The Rheology Handbook. Thomas Mezger

rates (at γ ̇ > 1000 s-1) the shear-thinning effect is limited. Thus, the viscosity values are changing only comparatively little also in the sheared state. As the viscosity here is not very dependent on the shear rate, therefore showing only moderate shear-thinning flow behavior, some users talk about “quasi-Newtonian behavior”. Even when this term is not scientific, sometimes for practical users it is useful to a certain degree. Associative thickener molecules with a comparatively higher proportion of hydrophobic groups are causing a more pronounced shear-thinning effect, whereas associative thickener molecules with a comparatively higher hydrophilic proportion are leading to more ideal-viscous (Newtonian) flow behavior.

      The great advantage can be found in both: On the one hand, in the range of low shear rates the viscosity values are not too high but are usually sufficient as required for sedimentation stability. On the other hand, in the range of high shear rates the viscosity values are usually significantly higher compared to the other two thickener types mentioned above (clay and dissolved polymers). This may help, for example, to prevent spattering when performing fast application processes.

      End of the Cleverly section

3.4Time-dependent flow behavior and

      viscosity function

      This section informs about time-dependent flow behavior. These tests are performed at constant test conditions for each test interval, since here, as well the degree of the shear load as well as the measuring temperature are kept at a constant value.

3.4.1Test description

      3.1.2.1.1Preset

      1 With controlled shear rate (CSR): constant shear rate γ ̇ = const. (see Figure 3.34)

      2 With controlled shear stress (CSS): constant shear stress τ = const. (similar to Figure 3.34)

      3.1.2.1.2Measuring result

      1 Time-dependent shear stress: τ(t), see Figure 3.35

      2 Time-dependent shear rate: γ ̇ (t), see Figure 3.36

      Further results: Time-dependent viscosity η(t), see Figure 3.37

      The shapes of the curves of τ(t) and η(t) are similar because τ and η are proportional since τ = η ⋅ γ ̇ , here with γ ̇ = const. However, the curves of γ ̇ (t) and η(t) are inversely, because γ ̇ and η are inversely proportional since η = τ/ γ ̇ here with τ = const.

       Figure 3.34: Preset of a constant shear rate

       Figure 3.35: Time-dependent shear stress curves:

      (1) with no change in viscosity with time

      (e. g. viscosity reference fluids, standard oils)

      (2) decreasing viscosity with time (e. g. emulsion paints, ketchups, yogurts)

      (3) increase in viscosity with time (e. g. hardening process of adhesives, gel formation)

       Figure 3.36: Time-dependent shear rate curves: for (1) to (3) see text of Figure 3.35

       Figure 3.37: Time-dependent viscosity curves: for (1) to (3) see text of Figure 3.35

3.4.2Time-dependent flow behavior of samples

      showing no hardening

      When presetting low shear rates or shear stresses, the duration for each individual measuring point must be long enough. Otherwise particularly with highly viscous and viscoelastic samples, time-dependent start-up effects or transient effects are obtained. In this case, the measured curve approaches the final value of τ or η from below (see also Chapters 3.3.1b and Note 1 in and 3.4.2.2a). When applying high shear rates, viscous shear-heating may occur to a higher extend and then, the time-dependent viscosity values may decrease additionally due to thermal effects. In this case, with low-viscosity liquids also turbulent flow effects must be taken into account (see also Chapter 3.3.3).

      Extended test profiles (including intervals at rest, for temperature equilibration, and pre-shearing)

      Sometimes, test programs are used showing several intervals with preset of a constant shear rate in each; for example:

      1 Rest intervals, presetting constantly γ ̇ = 0, either at the start of the test to enable relaxation of the sample after gap setting of the measuring system which may cause high internal stresses particularly when testing highly viscous and viscoelastic samples. Simultaneously, this period is suited to enable temperature equilibration, or after a pre-shear interval.

      2 Pre-shear intervals , presetting a constant low shear rate, to ensure a defined sample preparation, to distribute the sample in the shear gap homogeneously, and to equalize or to reduce pre-stresses deriving from diverse sample preparation steps.

      3.1.2.1.1Example: Testing lubricating grease (according to DIN 51810-1)

      Recommendations: measuring temperature of T = +25 °C, use of a CP 25-1 measuring geometry (cone-and-plate, diameter of 25 mm, and cone angle of 1°)

      Test program consisting of five intervals

       1 st interval: rest phase (for t = 1 min): at γ ̇ = 0

       2 nd interval: pre-shear phase (for t = 1 min): at γ ̇ = 100 s-1 = const

       3 rd interval: rest phase (for t = 2 min): at γ ̇ = 0

       4 th interval: shear rate ramp upwards (in t = 1 min): with γ ̇ = 0 to γ ̇ max

       with γ ̇ max = 1000 s-1 for greases exhibiting soft consistency (showing NLGI classes 000 to 1; NLGI is the National Lubrication Grease Institute in the USA),

       and with γ ̇ max = 500 s-1 for greases exhibiting rigid consistency (i. e., NLGI class 2),

       5 th interval: high-shear phase (for t = 5min): at γ ̇ = γ ̇ max = const

      Analysis: With the viscosity values η1 at the beginning and η2 at the end of the fifth interval, the “relative viscosity change” is calculated as follows:

      ηrel = (η1 - η2) ⋅ 100/η1 (specification of ηrel in [%])

       3.4.2.1Structural decomposition and regeneration

      (thixotropy and rheopexy)

      3.4.2.1.1a) Thixotropic behavior

      3.4.2.1.2Experiment 3.4: Shaking bottles containing ketchup and paraffin oil

      1 When shaking continuously, the ketchup is becoming thinner and thinner. During the subsequent period of rest, it is thickening more and more and after approximately 10 minutes it has returned to its original gel-like consistency.

      2 The paraffin oil is solid when at rest, but immediately turns to a liquid state when shaken. It takes approximately eight hours until the oil has reached its initially solid state again.

      The term thixotropy is a combination of Greek words and is not that easy to translate: Thixis means touching, in the sense of deranging when bringing in motion (e.