Viscosity

The viscosity is a measure of the viscosity of a fluid. The reciprocal of the viscosity, the fluidity, a measurement of the flowability of a fluid. The greater the viscosity, the more viscous (less flowable) the fluid; the lower the viscosity, the lower the viscosity ( flowable ), it is, so it can flow faster at the same conditions.

Normally, the viscosity in shear is associated with the term viscosity, but it is also possible to measure the viscosity in elongation, see the extensional viscosity side.

Particles viscous liquids are tied more closely to each other and thus less mobile; therefore we also speak of the internal friction. It results not only from the forces of attraction between the particles of the fluid (cohesion).

Terms such as ductility, brittleness and plasticity The viscosity of solids is generally very high (and therefore difficult to determine ), instead often used.

In the rheology is the viscosity of a central size Represent has meaning where fluids are used or occur, eg in paints, coatings, lubricants, plastics, adhesives, food as batters and puddings, but also in virtually all areas medicine ( blood).

The term viscosity goes to the typical viscous juice of the berries in the plant genus mistletoe (Viscum ) back. For these mistletoes of lime was obtained. " Viscous " means "the sticky, viscous like bird-lime ".

• 2.1 Definition of viscosity 2.1.1 Newtonian fluids
• 2.1.2 Non - Newtonian fluids

• 3.1 Kinetic Theory of Gases

Context of the three sizes

A distinction is made between the dynamic and the kinematic viscosity. The dynamic viscosity and kinematic viscosity are about the density directly related. Fluidity is the reciprocal value of the dynamic viscosity:

Units

In the SI unit system applies: A substance that is located between two plates, the viscosity has 1 Ns / m when measured at a size of the plates of 1 m and a plate separation of 1 m, a force of 1 N is needed to the plates / s against each other to move at a speed of 1 m. Therefore applies to the physical unit of dynamic viscosity:

The unit of fluidity is accordingly:

For the SI unit of kinematic viscosity is true:

In practice, moreover, the thousandth part of the SI unit mPa · s (milli Pascal second) is used for media of low viscosity for the dynamic viscosity in addition to the Pa · s ( Pascal seconds ).

In CGS system is the dynamic viscosity is measured in poise (P), where 1 Ns/m2 = 1 Pa.s = 10 poise = 1000 centipoise = 1000 cP = 1 kg / ms and the kinematic viscosity in Stokes (St), 1 pc = 10-4 m2 / s

The Engler degree is an obsolete unit of viscosity. This unit is the viscosity at in comparison to water.

Viscosity of liquids

The effect of internal friction can be simplified by the motion of two superimposed, interlocked molecular layers present ( see Figure 1 point ). While flowing the molecules to slide past each other, and to overcome the teeth requires a certain force. The relationship between this force and the properties of this fluid defines the viscosity. Be seen, this connection is particularly well to the homologous series of alkanes ( chain-like hydrocarbons), here the viscosity increases with the chain length and with it the increasing intermolecular acting van der Waals forces continuously. In the mid- alkanes (from nonane, nine C- atoms) it already has a value similar to that of water.

Can illustrate Very good one, the viscosity also at the following example: wind glides over the waters of an ocean, this produces a movement of the water layer at the surface. The deeper you dive now, the smoother the water until you reach a point where no flow exists. The individual liquid layers move at different speeds, it creates a velocity gradient ( see Fig item 2).

Definition of viscosity

Imagine two spaced plates arranged in parallel to the surface. Between these plates is a liquid, which adheres to both plates. In our presentation of the room should be divided by the liquid layers. Now, the upper plate moves with the speed, then the adhesion layer is moved in close proximity to ground also at the speed. Since the lower plate rests, resting their neighboring layer. The inner fluid layers slide past each other at different speeds. The speed increases from the resting plate for moving to.

From the top, adhering to the plate layer is made ​​of a tangential force on the underlying layer. This consequently moves with the speed. This layer in turn acts on the underlying layer and it is moved with the velocity.

In the experiment, it can be shown that in the ideal case, the force which is necessary to move the upper plate, proportional to the area, the speed difference, and inversely proportional to the distance between the plates is:

This results in the equation

The proportionality constant is the dynamic viscosity. The change of velocity perpendicular to the movement direction, that the velocity

With or referred to, strain rate or shear rate is called. With the shear stress

Results in the context

Newtonian fluids

If it is very thin fluid layers, so the velocity profile is linear, as in the above derivation. This relationship was assumed in 1687 by Isaac Newton:

"The resistance Which Arises from the lack of slipperiness Originating in a fluid - other things being equal - is proportional to the velocity by Which the parts of the fluid are being separated from eachother. "

" The resistance which arises due to the lack of lubricity within a liquid is - provided that all other conditions remain the same -. Proportional to the velocity with which the liquid particles are separated from each other "

Liquids that follow this linear relationship are therefore referred to as Newtonian fluids. Is dependent, refers to the liquid as non- Newtonian. The Newtonian law of viscosity laminar flow as well as temperature and pressure independence of the fluid properties is always assumed. For these substances, raises the one shown in the shear stress - shear rate diagram, linear velocity profile ( curve 2: Newtonian fluid ).

In the rheological models, the Newtonian behavior of the Newton element, a damping cylinder is similar to a shock absorber shown.

Non- Newtonian fluids

However, many substances do not follow this law, but show a time or shear rate- dependent behavior. We distinguish different types of deviations:

• Yield point, it has only a certain minimum shear stress to be present in order to achieve a flow ( plastic flow ). This kind fluid is also referred to as Bingham fluid
• Intrinsic viscosity / dilatancy, while the viscosity is not constant, but varies with the shear rate
• Thixotropy / rheopexy here to show time-dependent structural changes, so that depending on the length of time different viscosity values ​​can be found since the last flow movement.

In the general case the shear rate must be calculated from the yaw angle with the liquid and not on the velocity. The ratio is called in this case also apparent viscosity.

Viscoelastic material can be described by the complex viscosity, it is assumed in the sinusoidal by a shear.

Temperature dependence

The dynamic viscosity of most liquids decreases with increasing temperature and often can be described by the Arrhenius relationship Andrade:

Where a material constant and the activation energy ( also space energy exchange ), the universal gas constant and absolute temperature, respectively. For liquids near the glass transition temperature ( up to 100 K above) usually applies the WLF relationship, since the free volume is very low and thus dominates this size near the glass transition temperature has a much stronger temperature dependence than the chain mobility, which is behind the Arrhenius - Andrade relationship.

The degree of dependence of the kinematic viscosity of the oil temperature will be described in by the viscosity index.

Measurement of viscosity

The viscosity of fluids can be measured with a viscometer. A rheometer allows it, but also for further rheological properties, even of solids to determine. In both types of devices, the sample to be measured is introduced in the gap between two members ( e.g., two co-axial cylinders or two parallel plates ) according to the viscosity definition. A part of the assembly is rotated or oscillated at a defined speed, while the other rests. From the geometry of the measuring arrangement, and the speed of the moving part there is the shear rate. The necessary to maintain the motion torque is measured, from which then leaves the shear stress and thus determine the viscosity.

A quick and easy, but also very inaccurate method of determining viscosity is the viscosity cup.

In addition to determining the shear viscosity using the method described above, the extensional viscosity of a substance can be determined for example by the Capillary Breakup Extensional Rheometer.

Typical viscosity values

Viscosity of gases

For gases the viscosity can be estimated by microscopic observation of the momentum flux:

With the mean free path of the gas particles, the mass of the gas particles, the average particle velocity and the particle number density.

The viscosity of gases at low pressures ( ≈ 0.1 to 10 bar ) irrespective of the pressure. This applies as long as the mean free path is small compared to the vessel dimensions and large compared to the molecular dimensions. In other words, for a very thin or a very dense gas, the viscosity is yet again by the pressure or the density of the gas.

In principle, however, is dependent on the viscosity of the temperature. As the temperature increases, the viscosity increases as the average particle velocity is proportional to grow ( see below). This behavior is exactly the opposite of most liquids. The following table lists some gases on the viscosity and mean free path.

Kinetic theory of gases

After, Hirschfelder the viscosity of pure gases can be calculated in a wide temperature range ( approximately from 200 to 3000 Kelvin ) using the kinetic theory of gases.

Here, the molecular mass, the Boltzmann constant, temperature, the Lennard-Jones diameter and the reduced impact collision integral which depends on the reduced temperature. is the energy of the Lennard-Jones potential. Values ​​for the Lennard-Jones parameters and the reduced collision integral are listed in Lienhard's textbook on heat transfer in chapter 11. The reduced collision integral is defined so that for an ideal gas, are considered in the particle interactions such as collisions of hard spheres is considered.

Physics of Reibungstensors

The viscosity is based out of the experiment, after which a force is required to maintain a shear flow. This force causes a momentum exchange within the flow or to the edge, which is why it belongs to the category of surface forces. This allows this power to formulate the most general form as the divergence of a tensor:

Wherein the component of the stress tensor by the viscosity and viscous stress tensor is, or Reibungstensor.

From the experiment it follows immediately that the Reibungstensor is a function of the shear of the flow:

Since there is no friction in a homogeneous flow, or contains the Reibungstensor no components that are independent of the shear. With the assumption that the velocity gradient is small in terms of hydrodynamics, a linear approach between the friction and the velocity gradient is established.

Furthermore, the internal friction is zero when the flow is in a rigid rotation, wherein said constant angular velocity. The linear combinations of the derivatives of the velocities are just the symmetrical components of

Why here and in the following the Einstein summation convention is observed.

With the further assumption of an isotropic liquid, the immediate material properties are described by scalar quantities. Thus, the Reibungstensor:

Here the first term describes the friction by volume loyal deformation ( for the term in the parenthesis is zero). The second term describes the internal friction due to volume change. This term will vanish for the frequent case of incompressibility.