Study of the dependence of the viscosity of solutions on concentration using a viscometer. Measuring blood viscosity: Educational and methodological development of laboratory work for the course “Medical and biological science”

This term has other meanings, see Viscosity (meanings).

Behavior of a liquid with low (top) and high (bottom) viscosity
Viscosity

(
internal friction
) is one of the transfer phenomena, the property of fluid bodies (liquids and gases) to resist the movement of one part of them relative to another. As a result, the work expended on this movement is dissipated in the form of heat.

The mechanism of internal friction in liquids and gases is that chaotically moving molecules transfer momentum from one layer to another, which leads to equalization of velocities - this is described by the introduction of a friction force. The viscosity of solids has a number of specific features and is usually considered separately.

There are dynamic viscosity (unit in the International System of Units (SI) - ·, in the GHS system - poise; 1 Pa s = 10 poise) and kinematic viscosity (unit in SI - m² / s, in the GHS - Stokes, non-systemic unit - Angler degree). Kinematic viscosity can be obtained as the ratio of dynamic viscosity to the density of a substance and owes its origin to classical methods of measuring viscosity, such as measuring the time of flow of a given volume through a calibrated orifice under the influence of gravity. A device for measuring viscosity is called a viscometer.

The transition of a substance from a liquid to a glassy state is usually associated with the achievement of a viscosity of the order of 1011-1012 Pa s.

Content

• 1 Viscous friction force
• 2 Second viscosity
• 3 Viscosity of gases 3.1 Effect of temperature on the viscosity of gases

General information

This is what happens when a ball falls into a non-viscous liquid - coffee

Viscosity determines the internal resistance of a fluid to the force exerted to cause the fluid to flow. There are two types of viscosity - absolute and kinematic. The first is usually used in cosmetics, medicine and cooking, and the second is more often used in the automotive industry.

Absolute viscosity and kinematic viscosity

Absolute viscosity

fluid, also called dynamic, measures the resistance to the force causing it to flow.
It is measured regardless of the properties of the substance. Kinematic viscosity
, on the contrary, depends on the density of the substance. To determine kinematic viscosity, the absolute viscosity is divided by the density of the liquid.

Kinematic viscosity depends on the temperature of the liquid, therefore, in addition to the viscosity itself, it is necessary to indicate at what temperature the liquid acquires such viscosity. Engine oil viscosity is typically measured at temperatures of 40°C (104°F) and 100°C (212°F). When changing oil in cars, auto mechanics often take advantage of the property of oils to become less viscous as the temperature rises. For example, in order to remove the maximum amount of oil from the engine, it is preheated, as a result the oil flows out more easily and quickly.

Newtonian and non-Newtonian fluids

Viscosity varies differently depending on the type of liquid. There are two types - Newtonian and non-Newtonian fluids. Newtonian fluids are those whose viscosity changes regardless of the force deforming it. All other liquids are non-Newtonian. They are interesting because they deform at different rates depending on the shear stress, that is, deformation occurs at a higher or, conversely, lower speed depending on the substance and the force that presses on the liquid. Viscosity also depends on this deformation.

Ketchup is a classic example of a non-Newtonian fluid. While it is in the bottle, it is almost impossible to force it out with a little force. If, on the contrary, we apply great force, for example, we start shaking the bottle vigorously, then the ketchup will easily flow out of it. Thus, a large voltage makes ketchup fluid, while a small voltage has almost no effect on its fluidity. This property is inherent only in non-Newtonian liquids.

Honey is very viscous

Other non-Newtonian fluids, on the contrary, become more viscous with increasing voltage. An example of such a liquid is a mixture of starch and water. A person can calmly run through a pool filled with it, but will begin to sink if he stops. This happens because in the first case the force acting on the fluid is much greater than in the second. There are non-Newtonian fluids with other properties - for example, in them the viscosity changes not only depending on the total amount of stress, but also on the time during which the force is applied to the fluid. For example, if the overall stress is caused by a larger force and is applied to the body for a short period of time, rather than being distributed over a longer period with less force, then a liquid, such as honey, becomes less viscous. That is, if you stir honey vigorously, it will become less viscous compared to stirring it with less force but for a longer time.

Second viscosity

Main article: Bulk viscosity

The second viscosity, or volumetric viscosity, is internal friction when momentum is transferred in the direction of motion. It affects only when taking into account compressibility and (or) taking into account the heterogeneity of the coefficient of the second viscosity in space.

If dynamic (and kinematic) viscosity characterizes pure shear deformation, then the second viscosity characterizes volumetric compression deformation.

Bulk viscosity plays a large role in the attenuation of sound and shock waves, and is determined experimentally by measuring this attenuation.

Unit of measurement of dynamic viscosity in the SI system

Physical quantities. Liquid viscosity

Viscosity is a property of a liquid that determines the liquid’s resistance to external influences. Viscosity can be thought of as the internal friction between individual layers of liquid as they move relative to each other.

There are two main parameters for determining the viscosity of a liquid: dynamic (or absolute) viscosity and kinematic viscosity. Dynamic viscosity is represented as the ratio of a unit of force required to displace a layer of liquid by a unit distance to a unit area of ​​the layer.

Constitutive equation for dynamic viscosity

In the international system of SI units, when expressing the unit of shear pressure F/S in pascals, the velocity gradient grad υ (change in fluid velocity related to the distance between layers) in seconds to the minus first power, the dynamic viscosity µ will be expressed in pascal-seconds (P s ) . In the metric system, the unit of viscosity is represented in grams/centimeter per second, called poise. The accepted designation poise is P

1 P s = 10 poise.

The units of measurement of dynamic viscosity, pascal-second and poise, are significant in size and use submultiple units - millipascal-second MPa and centipoise cP

Gas viscosity

In the kinetic theory of gases, the coefficient of internal friction is calculated by the formula

η = 1 3 ⟨ u ⟩ ⟨ λ ⟩ ρ {\displaystyle \eta ={\frac {1}{3}}\langle u\rangle \langle \lambda \rangle \rho } ,

where ⟨ u ⟩ {\displaystyle \langle u\rangle } is the average speed of thermal motion of molecules, ⟨ λ ⟩ {\displaystyle \langle \lambda \rangle } is the average free path. In particular, it follows from this expression that the viscosity of not very rarefied gases is practically independent of pressure, since the density ρ {\displaystyle \rho } is directly proportional to pressure, and ⟨ λ ⟩ {\displaystyle \langle \lambda \rangle } - inversely proportional. The same conclusion follows for other kinetic coefficients for gases, for example, for the thermal conductivity coefficient. However, this conclusion is valid only until the gas rarefaction becomes so small that the ratio of the mean free path to the linear dimensions of the vessel (Knudsen number) becomes equal in order of magnitude to unity; in particular, this occurs in Dewar flasks (thermos flasks).

With increasing temperature, the viscosity of most gases increases, this is explained by an increase in the average speed of gas molecules u {\displaystyle u} , which increases with temperature as T {\displaystyle {\sqrt {T}}}

Effect of temperature on gas viscosity

Unlike liquids, the viscosity of gases increases with increasing temperature (for liquids it decreases with increasing temperature).

Sutherland formula

can be used to determine the viscosity of an ideal gas as a function of temperature:[3]

μ = μ 0 T 0 + CT + C ( TT 0 ) 3 / 2 , {\displaystyle {\mu }={\mu }_{0}{\frac {T_{0}+C}{T+C} }\left({\frac {T}{T_{0}}}\right)^{3/2},}

Where:

• μ—dynamic viscosity in (Pa s) at a given temperature T;
• μ0 is the reference viscosity in (Pa s) at a certain reference temperature T0;
• T—set temperature in Kelvin;
• T0—control temperature in Kelvin;
• C is the Sutherland constant for the gas whose viscosity is to be determined.

This formula can be applied for temperatures in the range 0 < T < 555 K and at pressures less than 3.45 MPa with an error of less than 10% due to the dependence of viscosity on pressure.

The Sutherland constant and reference viscosities of gases at various temperatures are given in the table below:

What is kinematic viscosity?

Kinematic viscosity is a property of liquids and gases that indicates how easily a given substance can flow. In practice, this is closely related to how thick the substance is. Absolute and kinematic viscosity varies depending on temperature.

To obtain kinematic viscosity, the absolute viscosity of a substance is divided by its density. Kinematic viscosity is represented by the Greek letter nu, which resembles "v;" absolute viscosity is represented as mu, which resembles “u;” and density is represented as rho, which resembles "p". Therefore, the equation is v = u/p.

Absolute viscosity, also called dynamic viscosity, measures a substance's resistance to flow. This is determined experimentally by placing a liquid or gas between two plates and applying a known pressure to move the top plate - dynamic viscosity depends on the pressure, the amount of time it was applied, and the distance the plate was moved during that time. Dynamic or absolute viscosity is based on the International System of Units (SI) units of Pascal seconds (Pa*s), which means that if a pressure of 1 Pa is applied for 1 second, the plate will move the same distance as the distance between two plates. Centipoise (cP) is also a common unit of measurement for dynamic viscosity - 1 cP is the viscosity of water at room temperature. Imperial units, pound-second per square foot (lb*s/ft^2), are used very rarely.

Density measures the mass of a substance relative to its volume, which means it has units of mass per volume. Units: kg/m^3 in SI units or slug/ft^3 in imperial units. Density can be understood by comparing it to weight - a piece of denser material will weigh more than the same size piece of less dense material.

Since kinematic viscosity is dynamic viscosity divided by density, it has units of square meters per second (m^2/s) in the SI system or square feet per second (ft^2/s) in the imperial system. Regarding absolute viscosity, imperial units are almost never used. Centistokes (cSt) is a commonly used unit - one cSt is the kinematic viscosity of water at room temperature. One cSt is equal to 10^-6 m^2/s.

Heat affects material properties, so both types of viscosity change at higher temperatures. When a liquid heats up, it flows more easily and hence the viscosity decreases. Kinematic viscosity is affected somewhat less than absolute viscosity because heat also reduces density because molecules move further apart when a substance is heated. The viscosity of gases increases at higher temperatures - as the gas expands, it puts more pressure on the plate, making it more difficult to move.

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Viscosity of liquids

Dynamic viscosity

Internal friction of liquids, like gases, occurs when the liquid moves due to the transfer of momentum in a direction perpendicular to the direction of movement. The general law of internal friction is valid - Newton's law:

τ = − η ∂ v ∂ n , {\displaystyle \tau =-\eta {\frac {\partial v}{\partial n}},}

The viscosity coefficient η {\displaystyle \eta } (coefficient of dynamic viscosity, dynamic viscosity) can be obtained based on considerations of molecular motions. Obviously, η {\displaystyle \eta } will be smaller, the shorter the “settlement” time t of the molecules. These considerations lead to an expression for the viscosity coefficient called the Frenkel-Andrade equation:

η = C ew / k T {\displaystyle \eta =Ce^{w/kT}}

A different formula representing the viscosity coefficient was proposed by Baczynski. As shown, the viscosity coefficient is determined by intermolecular forces depending on the average distance between the molecules; the latter is determined by the molar volume of the substance VM {\displaystyle V_{M}} . Numerous experiments have shown that there is a relationship between molar volume and viscosity coefficient:

η = c VM − VC , {\displaystyle \eta ={\frac {c}{V_{M}-V_{C}}},}

Where:

• c {\displaystyle {c}} is a constant characteristic of a particular liquid;
• VC {\displaystyle V_{C}} is the intrinsic volume occupied by liquid particles.

This empirical relationship is called the Baczynski formula[6].

The dynamic viscosity of liquids decreases with increasing temperature and increases with increasing pressure.

Kinematic viscosity

In technology, in particular, when calculating hydraulic drives and tribology, one often has to deal with the quantity:

ν = η ρ , {\displaystyle \nu ={\frac {\eta }{\rho }},}

and this quantity is called kinematic viscosity [7].

Here ρ {\displaystyle \rho } is the density of the liquid; η {\displaystyle \eta } is the coefficient of dynamic viscosity.

Kinematic viscosity in older sources is often given in centistokes (cSt). This value is converted into the following: 1 cSt = 1 mm²/s = 10−6 m²/s.

Conditional viscosity

Conditional viscosity is a value that indirectly characterizes the hydraulic resistance to flow, measured by the flow time of a given volume of solution through a vertical tube (of a certain diameter). Measured in degrees Engler (named after the German chemist K. O. Engler), denoted by °ВУ. It is determined by the ratio of the time of flow of 200 cm³ of the test liquid at a given temperature from a special viscometer to the time of flow of 200 cm³ of distilled water from the same device at 20 ° C. Conditional viscosity up to 16 °ВУ is converted into kinematic according to the GOST table, and conditional viscosity exceeding 16 °ВУ, according to the formula:

ν = 7 , 4 ⋅ 10 − 6 E t , {\displaystyle \nu =7,4\cdot 10^{-6}E_{t},}

where ν {\displaystyle \nu } is the kinematic viscosity (in m2/s), and E t {\displaystyle E_{t}} is the conditional viscosity (in °VU) at temperature t.

Newtonian and non-Newtonian fluids

Newtonian fluids are those for which the viscosity does not depend on the rate of deformation. In the Navier-Stokes equation for a Newtonian fluid, there is a viscosity law similar to the above (in fact, a generalization of Newton’s law, or the Navier-Stokes law [8]):

σ ij = η ( ∂ vi ∂ xj + ∂ vj ∂ xi ) , {\displaystyle \sigma _{ij}=\eta \left({\frac {\partial v_{i}}{\partial x_{j}} }+{\frac {\partial v_{j}}{\partial x_{i}}}\right),}

where σ i, j {\displaystyle \sigma _{i,j}} is the viscous stress tensor.

Among non-Newtonian liquids, based on the dependence of viscosity on the strain rate, pseudoplastics and dilatant liquids are distinguished. A model with non-zero shear stress (viscosity action similar to dry friction) is the Bingham model. If the viscosity changes over time, the fluid is said to be thixotropic. For non-Newtonian liquids, the viscosity measurement technique is of paramount importance.

As temperature increases, the viscosity of many liquids decreases. This is explained by the fact that the kinetic energy of each molecule increases faster than the potential energy of interaction between them. Therefore, they always try to cool all lubricants, otherwise there is a risk of simple leakage through the components.

Viscosity value

In most cases, the coefficient of dynamic viscosity is measured in centipoise (cP) in accordance with the CGS unit system (centimeter, gram, second). In practice, viscosity is related to the ratio of the mass of the liquid to its volume, that is, with the density of the liquid:

ρ = m/V

Here:

• ρ – liquid density;
• m – liquid mass;
• V is the volume of liquid.

The relationship between dynamic viscosity (μ) and density (ρ) is called kinematic viscosity ν (ν - in Greek - nu):

ν = μ / ρ = [m2/s]

By the way, the methods for determining the viscosity coefficient are different. For example, kinematic viscosity is still measured in accordance with the GHS system in centistokes (cSt) and in fractional values ​​- stokes (St):

• 1St = 10-4 m2/s = 1 cm2/s;
• 1cSt = 10-6 m2/s = 1 mm2/s.

Viscosity of amorphous materials

The viscosity of amorphous materials (for example, glass or melts) is a thermally activated process [9]:

η ( T ) = A ⋅ exp ⁡ ( QRT ) , {\displaystyle \eta (T)=A\cdot \exp \left({\frac {Q}{RT}}\right),}

Where:

• Q {\displaystyle Q}—viscosity activation energy (J/mol);
• T {\displaystyle T} — temperature ();
• R {\displaystyle R} is the universal gas constant (8.31 J/mol K);
• A {\displaystyle A} is some constant.

Viscous flow in amorphous materials is characterized by a deviation from the Arrhenius law: the activation energy of viscosity Q {\displaystyle Q} changes from a large value QH {\displaystyle Q_{H}} at low temperatures (in the glassy state) to a small value QL {\displaystyle Q_{ L}} at high temperatures (in a liquid state). Depending on this variation, amorphous materials are classified as either strong when ( QH − QL ) < QL {\displaystyle \left(Q_{H}-Q_{L}\right) , or brittle when ( QH − QL ) ≥ QL {\displaystyle \left(Q_{H}-Q_{L}\right)\geq Q_{L}} . The fragility of amorphous materials is numerically characterized by the Doremus fragility parameter RD = QHQL {\displaystyle R_{D}={\frac {Q_{H}}{Q_{L}}}} : strong materials have RD < 2 {\displaystyle R_{D} <2} , while brittle materials have RD ≥ 2 {\displaystyle R_{D}\geq 2} .

The viscosity of amorphous materials is very accurately approximated by a two-exponential equation [10]:

η ( T ) = A 1 ⋅ T ⋅ [ 1 + A 2 ⋅ exp ⁡ BRT ] ⋅ [ 1 + C exp ⁡ DRT ] {\displaystyle \eta (T)=A_{1}\cdot T\cdot \left[ 1+A_{2}\cdot \exp {\frac {B}{RT}}\right]\cdot \left[1+C\exp {\frac {D}{RT}}\right]}

with constants A 1 {\displaystyle A_{1}} , A 2 {\displaystyle A_{2}} , B {\displaystyle B} , C {\displaystyle C} and D {\displaystyle D} associated with the thermodynamic parameters of the connecting bonds of amorphous materials.

In narrow temperature ranges near the glass transition temperature T g {\displaystyle T_{g}} this equation is approximated by VTF-type formulas or compressed Kohlrausch exponentials.

Viscosity

If the temperature is significantly lower than the glass transition temperature T < T g {\displaystyle T , the biexponential viscosity equation reduces to an Arrhenius-type equation

η ( T ) = ALT ⋅ exp ⁡ ( QHRT ) , {\displaystyle \eta (T)=A_{L}T\cdot \exp \left({\frac {Q_{H}}{RT}}\right) ,}

with high activation energy QH = H d + H m {\displaystyle Q_{H}=H_{d}+H_{m}} , where H d {\displaystyle H_{d}} is the enthalpy of breaking connecting bonds, that is, creating configurons, and H m {\displaystyle H_{m}} is the enthalpy of their motion. This is due to the fact that at T < T g {\displaystyle T amorphous materials are in a glassy state and have the vast majority of connecting bonds unbroken.

For T ≫ T g {\displaystyle T\gg T_{g}} the biexponential viscosity equation also reduces to an Arrhenius-type equation

η ( T ) = AHT ⋅ exp ⁡ ( QLRT ) , {\displaystyle \eta (T)=A_{H}T\cdot \exp \left({\frac {Q_{L}}{RT}}\right) ,}

but with low activation energy QL = H m {\displaystyle Q_{L}=H_{m}} . This is due to the fact that at T ≫ T g {\displaystyle T\gg T_{g}} amorphous materials are in a straightened state and have the vast majority of connecting bonds destroyed, which facilitates the fluidity of the material.

Viscosity of some substances

For aircraft and shipbuilding, it is most important to know the viscosities of air and water.

Air viscosity

Dependence of the viscosity of dry air on pressure at temperatures of 300, 400 and 500 K.
The viscosity of air depends mainly on temperature. At 15.0 °C, the viscosity of air is 1.78 10−5 kg/(m s), 17.8 μPa s or 1.78 10−5 Pa s. You can find the viscosity of air as a function of temperature using programs for calculating gas viscosities[11].

Water viscosity

Dependence of the dynamic viscosity of water on temperature in the liquid state (Liquid Water) and in the form of vapor (Vapor)
The dynamic viscosity of water is 8.90·10−4 Pa·s at a temperature of about 25 °C. As a function of temperature: T = A × 10B/(T−C), where A = 2.414 10−5 Pa s; B = 247.8 K; C = 140 K.

The viscosity values ​​of liquid water at different temperatures up to the boiling point are given in the table:

Dynamic viscosity of various substances

Below are the values ​​of the coefficient of dynamic viscosity of some Newtonian liquids:
Viscosity of certain types of gases

Viscosity of liquids at 25 °C

Relationship between dynamic and kinematic viscosity

The viscosity of a liquid determines the ability of the liquid to resist shear as it moves, or more precisely, the shear of layers relative to each other. Therefore, in industries where pumping of various media is required, it is important to know exactly the viscosity of the pumped product and select the correct pumping equipment.

There are two types of viscosity in technology.

1. Kinematic viscosity is more often used in a passport with fluid characteristics.
2. Dynamic is used in engineering calculations of equipment, research work, etc.

The conversion of kinematic viscosity to dynamic viscosity is carried out using the formula given below, through density at a given temperature:

Where:

v is kinematic viscosity,

n is dynamic viscosity,

p —density.

Thus, knowing a particular viscosity and density of a liquid, you can convert one type of viscosity to another using the specified formula or through the converter above.

Viscosity measurement

The concepts for these two types of viscosity are inherent only to liquids due to the peculiarities of the measurement methods.

Measuring kinematic viscosity uses the method of fluid flow through a capillary (for example, using an Ubbelohde device). Dynamic viscosity is measured by measuring the resistance to motion of a body in a liquid (for example, the resistance to rotation of a cylinder immersed in a liquid).

What does the viscosity value depend on?

The viscosity of a liquid depends largely on temperature. With increasing temperature, the substance becomes more fluid, that is, less viscous. Moreover, the change in viscosity, as a rule, occurs quite sharply, that is, nonlinearly.

Since the distance between the molecules of a liquid substance is much smaller than that of gases, the internal interaction of molecules in liquids decreases due to a decrease in intermolecular bonds.

The shape of the molecules and their size, as well as their relative positions and interactions, can determine the viscosity of a liquid. Their chemical structure also influences.

For example, for organic compounds, viscosity increases in the presence of polar rings and groups.

For saturated hydrocarbons, growth occurs when the molecule of the substance becomes “heavier.”

Notes

1. In general this is not the case.
2. About some mistakes in hydrodynamics courses, p. 3-4.
3. Alexander J. Smits, Jean-Paul Dussauge Turbulent shear layers in supersonic flow. - Birkhäuser, 2006. - P. 46. - ISBN 0-387-26140-0.
4. data constants for sutherland's formula
5. Viscosity of liquids and gases
6. Khmelnitsky R. A.
   Physical and colloidal chemistry: Textbooks for agricultural specialists. universities - M.: Higher School, 1988. - P. 40. - 400 p. — ISBN 5-06-001257-3.
7. Popov D.N.
   Dynamics and regulation of hydro- and pre-hydrosystems. : Textbook. for mechanical engineering universities. - M.: Mechanical Engineering, 176. - P. 175. - 424 p.
8. Sedov L.I. Continuum mechanics. T. 1. - M.: Nauka, 1970. - P. 166.
9. Frenkel Ya. I.
   Kinetic theory of liquids. -Leningrad, Science, 1975. - page 226
10. Ojovan M. Viscous flow and the viscosity of melts and glasses. Physics and Chemistry of Glasses, 53 (4) 143–150 (2012).
11. Gas Viscosity Calculator

Literature

• RH Doremus. J. Appl. Phys., 92, 7619–7629 (2002).
• M. I. Ojovan, W. E. Lee. J. Appl. Phys., 95, 3803–3810 (2004).
• MI Ojovan, KP Travis, RJ Hand. J. Phys.: Condensed Matter, 19, 415107 (2007).
• L. I. Sedov. Continuum mechanics. T. 1. - M.: Nauka, 1970. - 492 p.
• P. N. Gedyk, M. I. Kalashnikova. Lubrication of metallurgical equipment. - M.: Metallurgy, 1976. - 380 p.
• I. F. Golubev. Viscosity of gases and gas mixtures. - M.: Fizmatlit, 1959.

Unit converter

Hydraulics and hydromechanics - fluids

Hydraulics
is the science of the laws of motion and equilibrium of fluids and the methods of applying these laws to solving problems in engineering practice.
Hydraulics is characterized by a special approach to the study of the phenomena of fluid flow; it establishes approximate dependencies, limiting itself in many cases to consideration of one-dimensional motion, making extensive use of experiment, both in laboratory and natural conditions. Fluid mechanics
is an applied science (a branch of continuum mechanics) that studies the equilibrium and movement of fluid.
Fluid mechanics is subdivided into hydrostatics
, which studies fluid in equilibrium, and
hydrodynamics
, which studies fluid motion.

Kinematic Viscosity Converter

Kinematic viscosity
is defined as the ratio of dynamic viscosity to the density of a substance.

In the International System of Units (SI), kinematic viscosity is measured in m²/s. In the GHS system, the unit of measurement for kinematic viscosity is Stokes (St). In technical literature, kinematic viscosity is often indicated in centistokes (cSt). 1 St = 10⁻⁴ m²/s, 1 cSt = 10⁻⁶ m²/s. The kinematic viscosity of water at 20°C is approximately 1 cSt.

Using the Kinematic Viscosity Converter converter

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