserved at the microscopic level in interparticle collisions. Thus, rather than being dictated by the fast and complex microscopic interaction timescale, their dynamics occurs on macroscopic timescales, as described by the various equations of transport theory and hydrodynamics. Newton's law of viscosity

4060-509: The multiple bonds to produce polyethylene , polybutylene , and polystyrene . The alkyne acetylene polymerizes to produce polyacetylene . Oligomers (chains of a few monomers) may be produced, for example in the Shell higher olefin process , where α-olefins are extended to make longer α-olefins by adding ethylene repeatedly. Some hydrocarbons undergo metathesis , in which substituents attached by C–C bonds are exchanged between molecules. For

4130-401: The reactions of alkenes and oxygen. This process is the basis of rancidification and paint drying . Benzene burns with sooty flame when heated in air: Saturated hydrocarbons react with chlorine and fluorine . In the case of chlorination, one of the chlorine atoms replaces a hydrogen atom. The reactions proceed via free-radical pathways , in which the halogen first dissociates into

4200-515: The relative velocity of different fluid particles. As such, the viscous stresses must depend on spatial gradients of the flow velocity. If the velocity gradients are small, then to a first approximation the viscous stresses depend only on the first derivatives of the velocity. (For Newtonian fluids, this is also a linear dependence.) In Cartesian coordinates, the general relationship can then be written as where μ i j k ℓ {\displaystyle \mu _{ijk\ell }}

4270-737: The simple non-ring structured hydrocarbons have higher viscosities , lubricating indices, boiling points, and solidification temperatures. At the opposite extreme from methane lie the heavy tars that remain as the lowest fraction in a crude oil refining retort. They are collected and widely utilized as roofing compounds, pavement material ( bitumen ), wood preservatives (the creosote series) and as extremely high viscosity shear-resisting liquids. Some large-scale non-fuel applications of hydrocarbons begin with ethane and propane, which are obtained from petroleum and natural gas. These two gases are converted either to syngas or to ethylene and propylene respectively. Global consumption of benzene in 2021

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4340-517: The source of virtually all synthetic organic compounds, including plastics and pharmaceuticals. Natural gas is consumed almost exclusively as fuel. Coal is used as a fuel and as a reducing agent in metallurgy . A small fraction of hydrocarbon found on earth, and all currently known hydrocarbon found on other planets and moons, is thought to be abiological . Hydrocarbons such as ethylene, isoprene, and monoterpenes are emitted by living vegetation. Some hydrocarbons also are widespread and abundant in

4410-555: 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. Such materials are best described as viscoelastic —that is, possessing both elasticity (reaction to deformation) and viscosity (reaction to rate of deformation). Viscoelastic solids may exhibit both shear viscosity and bulk viscosity. The extensional viscosity

4480-715: The term containing κ {\displaystyle \kappa } drops out. Moreover, κ {\displaystyle \kappa } is often assumed to be negligible for gases since it is 0 {\displaystyle 0} in a monatomic ideal gas . One situation in which κ {\displaystyle \kappa } can be important is the calculation of energy loss in sound and shock waves , described by Stokes' law of sound attenuation , since these phenomena involve rapid expansions and compressions. The defining equations for viscosity are not fundamental laws of nature, so their usefulness, as well as methods for measuring or calculating

4550-583: The top plate moving at constant speed. In many fluids, the flow velocity is observed to vary linearly from zero at the bottom to u {\displaystyle u} at the top. Moreover, the magnitude of the force, F {\displaystyle F} , acting on the top plate is found to be proportional to the speed u {\displaystyle u} and the area A {\displaystyle A} of each plate, and inversely proportional to their separation y {\displaystyle y} : The proportionality factor

4620-513: The two systems differ only in how force and mass are defined. In the BG system the pound is a basic unit from which the unit of mass (the slug ) is defined by Newton's Second Law , whereas in the EE system the units of force and mass (the pound-force and pound-mass respectively) are defined independently through the Second Law using the proportionality constant g c . Kinematic viscosity has units of square feet per second (ft /s) in both

4690-403: The viscosity depends only space- and time-dependent macroscopic fields (such as temperature and density) defining local equilibrium. Nevertheless, viscosity may still carry a non-negligible dependence on several system properties, such as temperature, pressure, and the amplitude and frequency of any external forcing. Therefore, precision measurements of viscosity are only defined with respect to

4760-609: The viscosity of a Newtonian fluid does not vary significantly with the rate of deformation. Zero viscosity (no resistance to shear stress ) is observed only at very low temperatures in superfluids ; otherwise, the second law of thermodynamics requires all fluids to have positive viscosity. A fluid that has zero viscosity (non-viscous) is called ideal or inviscid . For non-Newtonian fluid 's viscosity, there are pseudoplastic , plastic , and dilatant flows that are time-independent, and there are thixotropic and rheopectic flows that are time-dependent. The word "viscosity"

4830-571: The viscosity rank-2 tensor is isotropic reduces these 81 coefficients to three independent parameters α {\displaystyle \alpha } , β {\displaystyle \beta } , γ {\displaystyle \gamma } : and furthermore, it is assumed that no viscous forces may arise when the fluid is undergoing simple rigid-body rotation, thus β = γ {\displaystyle \beta =\gamma } , leaving only two independent parameters. The most usual decomposition

4900-500: The viscosity, must be established using separate means. A potential issue is that viscosity depends, in principle, on the full microscopic state of the fluid, which encompasses the positions and momenta of every particle in the system. Such highly detailed information is typically not available in realistic systems. However, under certain conditions most of this information can be shown to be negligible. In particular, for Newtonian fluids near equilibrium and far from boundaries (bulk state),

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