The Rheology Handbook. Thomas Mezger

/ +50 / +60 / + 70 / +80 / +90 / +100 °C1.79 / 1.31 / 1.00 / 0.798 / 0.653 / 0.547 / 0.467 / 0.404 / 0.354 / 0.315 / 0.282mercury1.55blood plasma at +20 / +37 °C1.7 / 1.2wine, fruit juices (undiluted)2 to 5milk, coffee cream2 to 10blood (from a healthy body) at +20 / +37 °C5 to 120 / 4 to 15 (at γ ̇ = 0.01 to 1000 s-1)light oils10glycol20sulphuric acid25sugar solutions (60 %)57motor oilsSAE 10W-30, at +23 / +50 / +100 °C50 to 1000175 / 52 / 20olive oilsapprox. 100gear oils300 to 800glycerine1480honey, concentrated syrupsapprox. 10 Paspolymer melts (at processing conditions, e. g. between T = +150 and +300 °C, and at γ ̇ = 10 to 1000 s-1)10 to 10,000 Paspolymer melts: zero-shear viscosity at γ ̇ ≤ 0.1 s-1 and at T = +150 to +300 °C1 kPas to 1 MPassilicone (PDMS, uncrosslinked, zero-shear viscosity)10 to 100 kPashotmelts (maximum processing viscosity for melt extruders)100 kPasbitumen (example): at T = +80 / +60 / +40 / +20 °C and at T = 0 °C200 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

      b) Kinematic viscosity

      Definition of the kinematic viscosity:

      Equation 2.10

      ν = η/ρ

      ν (ny, pronounced: nu or new), with the density ρ [kg/m3], (rho, pronounced: ro).

      For the unit of density holds: 1 g/cm3 = 1000 kg/m3

      The unit of kinematic viscosity is [mm2/s]; and: 1 mm2/s = 10-6 m2/s

      A previously used unit was [St] (stokes); with: 1 St = 100 cSt. This unit was named in honor to the mathematician and physicist George G. Stokes (1819 to 1903) [2.12].

      The following holds: 1 cSt (centistokes) = 1 mm2/s.

      Example

      Conversion of the values of kinematic viscosity and shear viscosity

      Preset: A liquid shows ν = 60 mm2/s = 60 ⋅ 10-6 m2/s, and ρ = 1.1 g/cm3 = 1100 kg/m3

      Calculation: η = ν ⋅ ρ = 60 ⋅ 10-6 ⋅ 1100 (m2/s) ⋅ (kg/m3) = 66 ⋅ 10-3 kg/(s ⋅ m) = 66 mPas

      Usually, kinematic viscosity values are measured by use of flow cups, capillary viscometers, falling-­ball viscometers or Stabinger viscometers (see Chapters 11.3 to 11.6).

2.3Shear load-dependent flow behavior

       Figure 2.4: Double-tube test

      Experiment 2: The double-tube test, or the contest of the two fluids (see Figure 2.4)

      In the beginning, fluid F1 is flowing faster than fluid F2. With decreasing fluid level, F1 shows reduced flow velocity. F2, however, continues to flow with a hardly visible change in velocity. Therefore finally, F2 empties its tube before F1 does. F1, a wallpaper paste, is an aqueous methylcellulose solution, and F2 is a mineral oil. Flow behavior of polymer solutions such as the wall paper paste is explained in Chapter 3.3.2.1: shear-thinning flow behavior.

2.3.1Ideal-viscous flow behavior

      a) Viscosity law

      Formally, ideal-viscous flow behavior is described by the viscosity law:

      Equation 2.11

      τ = η ⋅ γ ̇

      Isaac Newton (1643 to 1727) wrote in 1687 in his textbook Principia [2.18] in a quite inaccurate form about the flow resistance of liquids (“defectus lubricitatus”; see also Chapter 14.1: 1687). Therefore, and especially in English spoken countries, ideal-viscous flow behavior often is also called Newtonian flow behavior. In rheology, both terms have the same meaning. Based on later research on fluid dynamics by D. Bernoulli (in 1738, Hydrodynamica [2.19]), L. Euler (in 1739/1773, Scientia Navalis, and Construction des vaisseaux [2.20]), Joh. Bernoulli (in 1740, Hydraulica [2.21]), and C. L. M. H. Navier (in 1823 [2.22]), finally G. G. Stokes (in 1845 [2.12]) stated the modern form of what was called later Newton’s viscosity law. Therefore sometimes, the viscosity law is also termed the “Newton/Stokes law” [2.23].

      Examples of ideal-viscous materials

      Low-molecular liquids (and this means here: with a molar mass below 10,000 g/mol) such as water, solvents, mineral oils (without polymer additives), silicone oils, viscosity standard fluids (of course!), blood plasma; but also pure and clean bitumen (without associative superstructures, and at a sufficiently high temperature).

      Flow behavior is illustrated graphically by flow curves (previously sometimes also called rheograms) and viscosity curves. Flow curves are showing the interdependence of shear stress τ and shear rate γ ̇ . Usually, γ ̇ is presented on the x-axis (abscissa), and τ on the y-axis (ordinate). However, τ might also be displayed on the x-axis and γ ̇ on the y-axis, but this is meanwhile rarely used in industrial laboratories.

      Viscosity curves are derived from flow curves. Usually, η is presented on the y-axis and γ ̇ on the x-axis. Alternatively, the function η(τ) can be shown with η on the y-axis and τ on the x-axis, however, this is less frequently carried out in industrial labs.

      Generally, the slope value of each point (x; y) of a curve can be calculated as: y/x. This counts for each point of a flow curve with the pair of values ( γ ̇ ; τ). The result of this calculation again corresponds to the viscosity value, this is because: η = τ/ γ ̇ . Therefore, the η( γ ̇ )-curve can be calculated point by point from the τ( γ ̇ )-curve. Correspondingly, a steeper slope of the flow curve results in a higher level of the viscosity curve (see Figures 2.5 and 2.6). Usually today, this calculation is performed by a software program.