Viscosity Newton's Theory Measurement Of Viscosity

When a shear stress is applied to a solid body, the body deforms until the deformation results in an opposing force to balance that applied, an equilibrium. However, when a shear stress is applied to a fluid, such as a wind blowing over the surface of the ocean, the fluid flows, and continues to flow while the stress is applied. When the stress is removed, in general, the flow decays due to internal dissipation of energy. The "thicker" the fluid, the greater its resistance to shear stress and the more rapid the decay of its flow.

In general, in any flow, layers move at different velocities and the fluid's "thickness" arises from the shear stress between the layers that ultimately opposes any applied force.

Here, the constant μ is known as the coefficient of viscosity, viscosity, or dynamic viscosity. Many fluids, such as water and most gases, satisfy Newton's criterion and are known as Newtonian fluids. Non-Newtonian fluids exhibit a more complicated relationship between shear stress and velocity gradient than simple linearity.

In many situations, we are concerned with the ratio of the viscous force to the inertial force, the latter characterised by the fluid density ρ. This ratio is characterised by the kinematic viscosity, defined as follows:

Viscosity is the principal means by which energy is dissipated in fluid motion, typically as heat.

2 Measurement of viscosity

Viscosity is measured with various types of viscometer, typically at 25°C ( standard state).

2.1 Units

2.1.1 Dynamic viscosity

The SI physical unit of dynamic viscosity is the Pascal-second ( Pa· s), which is identical to 1 N· s/ m² or 1 kg/ m· s). In France there have been some attempts to establish the poiseuille (Pl) as a name for the Pa· s but without international success. Care must be taken in not confusing the poiseuille with the poise!

The cgs physical unit for dynamic viscosity is the poise (P) named after Jean Louis Marie Poiseuille. It is more commonly expressed, particularly in ASTM standards, as centipoise (cP).

1 poise = 100 centipoise = 1 g/ cm· s = 0.1 Pa·s.

The unit is based on water having a viscosity of 1.0 cP (at 20°C).

2.1.2 Kinematic viscosity

The SI physical unit of kinematic viscosity is the ( m²/ s). The cgs physical unit for kinematic viscosity is the stokes (abbreviated S or St), named after George Gabriel Stokes . It is sometimes expressed in terms of centistokes (cS). US usage is the stoke.

1 stokes = 100 centistokes = 1 cm²/ s = 0.0001 m²/ s.

3 Molecular origins

It seems natural to see the origin of viscosity in terms of the attractive and repulsive forces between molecules. However, gases have substantial viscosity even though their inter-molecular forces are weak, suggesting some other mechanism.

3.1 Gases

Viscosity in gases arises principally from the molecular diffusion that transports momentum between layers of flow. The kinetic theory of gases allows accurate prediction of the behaviour of gaseous viscosity, in particular that, within the regime where the theory is applicable:

Viscosity is independent of pressure; and
Viscosity increases as temperature increases.

3.2 Liquids

In liquids, the additional forces between molecules become important. This leads to an additional contribution to the shear stress though the exact mechanics of this are still controversial. Thus, in liquids:

Viscosity is independent of pressure (except at very high pressure); and
Viscosity tends to fall as temperature increases.

The dynamic viscosities of liquids are typically several orders of magnitude higher than dynamic viscosities of gases.

4 Viscosity of some common materials

Some dynamic viscosities of Newtonian fluids are listed below:

Gases (at 0 ° C):

	viscosity (Pa·s)
hydrogen	8.4 × 10^-6
air	17.4 × 10^-6
xenon	21.2 × 10^-6

Liquids (at 20 ° C):

	viscosity (Pa·s)
ethyl alcohol	0.248 × 10^-3
acetone	0.326 × 10^-3
methanol	0.59 × 10^-3
benzene	0.64 × 10^-3
water	1.025 × 10^-3
nitrobenzol	2.0 × 10^-3
mercury	17.0 × 10^-3
sulfuric acid	30 × 10^-3
olive oil	81 × 10^-3
castor oil	0.985
glycerol	1.485
pitch	10⁷

Many fluids such as honey have a wide range of viscosities.

5 Can solids have a viscosity?

It is commonly asserted that amorphous solids, such as glass have viscosity, arguing on the basis that all solids flow, to some possibly minuscule extent, in response to shear stress. Advocates of such a view hold that the distinction between solids and liquids is unclear and that solids are simply liquids with a very high viscosity, typically greater than 10¹² Pa·s. This position is often adopted by supporters of the widely held urban myth that glass flow can be observed in old buildings.

However, others argue that solids are, in general, elastic for small stresses while fluids are not. Even if solids flow at higher stresses, they are characterized by their low-stress behavior. Viscosity may be an appropriate characteristic for solids in a plastic regime. The situation becomes somewhat confused as the term viscosity is sometimes used for solid materials, for example Maxwell materials, to describe the relationship between stress and the rate of change of strain, rather than rate of shear.

These distinctions may be largely resolved by considering the constitutive equations of the material in question, which take into account both its viscous and elastic behaviors. Materials for which both their viscosity and their elasticity are important in a particular range of deformation and deformation rate are called viscoelastic.

6 Eddy viscosity

In the study of turbulence in fluids, a common practical strategy for calculation is to ignore the small-scale vortices (or eddies) in the motion and to calculate a large-scale motion with an eddy viscosity that characterizes the transport and dissipation of energy in the smaller-scale flow. Typical values of eddy viscosity used in modeling ocean circulation are in excess of 10⁷ Pa·s.

7 Fluidity

The reciprocal of viscosity is fluidity, usually symbolised by φ (=1/μ), measured in reciprocal poise ( cm· s/ g), sometimes called the rhe. Fluidity is seldom used in engineering practice.

8 Etymology

The word "viscosity" derives from the Latin word "viscum" for mistletoe. From the mistletoe berries a viscous glue has been made and used for lime-twigs to catch birds.

9 Bibliography

Massey, B S (1983) Mechanics of Fluids, fifth edition, BooksEnthsiast.com

Download free Viscosity- und Rheology E-book in English and German:

Viscosity is also an out-of-print image and animation editing utility published by Sonic_Foundry|Sonic Foundry]. It can work with PNG, GIF, JPG/JPEG, BMP, AVI and its native VSC format.

<Hide>

Home > Viscosity

1 Newton's theory