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For ideal-viscous fluids measured at a constant temperature, the value of the ratio of shear stress τ and corresponding shear rate γ ̇ is a material constant. Definition of the shear viscosity, in most cases just called “viscosity“:

Equation 2.8

η = τ/ γ ̇

η (eta, pronounced: etah or atah), the unit of the shear viscosity is [Pas], (pascal-seconds).

The following holds: 1Pas = 1N ⋅ s/m2 = 1 kg/s ⋅ m

For low-viscosity liquids, the following unit is usually used:

1 mPas (milli-pascal-seconds) = 10-3 Pas

Sometimes, for highly viscous samples the following units are used:

1 kPas (kilo-pascal-seconds) = 1000 Pas = 103 Pas, or even

1 MPas (mega-pascal-seconds) = 1000 kPas = 1,000,000 Pas = 106 Pas

A previously used unit was [P], (“poise”; at best pronounced in French); and: 1 P = 100 cP; however, this is not an SI unit [2.15]. This unit was named in honor to the doctor and physicist Jean L. M. Poiseuille (1799 to 1869) [2.7].

The following holds: 1 cP (centi-poise) = 1 mPas, and 1 P = 0.1 Pas = 100 mPas

Sometimes, the term dynamic viscosity is used for η (as in DIN 1342-1). However, some people use the same term to describe either the complex viscosity determined by oscillatory tests, or to mean just the real part of the complex viscosity (the two terms are explained in Chapter 8.2.4b). To avoid confusion and in agreement with the majority of current international authors, here, the terms viscosity or shear viscosity will be used for η. Table 2.3 lists viscosity values of various materials.

The inverse value of viscosity is referred to as fluidity Φ (phi, pronounced: fee or fi) [2.17]. However today, this parameter is rarely used. The following holds:

Equation 2.9

Φ = 1/η with the unit [1/Pas] = [Pas-1]

Table 2.3: Viscosity values, at T = +20 °C when without further specification; own data and from [2.2] [2.3] [2.16]
Material	Viscosity η [mPas]
gases/air	0.01 to 0.02 / 0.018
pentane/acetone/gasoline, petrol (octane)/ethanol	0.230 / 0.316 / 0.538 / 1.20
water at 0 / +10 / +20 / +30 / +40 / +50 / +60 / + 70 / +80 / +90 / +100 °C	1.79 / 1.31 / 1.00 / 0.798 / 0.653 / 0.547 / 0.467 / 0.404 / 0.354 / 0.315 / 0.282
mercury	1.55
blood plasma at +20 / +37 °C	1.7 / 1.2
wine, fruit juices (undiluted)	2 to 5
milk, coffee cream	2 to 10
blood (from a healthy body) at +20 / +37 °C	5 to 120 / 4 to 15 (at γ ̇ = 0.01 to 1000 s-1)
light oils	10
glycol	20
sulphuric acid	25
sugar solutions (60 %)	57
motor oilsSAE 10W-30, at +23 / +50 / +100 °C	50 to 1000175 / 52 / 20
olive oils	approx. 100
gear oils	300 to 800
glycerine	1480
honey, concentrated syrups	approx. 10 Pas
polymer melts (at processing conditions, e. g. between T = +150 and +300 °C, and at γ ̇ = 10 to 1000 s-1)	10 to 10,000 Pas
polymer melts: zero-shear viscosity at γ ̇ ≤ 0.1 s-1 and at T = +150 to +300 °C	1 kPas to 1 MPas
silicone (PDMS, uncrosslinked, zero-shear viscosity)	10 to 100 kPas
hotmelts (maximum processing viscosity for melt extruders)	100 kPas
bitumen (example): at T = +80 / +60 / +40 / +20 °C and at T = 0 °C	200 Pas / 1 kPas / 20 kPas / 0.5 MPas and 1 MPas, i. e., then almost like a viscoelastic solid

For “Mr. and Ms. Cleverly”

Note 1: Usually, samples with high viscosity values are viscoelastic

Many rheological investigations showed that at values of η > 10 kPas, the elastic portion should no longer be ignored. These kinds of samples should no longer be considered simply viscous only, but visco-elastic (see also Chapter 5).

Note 2: Shear viscosity η and extensional viscosity ηE

For ideal-viscous fluids under uniaxial tension the following applies for the values of the extensional viscosity (in Pas) and shear viscosity η (also in Pas): ηE( ε ̇ ) = 3 ⋅ η( γ ̇ ), if the values of the extensional strain rate ε ̇ [s-1] and shear rate γ ̇ [s-1] are equal in size (see also Chapter 10.8.4.1: Trouton relation).

End of the Cleverly section