What Is a Viscous Fluid?

A macroscopic property of the fluid is related to the stress applied to the fluid and the resulting deformation rate in a certain relationship, which is represented by the internal friction of the fluid.

Chinese name: viscosity

Foreign name: viscosity

Viscous liquid-honey

The viscosity of asphalt is about 230 billion times the viscosity of water

Flow differences of liquids of different viscosities

Viscous effect

Due to the viscous energy dissipation effect, the moving fluid will gradually stop without external energy supplement. Viscosity has an important effect on the fluid movement near the surface of the object, which reduces the flow rate layer by layer and is zero on the object surface. Under certain conditions, the fluid can also be separated from the object surface (see boundary layer).

Characterization of stickiness

A. () Viscosity A. Definition of viscosity coefficient (viscosity)

The viscosity is expressed by the viscosity coefficient (ie, viscosity) ^[1] . Newton's law of viscosity (see Newtonian fluids) states that in pure shear flow, the shear stress between two layers of fluid

It can be expressed as:

Where

Is the velocity gradient along the y direction (vertical to the direction of fluid velocity), also known as the shear deformation rate;

Is the proportionality constant, that is, the viscosity coefficient, which is equal to the value of the tangential force on the unit area when the velocity gradient is one unit.

In the centimeter-gram-second system commonly used, the unit of the viscosity coefficient is Poise.

The SI system uses Pa · s (1 poise = 1 dyne · s / cm ² = 10 ^-1 Pa · s), and its dimension is ML ^-1 T ^-1 . For most fluids, the common unit is centipoise (10 ^-3 Pa · s).

B. Viscosity B. Viscosity coefficient of common fluids

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 ° C, the viscosity coefficient of water is 1.0087 centipoise. Gas viscosity coefficients range from 2.1 x 10 ^-4 poises for argon to 0.8 x 10 ^-4 poises for hydrogen, both of which are in the order of 10 ^-4 poise.

C. C. Calculation of viscosity coefficient

Viscosity coefficient

It is significantly temperature dependent, but rarely changes with pressure, and its relationship to temperature is quite different for liquids and gases. For liquids, as temperature increases, the viscosity coefficient

For gas, the viscosity coefficient increases as the temperature increases.

For gas, the relationship between the viscosity coefficient M and the temperature T can be expressed as the Sutherland formula:

Where B 110.4 Kelvin;

Are the reference temperature and the reference viscosity coefficient. This formula is applicable to air in a considerable range ( T <2000 K). However, because the above formula is more complicated, more practical power formulas are used:

To approximate the true sticky relationship. The power n range is 1 / 2n1, which depends on the nature of the gas and the temperature range considered. At high temperatures, such as 3,000 K or more, n can be taken as approximately 1/2; at low temperatures, it can be taken as 1. For air, in the temperature range of 90 K <T <300 K, the formula can be used:

It differs from Sutherland's formula by only 5%.

For water, the relationship between viscosity coefficient and temperature can be approximated as:

(Parking).

For general fluid motion, it is assumed that: the stress tensor of the moving fluid should tend to the stress tensor of the stationary fluid after the motion stops; the bias stress tensor

Each component is a local velocity gradient tensor

Linear homogeneous function of each component; The fluid is isotropic, from which the generalized Newtonian viscosity law can be derived (see Newtonian fluid):

Where

Are stress tensor and deformation rate tensor; p pressure function;

Is the Kronecker symbol;

Is the viscosity coefficient;

Is the second viscosity coefficient, also known as the expansion viscosity coefficient. For incompressible fluids, due to

Automatically does not appear, there is only one viscosity coefficient in generalized Newton's law

. For compressible fluids, it is generally as viscous as Hooke's elastomer (see Hooke's Law).

and

. It is a viscosity coefficient that measures the amount of internal work caused by the expansion or contraction of a fluid. Except for extreme conditions such as high temperature and high frequency sound waves, the general motion of gas can be approximated as

. This fact is proved in the theory of molecular motion. That year was just an assumption made by Stokes.

Sticky physical explanation

The gas is used as an example to explain the cause of the viscosity. The velocity of a gas molecule is a superposition of the average velocity and the velocity of thermal motion. The former is the macroscopic velocity of the gas mass, and the latter determines the temperature of the gas. If two adjacent gas groups move at different macro speeds, because there are many molecules exchanged between them, the exchange of momentum is brought about, and the velocity of the gas groups tends to be averaged. This is the origin of gas viscosity. Based on this image, the expression of the gas viscosity coefficient can be obtained using the Boltzmann square in statistical physics:

Where k is the Boltzmann constant; m is the molecular mass; C is the proportionality constant of the molecular force. The above formula shows that the viscosity coefficient has nothing to do with the gas density and is directly proportional to the temperature. Both conclusions have been confirmed experimentally. The theory of liquid molecular kinematics is not yet mature. At present, no simple physical image similar to the theory of gas molecular kinematics has been established to explain the mechanism of liquid viscosity.

Viscosity coefficient measurement

Various experimental methods can be used to determine the viscosity coefficient of fluids at different temperatures. For example, between two coaxial cylinders with different radii, filled with fluid to be measured viscosity. When the outer cylinder rotates, the fluid closest to the outer cylinder wall can also move at the same speed. Due to the viscosity, the inner cylinder also moves with it. Because the inner cylinder is suspended from a fixed wire at the upper end, it stops rotating after rotating to a certain angle. If the twist angle of the wire is measured, the torsional moment can be calculated. Since the torsional moment at equilibrium is equal to the moment formed by the shear force of the liquid, the magnitude of the shear force and the viscosity coefficient of the fluid can be obtained. Another method is to find a certain volume of fluid, the time required to flow through a thin tube under a given pressure, so as to find its viscosity coefficient.