The Rheology Handbook. Thomas Mezger

(no. 2). Only in this case, steady-state viscosity η = η( γ ̇ ) will be obtained. Until reaching this time point, the lower flow resistance of the – up to then only partially flowing – liquid will be detected. Up to then, measured are still the clearly lower values of the still time-dependent, transient viscosity η+ = η( γ ̇ , t). Considering the entire shear gap in this period of time, the shear gradient still will be not constant and therefore, the shear process will be still inhomogeneously.

      Example 1: Useful measuring point duration to avoid transient effects

      According to the rule of thumb (see above): When presetting γ ̇ = 0.1 s-1, the measuring point duration should be set to t ≥ 10 s; and when γ ̇ = 0.01 s-1, then t ≥ 100 s. These values should only be taken as a rough guide for a first try: Sometimes a longer duration is necessary and in some few cases a shorter duration is already sufficient.

      Example 2: Suggestions for test profile presets, with γ ̇ (t) as a ramp function

      1) Linear preset

      Preset: γ ̇ = 0 to 1000 s-1 with 20 measuring points in a period of t = 120 s for the total test interval. The shear rates are increased in steps showing always the same distance between their values when presenting the curves on a linear scale (they are therefore equidistant; see Figure 3.1). In this case, each one of the measuring points is generated by the rheometer in the same period of time. In this example, the test program results in a duration of t = 6 s for each single measuring point.

      2) Logarithmic preset

      Preset: γ ̇ = 0.01 to 1000 s-1 with 25 measuring points. The shear rates are increased in logarithmic steps, now showing the same distance in between neighboring points, but of course, only when using a logarithmic scale. Here, a variable logarithmic measuring point duration should be preset, for example, beginning with t = 100 s and ending with t = 5 s. Therefore, when using this method, longer measuring point durations are occurring at lower shear rates, and shorter durations at the higher ones. As a consequence, for each single measuring point in the low-shear range the transient effects of the sample will be either reduced to a minimum or they have already completely decayed at the end of the prolonged duration of each measuring point.

      For “Mr. and Ms. Cleverly“

       Figure 3.5: Viscosity functions of a dispersion, occurrence of time-dependent effects in the low-shear range such as the “transient viscosity peak”, when presetting too short measuring point duration: (1) clearly too short; (2) better, but still too short; (3) sufficiently long

      Example 3: Occurrence of a “transient viscosity peak” when presetting a too short measuring point duration in the low-shear range (e. g. when testing dispersions and gels)

      Figure 3.5 presents three viscosity functions of the same dispersion all curves are measured in the range between γ ̇ = 0.01 and 100 s-1.

      Preset for the duration of each individual measuring point:

      Test 1: t = 10 s = const (i. e., with the same time for each one of the measuring points),

      Test 2: t = 60 to 5 s (i. e., with variable time, decreasing towards higher shear rates),

      Test 3: t = 120 to 5 s (similar to Test 2, but beginning with a longer time)

      Results: Dispersions and gels when showing stability at rest, thus, a gel-like viscoelastic structure, usually display a constantly falling η-curve from low to high shear rates, at least in the low-shear range (i. e. at γ ̇ < 1 s-1). This behavior is indicated by the curve of Test 3. In contrast, the η-curves of Tests 1 and 2 are showing “transient viscosity peaks”, since here, still time-dependent effects are measured. The shorter the selected measuring point duration in the low-shear range, the lower are the η-values determined in this range, and the higher are the shear rate values at the occurrence of the peaks.

      Summary: When testing dispersions and gels

      The longer the measuring point duration in the low-shear range, the greater is the chance to avoid transient effects.

      Note: Uncrosslinked polymers in the form of solutions and melts usually show a constant

      η-value in the low-shear range, which is the plateau value of the zero-shear viscosity η0 (see Chapter 3.3.2.1a, Figure 3.10). However, also here a “transient viscosity peak” might appear when presetting too short measuring point durations in this shear rate range.

      End of the Cleverly section

       Figure 3.6: Flow curve of a shear-thinning liquid

       Figure 3.7: Viscosity curve of a shear-thinning liquid

3.3.2Shear-thinning flow behavior

      Viscosity of a shear-thinning material depends on the degree of the shear load (shear rate or shear stress, respectively). The flow curve shows a decreasing curve slope (see Figure 3.6), i. e., viscosity decreases with increasing load (see Figure 3.7).

      Examples of shear-thinning materials

      Polymer solutions, polymer melts, organic binders (e. g. methylcellulose), many coatings (e. g. primers, without inorganic gellants), glues, many shampoos

      The terms shear-thinning and pseudoplastic are identical in their meaning (see also Chapter 14.3: 1925, with the concepts of Eugen C. Bingham [3.4], Wolfgang Ostwald jun. [3.2] [3.3] – the latter used the German term “strukturviskos” – and others on this subject [3.5]). However, pseudoplastic contains the word plastic, a behavior which cannot be exactly determined in a scientific sense since it is the result of inhomogeneous deformation and flow behavior (see also Chapter 3.3.4.2c and Figure 2.9: no. 4). This is the reason why the use of the term “pseudoplastic” is diminishing more and more in current literature.

      Note: Apparent shear viscosity

      Often the term “apparent viscosity” is used with different meanings about the measured viscosity values. Therefore, actually this term should be avoided as it is superfluous [3.33] [3.78].

      Meaning 1: Related to rheology it means that a sample does not show ideal-viscous flow behavior. If the ratio of shear stress to shear rate varies with the shear load, the corresponding values are often called the “apparent shear viscosity” at the corresponding shear rate, to illustrate that these kinds of values are different from constant viscosity values of ideal-viscous fluids (according to ASTM D4092). Each one of these viscosity values obtained represents a single point of the viscosity function only. Therefore, these viscosity values can only be evaluated in the appropriate form if information is also given about the shear conditions. Examples for accurate specifications are as follows:

      η( γ ̇ = 100 s-1) = 345 mPas, or η(τ = 500 Pa) = 12.5 Pas

      Meaning