Зунгааралт

Өөр өөр зунгааралт бүхий шингэний хөдөлгөөн. Дээд шингэн нь доод шингэнээс илүү бага зунгааралттай байгаа учир тайван байдалд удаан орно. Зунгааралт нь физик хэмжигдэхүүн юм

Зунгааралт гэдэг нь шингэний өөр өөр хурдтай эгэл хэсгүүдийн мөргөлдөөний улмаас үүсэх физик шинж чанар юм. Хэрэв хоолой дундуур шингэн шахагдаж байна гэж үзвэл хоолойн тэнхлэг орчимд шингэн хурдтай хөдлөх ба эсрэгээр хоолойн ханаруу дөхөх тусам шингэний хөдөлгөөний хурд багасаж улмаар тэг болно. Үүний шалтгаан нь уг зунгааралтаас үүссэн хүчдэл бөгөөд, (мөн хоолойн эхлэл болон төгсгөлийн хоорондох даралт нөлөөлнө), шингэний эгэл хэсгүүд хоорондын болон хоолойн ханатай үрэлцэх хүчийг даван туулж хөдөлгөөний хадгалахыг эрмэлзэнэ.

Шингэн нь ямар нэгэн эсэргүүцлийн хүчгүй, шүргэх хүчдэл үүсдэггүй бол тэдгээрийг идеаль шингэн эсвэл төгс шингэн гэж нэрлэнэ. Тэг зунгааралт нь зөвхөн супер шингэнд маш бага температуртай үед ажиглагдана. Өөрөөр хэлбэл бусад бүх шингэн нь эерэг зунгааралттай байх ба техникийн хэлээр тэдгээрийг бодит буюу зунгааралттай шингэн гэнэ. Ердийн ярианд шингэн нь усны үзүүлэх зунгааралтаас их бол өтгөн, усны зунгааралтаас бага буюу норгох чадвар нь бага бол хэт шингэн гэж үздэг. Зунгааралт хэт ихтэй шингэний жишээ бол зөгийн бал, цаашилбал давирхай, зарим төрлийн резин гэх мэтийг дурьдаж болох юм.

Үгийн гарал үүсэл

Зунгааралт (англи: viscosity) нь "viscum" гэдэг Латин үгнээс гаралтай бөгөөд энэ нь цагаан борц буюу "mistletoe" ургамалын нэр ба шувууг барьж авахад зориулсан уг ургамлаас гаргаж авсан цавууг ийнхүү нэрлэдэг байсан байна. Монгол хэлэнд наалдамхай зүйлийг зунгаг гэдэг үгээр илэрхийлэх ба үүнээс үүсгэн зунгааралт хэмжээх физик хэмжигдэхүүнийг нэрлэжээ.

Тодорхойлолт

Динамик (шүргэх) зунгааралт

Хоёр хавтгайн хоорондох ламинар урсгал. Хавтгайн хөдөлгөөн болон шингэний үе хоорондын ялгаатай хөдөлгөөн нь шүргэлтийг бий болгоно. Энэ үед бий болох хүчийг шингэний зунгааралтын тусламжтай тодорхойлж болно.

Ерөнхий параллель чиглэлтэй урсгалд (энэ тохиолдол шулуун хоолойд ажиглагдана) шүргэх хүчдэл нь хурдны градиенттэй тэнцүү байна.

Шингэний динамик (шүргэх) зунгааралт нь өөр өөр хурдтай хөдөлж буй шингэний үе давхрагын хооронд бий болох шүргэлцэх эсэргүүцлийг илэрхийлнэ. Үүнийг Чоеттегийн урсгал гэж алдаршсан жишиг бодлогон дээр тодорхойлж болох ба энэ урсгал нь хоёр хавтгайн дунд шингэн орших ба дээд хавтай $u$ хурдтайгаар хөдөлж эхлэхэп ажиглагдана. (Хоёр хавтгайг ихэвчлэн хязгаагүй гэж авч үзэх ба тухайн урсгалын орчимд ирмэг болоод саад үл тулгарна.)

Хэрэв дээд хавтгайн хурд хангалттай бага бол, шингэний эгэл хэсэг хавтгайтай параллель хөдлөх ба хурдны хуваарилалт бараг шугаман байдлаар хувьсаж ёроолын хурд тэг, дээд хавтгайн хурд $u$ байна. Шингэнийг хавтгайтай параллель нимгэн үе давхргагаас бүрдэнэ гэж үзвэл дээрх байдлаар үе бүр өөрийн доод үеэсээ хурдан хөдлөх ба тэдгээр үеийн хоорондын үрэлт нь харьцангуй хөдөлгөөний улмаар бий болох хүчийг нэмэгдүүлнэ. Тухайлбал, шингэн дээд хавтгайд хөдөлгөөний эсрэг хүчээр үйлчилэх ба үүнтэй адилаар доод хавтгайд мөн хүч үйлчилнэ. Харин гадаад хүч нь дээд хавтгайн тогтмол хурдтай хөдөлгөөнийг хадгалахад чиглэнэ.

Хүч $F$ -ийн утга нь харьцангуй хурд $u$ , хавтгай бүрийн хөндлөн огтлолын талбай $A$ зэрэгт пропорциональ ба хавтгайн хоорондох зай $y$ -тай урвуу хамааралтай байна:

$F=\mu A{\frac {u}{y}}.$

Пропорционалийн коэффициент μ нь шингэний (өөрөөр хэлбэл динамик зунгааралт) зунгааралт юм.

Харьцаа $u/y$ нь хэв гажилтын утга эсвэл шүргэх хурд гэж нэрлэгдэх ба хавтгайгай перпендукляр шингэний хурдны уламжлал бөгөөд дифференциал хэлбэрийг хурдны градиент гэнэ. Исаак Ньютон зунгааралтын хүчний дифференциал хэлбэрийг дараах байдлаар өгчээ.

$\tau =\mu {\frac {\partial u}{\partial y}},$

Үүнд: $\tau =F/A$ ба ${\partial u}/{\partial y}$ нь хурдны градиент буюу орчны шүргэх хурдыг илэрхийлнэ. Энэ томъёонд урсгал нь босоо тэнхлэгтэй параллель байна. Энэ тэгшитгэл мөн хувьсах хурдтай үед хэрэглэгдэж болно. Өөрөөр хэлбэл хурд шугаман бус хуваарилалтай үед хүчинтэй.

Динамик зунгааралтын коэффициентийг ихэвчлэн Грек үсэг мю (μ) ашиглан тэмдэглэх ба инженер, химич, физикчдийн ихэнх нь үүнийг хэрэглэдэг. Гэхдээ, Онолын ба хэрэглээний химийн олон улсын холбооны гишүүнчлэлд Грек үсэг эта (η) хэрэглэхийг зөвлөдөг байна.

Кинематик зунгааралт

Кинематик зунгааралт (мөн "моментийн тархалтын коэф" гэж нэрлэх) нь динамик зунгааралт μ -г шингэний нягтад ρ харьцуулсанаар илэрхийлэгдэх ба ихэвчлэн Грек үсэг ню (ν)-гээр тэмдэглэгдэнэ.

$\nu ={\frac {\mu }{\rho }}$

Энэ нь Рейнольдсийн тоог шинжлэхэд тохиромжтой ухагдахуун болох ба Рейнольдсын тоо нь инерцийн хүч ба зунгааралтын хүчний харьцаагаар тдорхойлогдоно.

$Re={\frac {\rho uL}{\mu }}={\frac {uL}{\nu }}\;,$

Үүндe $L$ нь ердийн уртын хэмжигдэхүүн байна.

Эзлэхүүний зунгааралт

Шахагдах шингэн нь шүргэх хүчдэлгүйгээр шахагдах эсвэл тэлэлтийн үед урсгалыг эсэргүүцэж буй дотоод үрэлтийн хэлбэрийг харуулна. Эдгээр хэлбэр бүхий хүчнүүд нь тэлэлт ба шахагдах утгатай σ гэж тэмдэглэгдэх эзлэхүүний зунгааралт эсвэл бөөмийн зунгааралт (bulk) заримдаа хоёрдогч зунгааралт гэж нэрлэгдэх хүчин зүйлээр холбогддог.

Хэрэв шингэн нь дуу ба цохилтын долгион гэх мэт шиг sагшин зуур тэлж эсвэл агших тохиолдолд бөөмийн зунгааралт нь маш чухал параметр болно. Бөөмийн зунгааралт нь Дууны сулралын Стокесийн хууль ёсоор эдгээр долгион дахь энергийн алдагдлыг тайлбарладаг.

Зунгааралтын тенсор

Ерөнхийдөө шингэн дахь хүчдэлүүд нь хугацааны турш дахь (зунгааралтын хүчдэл) деформацийн өөрчлөлтийн утга, тайван төлөвөөс зарим хэсгийн деформаци (уян харимхайн хүчдэл) зэргээр илэрхийлэгдэнэ. Шингэний механикт тодорхойлолтоороо уян харимхайн хүчдэл нь зөвхөн гидростатикийн даралтыг агуулна.

Маш ерөнхий илэрхийлэлд шингэний зунгааралт нь шингэний гажилтын утга ба зунгааралтын хүчдэлийн хоорондын хамаарлаар илэрхийлэгдэнэ гэж үздэг. Шугаман зураглалын тодорхойлолтоор илэрхийлэгдэх Ньютоны шингэний загварт энэ хамаарал нь зунгааралтын тенсороор дүрслэгдэх ба үүнийг гажих утгын тенсороор (хурдны градиент) үржвэл зунгааралтын хүчдэлийн тенсорыг өгнө.

Зунгааралтын тенсор нь үл хамаарах 9 чөлөөний зэрэгтэй байна. Изотропи Ньютоны шингэний хувьд эдгээр нь хоёр үл хамаарах параметрээр буурах боломжтой. Ихэнхдээ тенсорын задаргаа нь хүчдэлийн зунгааралт μ болон бөөмийн зунгааралт σ болно.

Нюьтоны ба Нюьтоны бус шингэнүүд

Viscosity, the slope of each line, varies among materials

Зунгааралтын тухай Ньютоны хууль нь тогтоосон тэгшитгэл юм (Гукийн хууль, Фикийн хууль, Омын хууль гэх мэттэй адил). Өөрөөр хэлбэл энэ нь байгалийн хууль биш боловч маш ойролцоолсон байдлаар материалын шинж чанарыг илэрхийлж чадна.

Ньютоны хуулийн дагуу ажиллаж байгаа μ гэсэн зунгааралттай байгаа шингэн нь шүргэх хүчдэлээс хамааралтай байх бөгөөд Ньютоны шингэн гэж нэрлэгдэнэ. Хий, ус болон олон бусад ердийн шингэнүүдийг ердийн нөхцөлд Ньютоны шингэн гэж авч үзэж болох юм. Эдгээр шингэнтэй адил Ньютоны хуулиас ямар нэгэн байдлаар зөрдөг Ньютоны бус шингэнүүд байна. Тухайлбал:

• Өтгөрөх шингэн, Сунах хүчдэл ихсэхэд зунгааралт нэмэгддэг.
• Шингэрэх шингэн, Сунах хүчдэл ихэсхэд зунгааралт буурна.
• Тихотропи шингэнүүд, шахах, зайлах, хутгах, сэгсрэх үед улам шингэрэх шингэн.
• Реопектик шингэн, шахах, зайлах, хутгах, сэгсрэх үед улам өтгөрөх шингэн.
• Бингамын пластик шингэн, бага даралтанд хатуу материал шиг, гэвч даралт өгөхөд урсамтгай чанартай болно.

Шингэрэх шингэнүүд нт маш элбэг байх ба тэдгээрийг тихотропи шингэнээс ялгаатай авч үзэх хэрэгтэй.

Аль ч шингэний хувьд зунгааралт нь температур болон найрлагаасаа хамаардаг. Хий эсвэл бусад шахагдах шингэний хувьд температураас хамаарах ба заримдаа даралтаас хамаарах тал бий.

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.

Хатуу бие дахь зунгааралт

The viscous forces that arise during fluid flow must not be confused with the 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, 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. Such materials are therefore best described as possessing both elasticity (reaction to deformation) and viscosity (reaction to rate of deformation); that is, being viscoelastic.

Indeed, some authors have claimed that amorphous solids, such as glass and many polymers, are actually liquids with a very high viscosity (e.g.~greater than 10¹² Pa·s). 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, 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.

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 rheids.

Зунгааралтыг хэмжих

Viscosity is measured with various types of viscometers and rheometers. A rheometer is used for those 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. Close temperature control of the fluid is essential to acquire accurate measurements, particularly in materials like lubricants, whose viscosity can double with a change of only 5 °C.

For some fluids, viscosity is a constant over a wide range of shear rates (Newtonian fluids). The fluids without 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- e.g. Zahn cup, Ford viscosity cup- with usage of each type varying mainly according to the industry. The efflux time can also be converted to kinematic viscosities (centistokes, cSt) through the conversion equations.

Also used in coatings, a Stormer viscometer uses load-based rotation in order 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. These models such as the Dynatrol use vibration rather than rotation to measure viscosity.

Extensional viscosity can be measured with various rheometers that apply extensional stress.

Volume viscosity can be measured with an acoustic rheometer.

Apparent viscosity 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.

Нэгж

Динамик зунгааралт μ

The SI physical unit of dynamic viscosity is the pascal-second (Pa·s), (equivalent to (N·s)/m², or kg/(m·s)). If a fluid with a viscosity of one Pa·s is placed between two plates, and one plate is pushed sideways with a shear stress of one pascal, it moves a distance equal to the thickness of the layer between the plates in one second. Water at 20 °C has a viscosity of 0.001002 Pa·s, while a typical motor oil could have a viscosity of about 0.250 Pa·s.

The cgs physical unit for dynamic viscosity is the poise (P), named after Jean Léonard Marie Poiseuille. It is more commonly expressed, particularly in ASTM standards, as centipoise (cP). Water at 20 °C has a viscosity of 1.0020 cP.

1 P = 0.1 Pa·s,

1 cP = 1 mPa·s = 0.001 Pa·s = 0.001 N·s·m^-2 = 0.001 kg·m^-1·s^-1.

Кинематик зунгааралт ν

The SI unit of kinematic viscosity is m²/s.

The cgs physical unit for kinematic viscosity is the stokes (St), named after George Gabriel Stokes. It is sometimes expressed in terms of centistokes (cSt). In U.S. usage, stoke is sometimes used as the singular form.

1 St = 1 cm²·s⁻¹ = 10⁻⁴ m²·s⁻¹.

1 cSt = 1 mm²·s⁻¹ = 10⁻⁶ m²·s⁻¹.

Water at 20 °C has a kinematic viscosity of about 1 cSt.

The kinematic viscosity is sometimes referred to as diffusivity of momentum, because it is analogous to diffusivity of heat and diffusivity of mass. It is therefore used in dimensionless numbers which compare the ratio of the diffusivities.

Шингрэлт буюу өтгөрөлт

The reciprocal of viscosity is fluidity, usually symbolized by φ = 1 / μ or F = 1 / μ, 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 determine the viscosity of an ideal solution. For two components $a$ and $b$, the fluidity when a and b are mixed is

$F\approx \chi _{a}F_{a}+\chi _{b}F_{b},$,

which is only slightly simpler than the equivalent equation in terms of viscosity:

$\mu \approx {\frac {1}{\chi _{a}/\mu _{a}+\chi _{b}/\mu _{b}}},$

where χ_a and χ_b is the mole fraction of component a and b respectively, and μ_a and μ_b are the components' pure viscosities.

Стандарт бус нэгж

The Reyn is a British unit of dynamic viscosity.

Viscosity index is a measure for the change of kinematic viscosity with temperature. It is used to characterise lubricating oil in the automotive industry.

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 centistoke can be converted from SUS according to the arithmetic and the reference table provided in ASTM D 2161.

Молекул гарлага

Pitch has a viscosity approximately 230 billion (2.3X10¹¹) times that of water.

The viscosity of a system is determined by how molecules constituting the system interact. There are no simple but correct expressions for the viscosity of a fluid. The simplest exact expressions are the Green–Kubo relations for the linear shear viscosity or the Transient Time Correlation Function expressions derived by Evans and Morriss in 1985. Although these expressions are each exact, in order to calculate the viscosity of a dense fluid using these relations currently requires the use of molecular dynamics computer simulations.

Хийнүүд

Viscosity in gases arises principally from the molecular diffusion that transports momentum between layers of flow. The kinetic theory of gases allows accurate prediction of the behavior of gaseous viscosity.

Within the regime where the theory is applicable:

• Viscosity is independent of pressure and
• Viscosity increases as temperature increases.

James Clerk Maxwell published a famous paper in 1866 using the kinetic theory of gases to study gaseous viscosity. To understand why the viscosity is independent of pressure, consider two adjacent boundary layers (A and B) moving with respect to each other. The internal friction (the viscosity) of the gas is determined by the probability a particle of layer A enters layer B with a corresponding transfer of momentum. Maxwell's calculations show that the viscosity coefficient is proportional to the density, the mean free path, and the mean velocity of the atoms. On the other hand, the mean free path is inversely proportional to the density. So an increase in density due to an increase in pressure doesn't result in any change in viscosity.

Тархах эгэл хэсгийн дундаж чөлөөт мөртэй холбогдох нь

In relation to diffusion, the kinematic viscosity provides a better understanding of the behavior of mass transport of a dilute species. Viscosity is related to shear stress and the rate of shear in a fluid, which illustrates its dependence on the mean free path, λ, of the diffusing particles.

From fluid mechanics, for a Newtonian fluid, the shear stress, τ, on a unit area moving parallel to itself, is found to be proportional to the rate of change of velocity with distance perpendicular to the unit area:

$\tau =\mu {\frac {\mathrm {d} u_{x}}{\mathrm {d} y}}$

for a unit area parallel to the x-z plane, moving along the x axis. We will derive this formula and show how μ is related to λ.

Interpreting shear stress as the time rate of change of momentum, p, per unit area A (rate of momentum flux) of an arbitrary control surface gives

$\tau ={\frac {\dot {p}}{A}}={\frac {{\dot {m}}\langle u_{x}\rangle }{A}}.$

where $\langle u_{x}\rangle$ is the average velocity, along the x axis, of fluid molecules hitting the unit area, with respect to the unit area.

Further manipulation will show

${\dot {m}}=\rho {\bar {u}}A$

$\langle u_{x}\rangle ={\frac {1}{2}}\,\lambda {\frac {\mathrm {d} u_{x}}{\mathrm {d} y}}$, assuming that molecules hitting the unit area come from all distances between 0 and λ (equally distributed), and that their average velocities change linearly with distance (always true for small enough λ). From this follows:

$\tau =\underbrace {{\frac {1}{2}}\,\rho {\bar {u}}\lambda } _{\mu }\cdot {\frac {\mathrm {d} u_{x}}{\mathrm {d} y}}\;\;\Rightarrow \;\;\nu ={\frac {\mu }{\rho }}={\tfrac {1}{2}}\,{\bar {u}}\lambda ,$

where

${\dot {m}}$ is the rate of fluid mass hitting the surface,

ρ is the density of the fluid,

ū is the average molecular speed (${\bar {u}}={\sqrt {\langle u^{2}\rangle }}$),

μ is the dynamic viscosity.

Хийн зунгааралтанд температурын нөлөөлөл

Sutherland's formula can be used to derive the dynamic viscosity of an ideal gas as a function of the temperature:

${\mu }={\mu }_{0}{\frac {T_{0}+C}{T+C}}\left({\frac {T}{T_{0}}}\right)^{3/2}.$

This in turn is equal to

$\lambda \,{\frac {T^{3/2}}{T+C}}\,,$  where  $\lambda ={\frac {\mu _{0}(T_{0}+C)}{T_{0}^{3/2}}}\,$  is a constant for the gas.

in Sutherland's formula:

• μ = dynamic viscosity (Pa·s or μPa·s) at input temperature T,
• μ₀ = reference viscosity (in the same units as μ) at reference temperature T₀,
• T = input temperature (kelvin),
• T₀ = reference temperature (kelvin),
• C = Sutherland's constant for the gaseous material in question.

Valid for temperatures between 0 < T < 555 K with an error due to pressure less than 10% below 3.45 MPa.

According to Sutherland's formula, if the absolute temperature is less than C, the relative change in viscosity for a small change in temperature is greater than the relative change in the absolute temperature, but it is smaller when T is above C. The kinematic viscosity though always increases faster than the temperature (that is, d log(ν)/d log(T) is greater than 1).

Sutherland's constant, reference values and λ values for some gases:

Gas	C [K]	T0 [K]	μ0 [μPa s]	λ [μPa s K-1/2]
air	120	291.15	18.27	1.512041288
nitrogen	111	300.55	17.81	1.406732195
oxygen	127	292.25	20.18	1.693411300
carbon dioxide	240	293.15	14.8	1.572085931
carbon monoxide	118	288.15	17.2	1.428193225
hydrogen	72	293.85	8.76	0.636236562
ammonia	370	293.15	9.82	1.297443379
sulfur dioxide	416	293.65	12.54	1.768466086
helium	79.4	273	19	1.484381490

Шингэрүүлсэн хийн зунгааралт

The Chapman-Enskog equation may be used to estimate viscosity for a dilute gas. This equation is based on a semi-theoretical assumption by Chapman and Enskog. The equation requires three empirically determined parameters: the collision diameter (σ), the maximum energy of attraction divided by the Boltzmann constant (є/к) and the collision integral (ω(T^*)).

${\mu }_{0}\times 10^{6}={2.6693}{\frac {(MT)^{1/2}}{\sigma ^{2}\omega (T^{*})}},$

with

• T^* = κT/ε — reduced temperature (dimensionless),
• μ₀ = viscosity for dilute gas (μPa.s),
• M = molecular mass (g/mol),
• T = temperature (K),
• σ = the collision diameter (Å),
• ε / κ = the maximum energy of attraction divided by the Boltzmann constant (K),
• ω_μ = the collision integral.

Дуслын шингэнүүд

Video showing three liquids with different Viscosities

In liquids, the additional forces between molecules become important. This leads to an additional contribution to the shear stress though the exact mechanics of this are still controversial. Thus, in liquids:

• Viscosity is independent of pressure (except at very high pressure); and
• Viscosity tends to fall as temperature increases (for example, water viscosity goes from 1.79 cP to 0.28 cP in the temperature range from 0 °C to 100 °C); see temperature dependence of liquid viscosity for more details.

The dynamic viscosities of liquids are typically several orders of magnitude higher than dynamic viscosities of gases.

Холигдсон шингэний зунгааралт

The viscosity of the blend of 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 Viscosity Blending Number (VBN) (also called the Viscosity Blending Index) of each component of the blend:

(1)   ${\mbox{VBN}}=14.534\times \ln \left[\ln(\nu +0.8)\right]+10.975\,$

where ν is the kinematic viscosity in centistokes (cSt). It is important that the kinematic viscosity of each component of the blend be obtained at the same temperature.

The next step is to calculate the VBN of the blend, using this equation:

(2)   ${\mbox{VBN}}_{\text{Blend}}=\left[x_{A}\times {\mbox{VBN}}_{A}\right]+\left[x_{B}\times {\mbox{VBN}}_{B}\right]+\cdots +\left[x_{N}\times {\mbox{VBN}}_{N}\right]\,$

where x_X is the mass fraction of each component of the blend.

Once the viscosity blending number of a blend has been calculated using equation (2), the final step is to determine the kinematic viscosity of the blend by solving equation (1) for ν:

(3)   $\nu =\exp \left(\exp \left({\frac {{\text{VBN}}_{\text{Blend}}-10.975}{14.534}}\right)\right)-0.8,$

where VBN_Blend is the viscosity blending number of the blend.

Түгээмэл бодисын зунгааралт

Агаар

Pressure dependence of the dynamic viscosity of dry air at the temperatures of 300, 400 and 500 K

The viscosity of air depends mostly on the temperature. At 15 °C, the viscosity of air is 1.81X10⁻⁵ kg/(m·s), 18.1 μPa.s or 1.81X10⁻⁵ Pa.s. The kinematic viscosity at 15 °C is 1.48X10^-5 m²/s or 14.8 cSt. At 25 °C, the viscosity is 18.6 μPa.s and the kinematic viscosity 15.7 cSt. One can get the viscosity of air as a function of temperature from the Gas Viscosity Calculator

Ус

Dynamic viscosity of water

The dynamic viscosity of water is 8.90 × 10⁻⁴ Pa·s or 8.90 × 10⁻³ dyn·s/cm² or 0.890 cP at about 25 °C.
Water has a viscosity of 0.0091 poise at 25 °C, or 1 centipoise at 20 °C.
As a function of temperature T (K): (Pa·s) = A × 10^B/(T−C)
where A=2.414 × 10⁻⁵ Pa·s ; B = 247.8 K ; and C = 140 K.

Viscosity of liquid water at different temperatures up to the normal boiling point is listed below.

Temperature [°C]	Viscosity [mPa·s]
10	1.308
20	1.002
30	0.7978
40	0.6531
50	0.5471
60	0.4658
70	0.4044
80	0.3550
90	0.3150
100	0.2822

Бусад бодисууд

Example of the viscosity of milk and water. Liquids with higher viscosities make smaller splashes when poured at the same velocity.

Honey being drizzled.

Peanut butter is a semi-solid and can therefore hold peaks.

Some dynamic viscosities of Newtonian fluids are listed below:

Viscosity of selected gases at 100 kPa, [μPa·s]

Gas	at 0 °C (273 K)	at 27 °C (300 K)
air	17.4	18.6
hydrogen	8.4	9.0
helium		20.0
argon		22.9
xenon	21.2	23.2
carbon dioxide		15.0
methane		11.2
ethane		9.5

Viscosity of fluids with variable compositions

Fluid	Viscosity [Pa·s]	Viscosity [cP]
blood (37 °C)	(3–4)X10-3	3–4
honey	2–10	2,000–10,000
molasses	5–10	5,000–10,000
molten glass	10–1,000	10,000–1,000,000
chocolate syrup	10–25	10,000–25,000
molten chocolate*	45–130	45,000–130,000
ketchup*	50–100	50,000–100,000
lard	&0000000000000100.000000100	&.100,000
peanut butter*	&0000000000000250.000000250	&0000000000250000.000000250,000
shortening*	&0000000000000250.000000250	&0000000000250000.000000250,000

Viscosity of liquids
(at 25 °C unless otherwise specified)

Liquid :	Viscosity [Pa·s]	Viscosity [cP=mPa·s]
acetone	&-1-1-10000000000000.0003060	&0000000000000000.3060000.306
benzene	&-1-1-10000000000000.0006040.001	&0000000000000000.6040000.604
castor oil	&0000000000000000.9850000.985	&0000000000000985.000000985
corn syrup	&0000000000000001.3806001.3806	&0000000000001380.6000001,380.6
ethanol	&-1-100000000000000.0010740.001	&0000000000000001.0740001.074
ethylene glycol	&-1000000000000000.0161000.016	&0000000000000016.10000016.1
glycerol (at 20 °C)	&0000000000000001.2000001.2	&0000000000001200.0000001,200
HFO-380	&0000000000000002.0220002.022	&0000000000002022.0000002,022
mercury	&-1-100000000000000.0015260.002	&0000000000000001.5260001.526
methanol	&-1-1-10000000000000.0005440.001	&0000000000000000.5440000.544
motor oil SAE 10 (20 °C)	&-1000000000000000.0650000.065	&0000000000000065.00000065
motor oil SAE 40 (20 °C)	&0000000000000000.3190000.319	&0000000000000319.000000319
nitrobenzene	&-1-100000000000000.0018630.002	&0000000000000001.8630001.863
liquid nitrogen @ 77K	&-1-1-10000000000000.0001580	&0000000000000000.1580000.158
propanal	&-1-100000000000000.0019450.002	&0000000000000001.9450001.945
olive oil	&-1000000000000000.0810000.081	&0000000000000081.00000081
pitch	&0000000230000000.0000-0230,000,000	&0000230000000000.000000230,000,000,000
sulfuric acid	&-1000000000000000.0242000.024	&0000000000000024.20000024.2
water	&-1-100000000000000.0008940.001	&0000000000000000.8940000.894

Viscosity of solids

Solid	Viscosity [Pa·s]	Temperature [K]
asthenosphere	&000000000000000-4.00000070,000,000,000,000,000,000	900 °C
upper mantle	(0.7-1.0)X1021	1300-3000 °C
lower mantle	(1.0-2.0)X1021	3000-4000 °C

* These materials are highly non-Newtonian.

Note: Higher viscosity means thicker substance

Зуурмагийн зунгааралт /булинга/

Plot of slurry relative viscosity μ_r as calculated by empirical correlations from Einstein, Guth and Simha, Thomas, and Kitano et al..

The term slurry describes mixtures of a liquid and solid particles that retain some fluidity. The viscosity of slurry can be described as relative to the viscosity of the liquid phase:

$\mu _{s}=\mu _{r}\cdot \mu _{l},$

where μ_s and μ_l are respectively the dynamic viscosity of the slurry and liquid (Pa·s), and μ_r is the relative viscosity (dimensionless).

Depending on the size and concentration of the solid particles, several models exist that describe the relative viscosity as a function of volume fraction ɸ of solid particles.

In the case of extremely low concentrations of fine particles, Einstein's equation may be used:

$\mu _{r}=1+2.5\cdot \phi$

In the case of higher concentrations, a modified equation was proposed by Guth and Simha, which takes into account interaction between the solid particles:

$\mu _{r}=1+2.5\cdot \phi +14.1\cdot \phi ^{2}$

Further modification of this equation was proposed by Thomas from the fitting of empirical data:

$\mu _{r}=1+2.5\cdot \phi +10.05\cdot \phi ^{2}+A\cdot e^{B\cdot \phi },$

where A = 0.00273 and B = 16.6.

In the case of high shear stress (above 1 kPa), another empirical equation was proposed by Kitano et al. for polymer melts:

$\mu _{r}=\left(1-{\frac {\phi }{A}}\right)^{-2},$

where A = 0.68 for smooth spherical particles.

Аморф материалын зунгааралт

Common glass viscosity curves.

Viscous flow in amorphous materials (e.g. in glasses and melts) is a thermally activated process:

$\mu =A\cdot e^{Q/RT},$

where Q is activation energy, T is temperature, R is the molar gas constant and A is approximately a constant.

The viscous flow in amorphous materials is characterized by a deviation from the Arrhenius-type behavior: Q changes from a high value Q_H at low temperatures (in the glassy state) to a low value Q_L at high temperatures (in the liquid state). Depending on this change, amorphous materials are classified as either

• strong when: Q_H − Q_L < Q_L or
• fragile when: Q_H − Q_L ≥ Q_L.

The fragility of amorphous materials is numerically characterized by the Doremus’ fragility ratio:

$R_{D}={\frac {Q_{H}}{Q_{L}}}$

and strong material have R_D < 2 whereas fragile materials have R_D ≥ 2.

Common log of viscosity vs temperature for B₂O₃, showing two regimes

The viscosity of amorphous materials is quite exactly described by a two-exponential equation:

$\mu =A_{1}\cdot T\cdot \left[1+A_{2}\cdot e^{B/RT}]\cdot [1+C\cdot e^{D/RT}\right],$

with constants A₁, A₂, B, C and D related to thermodynamic parameters of joining bonds of an amorphous material.

Not very far from the glass transition temperature, T_g, this equation can be approximated by a Vogel-Fulcher-Tammann (VFT) equation.

If the temperature is significantly lower than the glass transition temperature, T ≪ T_g, then the two-exponential equation simplifies to an Arrhenius type equation:

$\mu =A_{L}T\cdot e^{Q_{H}/RT}$

with:

$Q_{H}=H_{d}+H_{m},\,$

where H_d is the enthalpy of formation of broken bonds (termed configuron s) and H_m is the enthalpy of their motion. When the temperature is less than the glass transition temperature, T < T_g, the activation energy of viscosity is high because the amorphous materials are in the glassy state and most of their joining bonds are intact.

If the temperature is highly above the glass transition temperature, T ≫ T_g, the two-exponential equation also simplifies to an Arrhenius type equation:

$\mu =A_{H}T\cdot e^{Q_{L}/RT},$

with:

$Q_{L}=H_{m}.\,$

When the temperature is higher than the glass transition temperature, T > T_g, the activation energy of viscosity is low because amorphous materials are melted and have most of their joining bonds broken, which facilitates flow.

Хуйлралтын зунгааралт

In the study of turbulence in fluids, a common practical strategy for calculation is to ignore the small-scale vortices (or eddies) in the motion and to calculate a large-scale motion with an eddy viscosity that characterizes the transport and dissipation of energy in the smaller-scale flow (see large eddy simulation). Values of eddy viscosity used in modeling ocean circulation may be from 5×10⁴ to 10⁶ Pa·s depending upon the resolution of the numerical grid.

Мөн үзэх

• 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
• Viscosity index
• Joback method (estimation of the liquid viscosity from molecular structure)
• Microviscosity
• Rheology
• Superfluid helium-4
• Stokes flow

Цааш унших

• Hatschek, Emil (1928). The Viscosity of Liquids. New York: Van Nostrand. Загвар:Oclc.
• Massey, B. S.; Ward-Smith, A. J. (2011). Mechanics of Fluids (Ninth ed.). London; New York: Spon Press. ISBN 978-0-415-60259-4. OCLC 690084654.

Гадаад линк

Wiktionary

Wiktionary: Зунгааралт – Энэ үгийг тайлбар толиос харна уу

• Fluid properties High accuracy calculation of viscosity and other physical properties of frequent used pure liquids and gases.
• Gas viscosity calculator as function of temperature
• Air viscosity calculator as function of temperature and pressure
• Fluid Characteristics Chart A table of viscosities and vapor pressures for various fluids
• Gas Dynamics Toolbox Calculate coefficient of viscosity for mixtures of gases
• Glass Viscosity Measurement Viscosity measurement, viscosity units and fixpoints, glass viscosity calculation
• Kinematic Viscosity conversion between kinematic and dynamic viscosity.
• Physical Characteristics of Water A table of water viscosity as a function of temperature
• Vogel–Tammann–Fulcher Equation Parameters
• Calculation of temperature-dependent dynamic viscosities for some common components
• "Test Procedures for Testing Highway and Nonroad Engines and Omnibus Technical Amendments". United States Environmental Protection Agency
• Artificial viscosity