A macro property of the fluid, which is related by a certain relationship between the stress applied to the fluid and the resulting deformation rate, is represented by the internal friction of the fluid.
The viscosity of asphalt is about 230 billion times that of water
Flow difference of liquid with different viscosity
Effect of viscosity
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Due to viscous energy dissipation, the moving fluid will gradually stop without external energy supplement.Viscosity plays an important role in the fluid movement near the object surface, making the flow rate reduce layer by layer and zero on the object surface. Under certain conditions, the fluid can also be separated from the object surface (see boundary layer).
Characterization of viscosity
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A. Definition of viscosity coefficient (viscosity)
The viscosity is determined by the viscosity coefficient (i.e. viscosity)[1]To represent.Newtonian viscosity law (see Newtonian fluid) indicates that in pure shear flow, the shear stress between two layers of fluid
It can be expressed as:
，
Where
Is alongyThe velocity gradient in the direction (perpendicular to the fluid velocity direction) is also called shear deformation rate;
Is a proportional constant, that is, the viscosity coefficient, which is equal to the value of the tangential force on the unit area of the fluid when the velocity gradient is a unit.
In the centimeter gram second system commonly used, the unit of viscosity coefficient is Poise.
SI pascal second (1 poise=1 dyne second/cmtwo=10-1Pascal second), its dimension is ML-1T-1。For most fluids, the common unit is centipoise (10-3Pascal second).
B. Viscosity coefficient of common fluid
Different fluids have different viscosity coefficients.The viscosity coefficient of a few liquids (such as glycerin) can reach 15 poise;The viscosity coefficient of olive oil is close to 1 poise.At 20 ℃, the viscosity coefficient of water is 1.0087 centipoise.The viscosity coefficient of gas ranges from 2.1 × 10 of argon-40.8 × 10 to hydrogen-4They are all 10-4Poi.
C. Calculation of viscosity coefficient
Coefficient of viscosity
It is significantly dependent on temperature, but rarely changes with pressure. Its relationship with temperature is completely different for liquids and gases.For liquids, viscosity coefficient increases with temperature
Decline;For gases, the viscosity coefficient increases with temperature.
For gas, the relationship between viscosity coefficient M and temperature T can be expressed as Sutherland formula:
WhereB≈ 110.4 open;
Is the reference temperature and the reference viscosity coefficient.This formula is within a considerable range（T<2000 ON) is applicable to air.However, due to the complexity of the above formula, the power formula is often used in practice:
To approximate the real viscous relationship.power nThe variation range of is 1/2 ≤ n ≤ 1, which depends on the nature of the gas and the temperature range considered.At high temperature, such as above 3000 ℃,nIt can be approximately taken as 1/2;It can be taken as 1 at low temperature.For air, in the temperature range of 90 ° C<T<300 ° C, the formula can be used:
The error between this formula and Sutherland's formula is only 5%.
For water, the relationship between viscosity coefficient and temperature can be approximately written as:
(berths).
For general fluid motion, it is assumed that: ① the stress tensor of the moving fluid should tend to the stress tensor of the stationary fluid after the motion stops; ②Deviator stress tensor
The components of are local velocity gradient tensors
Linear homogeneous function of each component; ③The fluid is isotropic, from which the generalized Newtonian viscosity law can be derived (see Newtonian fluid):
Where,
、
Stress tensor and deformation rate tensor;pPressure function;
Croneker symbol;
Is the viscosity coefficient;
Is the second viscosity coefficient, also called expansion viscosity coefficient.For incompressible fluids, due to
，
It does not appear automatically. There is only one viscosity coefficient in the generalized Newton's law
。For compressible fluid, it generally has two viscosities as Hooke's elastomer (see Hooke's Law)
and
。It is the viscosity coefficient that measures the internal friction work caused by the expansion or contraction of the fluid.In addition to the extreme cases of high temperature and high-frequency sound waves, the gas movement in general cases can be approximately considered as
。This fact is proved in the theory of molecular motion.That was just a hypothesis put forward by Stokes.
Physical explanation of viscosity
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Taking gas as an example, the cause of viscosity formation is explained.The velocity of gas molecules is composed of the average velocity and the thermal motion velocity. The former is the macro velocity of the gas cluster, and the latter determines the temperature of the gas.If two adjacent gas clusters move at different macroscopic speeds, because there are many molecules exchanged between them, momentum exchange will occur, which will lead to the average speed of the gas cluster. This is the origin of gas viscosity.According to this image, the expression of gas viscosity coefficient can be obtained by using the Boltzmann square in statistical physics:
WherekIs Boltzmann constant;mbymolecular mass ；CIs the proportional constant of the molecular force.The above formula shows that viscosity coefficient and gasdensityIt is independent and proportional to the temperature.These two conclusions have been confirmed by experiments.The molecular motion theory of liquid is not yet mature, and there is no establishment similar toKinetic theory of gas moleculesA simple physical image of is used to illustrate the mechanism of liquid viscosity.
Viscosity coefficient measurement
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Various experimental methods can be used to determinefluidThe viscosity coefficient of.For example, between two coaxial cylinders with different radii, the fluid with viscosity to be measured is filled.When the outer cylinder rotates, the fluid closest to the outer cylinder wall can also move at the same speed. Due to the effect of viscosity, the inner cylinder also moves with it.Since the inner cylinder is suspended on the metal wire fixed at the upper end, it stops rotating after rotating to a certain angle.If the torsion angle of the wire is measured, it can be calculatedTorsional moment。Due to the balance between torsional moment and liquidShear forceThe resulting moment is equal, so the shear force and fluid viscosity coefficient can be calculated.Another method is to find out the time required for a certain volume of fluid to flow out of a thin pipe under a given pressure, so as to find out its viscosity coefficient.
