Is the viscosity directly proportional to the density

Physical size
Surname kinematic viscosity
Size type kinematic viscosity
Formula symbol of size ν
Size and
System of units
unit dimension
Physical size
Surname dynamic viscosity
Size type dynamic viscosity
Formula symbol of size η
Size and
System of units
unit dimension
also given in Pa · s or mPas

The viscosity is a measure of that viscosity of a fluid. The reciprocal of viscosity is that Fluidity, a measure of that Fluidity of a fluid. The greater the viscosity, the thicker (less flowable) the fluid is; the lower the viscosity, the more fluid (flowable) it is.

Particles of viscous liquids are more strongly bound to one another and therefore more immobile; one therefore also speaks of the internal friction. It results not only from the forces of attraction between the particles of the fluid (cohesion).

In the case of solids, the terms ductility, brittleness and plasticity are used instead. Occasionally, toughness is used as a synonym for viscosity.

The term viscosity refers to the typically viscous juice of the berries in the plant genus mistletoe (Viscum) back. Bird glue was obtained from this mistletoe, so 'viscous' roughly means 'tough like bird glue'.

Flow behavior of liquids

The effect internal friction can be simplified by moving two superimposed, interlockedImagine the molecular layers (see fig. Point 1). When flowing, the molecules slide past each other and around them Interlocking to overcome it takes a certain amount of strength. The relationship between this force and the properties of the fluid in question is defined by the viscosity. This relationship can be recognized particularly well by the homologous series of alkanes (chain-like hydrocarbons), here the viscosity increases continuously with the chain length and thus with the increasing intermolecularly acting Van der Waals forces. In the case of the middle alkanes (from nonane, nine carbon atoms) it already has a value similar to that of water.

The viscosity can also be illustrated very well with the following example: if wind glides over the water of an ocean, this creates a movement of the water layer on the surface. The deeper you dive, the calmer the water becomes, until you reach a point where there is no current. The individual layers of liquid move at different speeds (corkscrew flow), a speed gradient is created (see Fig. Point 2):

When the wind stops blowing, the current collapses and the water rests on the surface again. The fact that the liquid practically rests on the surface even in deeper layers despite the wind is a result of the internal friction in the liquid.

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

Where η0 a material constant and E.A. the activation energy (also change of place energy), R. the general gas constant and T are the absolute temperature. For liquids close to the glass transition temperature (up to approx. 100 K above), the WLF relationship usually applies, since the free volume is very small and thus this variable dominates, which has a much stronger temperature dependence than the near the glass transition temperature Chain mobility that is behind the Arrhenius-Andrade relationship.

Definition of viscosity

Imagine two at a distance x arranged panels of the surface A. in front. Between these plates there is a liquid that adheres to both plates. In our imagination, the space with the liquid should be divided into layers. Now becomes plate 2 with the speed v moves, the layer moves in the immediate vicinity of plate 2 due to the adhesion also with the speed v. Since plate 1 is at rest, its neighboring layer is also at rest. The inner layers of liquid slide past each other at different speeds. The speed increases from the stationary plate to the moving one. In the simplest case there is a linear dependency (see figure). From the topmost layer adhering to the plate, a tangential force is exerted on the layer below. This consequently moves with the speed v1. This layer in turn acts on the layer below and moves it with the velocity v2.

In the experiment it can be shown that the force F.that is needed to move plate 2 is directly proportional to its area A., their speed v and inversely proportional to the distance between the plates x is:

F.˜A. and F.˜v and

From this it follows

and as an equation

The constant of proportionality η is the dynamic viscosity. It is often referred to simply as viscosity. A substance has a viscosity of 1 Ns / m² if, with a size of the plates of 1 m² and a plate spacing of 1 m, a force of 1 N is required to move the plates against each other at a speed of 1 m / s.

The following applies to the physical unit:

Is η independent of the speed vso the liquid is called Newtonian fluid designated. The linear velocity profile shown in Figure 2 was established for these liquids. If η depends on v, the liquid is called non-Newtonian.

Newtonian fluids

In the following, the simplified relationship according to Newton's law of viscosity is shown, always assuming laminar flow as well as temperature and pressure independence of the fluid properties. In addition, Newton assumed a linear dependence of the velocity gradient explained above, which is also the shear gradient (sometimes with D. called) is called:

If this is linked to the shear stress, the following relationship is obtained for the dynamic viscosity:

The shear stress τ results from the force causing the flow in relation to the affected surface, which moves at maximum speed. η becomes at Newtonian fluids viewed as a constant. However, many substances do not follow this law. A distinction is made between different types of deviation:

  • Structural viscosity / dilatance, the viscosity η is not a constant, but changes with the shear gradient
  • Thixotropy / rheopexy, this shows time-dependent structural changes, so that other viscosity values ​​can be found depending on the length of time since the last flow movement
  • Yield point, there must first be a certain minimum shear stress in order to achieve flow (plastic flow). This type of fluid is also known as Bingham fluid.

Such fluids are referred to as non-Newtonian fluids.

In the general case, the shear rate must be calculated from the shear angle in the liquid and not from the velocity gradient.

In addition, the relationship between the dynamic viscosityη and the density ρ defined as kinematic viscosity:

SI unit

The SI unit of

dynamic viscosity:
kinematic viscosity:

In the CGS system, the dynamic viscosity is expressed in Poise (P) measured, where 1 P = 0.1 Pa · s, and the kinematic viscosity in Stokes (St), 1 St = 10-4 m2/ s.

Typical viscosity values


substance η in mPa s 1)
water 1,0
Water (25 ° C) 0,891
petroleum 0,65
Pentane (25 ° C) 0,224
Hexane 0,320
Heptane 0,410
Octane 0,538
Nonane 0,711
chloroform 0,56
Decane 0,920
Ethanol 1,19
Benzene (25 ° C) 0,601
Glycerin 1480
Color varnish ~ 102
Paraffin oil 102 until 106
Polymer melts 103 until 1013 2)
bitumen ~ 1011
asphalt ~ 105
mercury 1,55
Glass (processing temperature) ~ 102 until 104
Glass (room temperature) ~ 1018 until 1020
Blood (37 ° C) 4 to 25
Grape juice 2 to 5
olive oil ~ 102
honey ~ 104
syrup ~ 105
Coffee cream ~ 10
Rock salt ~ 1013 until 1018

1) Unless otherwise noted, the values ​​refer to the viscosity at 20 ° C.
2) There is a very wide range of viscosities in polymers, which essentially depends on the chain length and its branching structure (and of course on the temperature). For example, silicone oils (PDMS) with defined viscosities between 0.6 mPas at 25 ° C and 1,000,000 mPas at 27 ° C are produced. However, polymer melts can also have much higher viscosities. In the case of a UHMW-HDPE (for hip joint implants), viscosities beyond the 1013 mPas measured at 150 ° C.

However, one must consider that with normal unfilled polymer melts at the latest from a viscosity of 10,000 mPas structural viscosity occurs, the intensity of which (i.e. how much the viscosity drops at high shear rates) increases with increasing viscosity.

In the case of the land uplift, a post-glacial effect of the earth's surface, it is around 1021 Pas.

Viscosity of gases


For gases, the viscosity can be estimated using a microscopic observation of the momentum flow:

with the free path λ for the gas particles, the mass of the gas particles m, the mean particle velocity v and the particle number density n.

The viscosity of gases is often independent of the pressure. This applies as long as the free path is small compared to the dimensions of the vessel and large compared to the dimensions of the molecule. In other words: for a very thin or a very dense gas, the viscosity is again dependent on the pressure or the density of the gas. The viscosity is basically dependent on the temperature. With increasing temperature, the viscosity increases, because the mean particle speed v proportional to T0,5 grows (see section “Kinetic Gas Theory”). This behavior is exactly the opposite for most liquids.

For air, the limits are in the order of a few mm up to cm (for example breathing valve when diving) and 0.4 nm (molecule diameter). The following table lists the viscosities and free path lengths for some gases.

gas η (273 K) in µPa · s λ (1 atm) in nm
air 17,1 59,8
Oxygen (O2) 19,2 63,3
Carbon dioxide (CO2) 13,8 39,0
Nitrogen (N.2) 16,6 58,8
argon 21,0 62,6
neon 29,7 124,0
helium 18,6 174,0
Hydrogen (H2) 8,4 111,0

Kinetic gas theory

According to Hirschfelder, the viscosity of pure gases can be calculated with the help of the kinetic gas theory in a large temperature range (approximately from 200 to 3000 Kelvin).

Here is m the molecular mass, kB. the Boltzmann constant, T the temperature, σ the Lennard-Jones joint diameter and the reduced shock integral, that of the reduced temperature depends. ε is the energy of the Lennard-Jones potential. Values ​​for the Lennard-Jones parameters and the reduced impact integral are given in Chapter 11 of Lienhard's textbook on heat transfer.


The reciprocal of the viscosity is the fluidity η − 1 with the unit .

See also


  • Joseph O. Hirschfelder, Charles F. Curtiss, and Robert Byron Bird: Molecular Theory of Gases and Liquids. Wiley, 1964, ISBN 0-471-40065-3
  • John H. Lienhard IV and John H. Lienhard V, A Heat Transfer Textbook. Phlogiston Cambridge, 3rd edition, 2005
  • Atkins, Peter W .: Physical chemistry / A. Höpfner (transl.). 3., corr. Weinheim, Wiley-VCH, 2002, ISBN 3-527-30236-0
  • Dealy JM .: Structure and Rheology of Molten Polymers. Munich, Hanser Fachbuchverlag, 2006
  • Gabriel C .: Influence of the molecular structure on the viscoelastic behavior of polyethylene melts. Chair for Polymer Materials, Erlangen, Friedrich-Alexander University Erlangen-Nuremberg, 2001
  • Piel C, Stadler FJ, Kaschta J, Rulhoff S, Münstedt H, Kaminsky W: Structure-property relationships of linear and long-chain branched metallocene high-density polyethylenes and SEC-MALLS. Macromolecular Chemistry and Physics 207 (1), 26-38, 2006
  • Gehm, Lothar: RHEOLOGY - Practice-oriented basics and glossary. VINCENZ 1998, ISBN 3-87870-449-6
  • Schwarzl, FR .: Polymer mechanics. Heidelberg, Berlin, New York, Springer, 1993

Categories: Soft Matter | Substance property