The Rheology Handbook. Thomas Mezger

      Δη = ηmax – ηmin

      Note 3: Alternative analysis methods (to method M1) from industrial practice

      Some users in industrial laboratories evaluate thixotropic behavior by the following simple methods to carry out quality control of coatings.

      Preset: Test, consisting of two measuring intervals: at first high-shear (HS), and then low-shear (LS) to enable structural regeneration of the sample. Analysis:

      N3-a) The thixotropy index :

      TI = (ηL – ηH) / tR

      with ηH in mPas at the end of the HS interval; and ηL in mPas at the regeneration time tR after the beginning of the LS interval (Examples: tR = 60 s; or 30 or 90 or 300 s)

      Calculation: Viscosity change in a previously defined time in the LS interval, in the form of the slope (Δη/Δt) of the η(t)-curve, with the unit (mPas/s). A straight line is therefore adapted between the last measuring point of the HS interval and the measuring point at time point tR in the subsequent LS interval. Evaluation: The faster the regeneration and the higher the corresponding

      η-value obtained, the higher is the TI value. Example: with ηH = 100 mPas and ηL = 1000 mPas after tR = 60 s, then: TI = (900 mPas/60 s) = 15 mPas/s.

      N3-b) The structure recovery index :

      SRI = lg ηL – lg ηH

      with ηH, ηL and tR as above. Calculation: Viscosity difference in the form of logarithmic viscosity values. Evaluation: The stronger the obtained regeneration, the higher the SRI value. Example: with ηH = 100 mPas and ηL = 1000 mPas (e. g. after tR = 30 s), then: SRI = (lg ηL – lg ηH) = 3 – 2 = 1. Usually here, specifications are given without any unit.

      N3-c) The viscosity ratio during structural regeneration: VR(SR) = η1 (τ1) / η2 (τ2)

      VR is a measure of the speed of structural recovery in the third test interval at a constantly low shear rate, with the viscosity values at the two time points t1 and later, at t2. As long as VR < 1, there is still a tendency for a continued structural recovery, and for VR = 1, the latter is finished.

      3.4.2.2.4Example

      for η1 = 100 mPas after t1 = 10 s, and η2 = 300 mPas after t1 = 60 s, results:

      VR = 100/300 = 0.333

      M2) The total thixotropy time

      The total thixotropy time is determined as the time difference between t2 at the end of the second interval indicating structural decomposition in terms of ηmin, and the time point in the third test interval when reaching the maximum value ηmax after structural regeneration. Thus, the total thixotropy time is the period of time required for the complete (100 %) regeneration, i. e. when reaching again the reference value of the viscosity-at-rest which was determined in the first test interval. Of course, this period of time might be shorter than (t3 – t2) if regeneration is finished already before time point t3 is reached.

      M3) The relative thixotropy time required to reach a certain percentage of regeneration

      For QC tests, analysis of the total thixotropy time according to method M2 may take a too long time. Therefore, then in the third test interval, the relative thixotropy time is determined as the period of time for the η-value to reach the relative value of, for example, 75 or 90 % compared to the reference value obtained in the first interval (which counts as the “100 % η-value” here).

      3.4.2.2.5Example (to method M3): Testing PVC plastisol pastes

      Evaluation of plastisols as used in automotive industry as underseals or seam sealants. Requirement: After the application of the plastisol, the conveyor line transporting the car should not be set in motion before the structural strength of the plastisol has regenerated to 75 % of the reference value at rest. Otherwise vibrations might cause sagging or even dripping of the coatings in an uncontrollable way. Previously performed laboratory tests resulted in a viscosity reference value η(100 %) = 2000 mPas at time point t1 (see Figure 3.41).

      Determination: Which period of time is required after time point t2 to reach 75 % of the reference viscosity value, thus here, η(75 %) = 1500 mPas?

      M4) The percentage of regeneration within a previously defined time period

      The percentage of regeneration taking place in the third interval is determined at certain time points which have been defined before the test by the user (e. g. after t = 30 and 60 s). The η-values are read off at these time points and the percentage is calculated in relation to the reference value of the first interval which counts as the 100 % value then.

      3.4.2.2.6Example (to method M4): Comparison of two coatings

      Different behavior of two coatings in the regeneration phase is illustrated by Table 3.3.

      Analysis: Coating 1 shows complete regeneration within 120 s already (related to the viscosity value). This may facilitate to obtain the required wet layer thickness. Here, with 87 % structural recovery attained after 30 s the final structural strength has almost been reached already. Coating 2 displays a slower structural regeneration, showing a long lasting and therefore good leveling behavior. However, this coating may show a certain tendency to sagging on vertical areas, which may prevent to achieve the desired layer thickness.

      For more information on tests to evaluate thixotropic behavior, see Chapter 8.5.2.2 (using oscillatory tests). Corresponding analysis can be performed in an adapted form for rheopexy and rheopectic behavior. However, this behavior is hardly occurring in industrial practice (see also the Note in Chapter 3.4.2.1c: shear-induced increase in viscosity).

Table 3.3: Regeneration of two coatings in terms of η(t) and in % (after a high-shear interval)
	Coating 1		Coating 2
	η [Pas]	Reg. [%]	η [Pas]	Reg. [%]
at the end of the first interval, at low-shear conditions; the reference value of the viscosity-at-rest	15	100	30	100
at the end of the second interval, at high-shear conditions	0.5	(3)	1.0	(3)
regeneration in the third intervalafter t = 30 safter t = 60 safter t = 120 s	131415	8793100	41015	133350

       Figure 3.42: Preset of a time-dependent shear rate profile consisting of three test intervals: upward ramp, high-shear phase, and downward ramp

      3.4.2.2.7b) Flow curves and hysteresis area (for evaluating thixotropic behavior)

      This testing and analysis method for determining thixotropic and rheopectic behavior is now outdated (DIN 53214 of 1982, meanwhile withdrawn). Nevertheless, it is still used in many industrial laboratories to carry out simple QC tests.

      Preset

      1 With controlled shear rate (CSR): profile γ ̇ (t), see Figure 3.42

      2 With controlled shear stress (CSS): profile τ(t), similar to Figure 3.42

      3.4.2.2.8Example 1: Preset of the shear rate

      1st interval (shear rate ramp upwards, in t = 120 s): with γ ̇ = 0 to 1000 s-1

      2nd interval (high-shear phase, for t = 60 s): at γ ̇ = 1000 s-1 = const

      3rd interval (shear rate ramp downwards, in t = 120 s): with γ ̇ = 1000 to 0 s -1

      Therefore here, the total test duration is t = 300 s.

       Figure 3.43: Flow curves obtained when controlling