The Rheology Handbook. Thomas Mezger

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СКАЧАТЬ i. e. η+ = η( γ ̇ , t). In this case, the period of time was too short for the sample to adapt evenly throughout the entire shear gap to the applied low-shear conditions. Action: The measuring point duration should be extended. As a rule of thumb: The measuring point duration should be at least as long as the value of the reciprocal shear rate (1/ γ ̇ ). After a first trial with this preset, the measuring point duration may have to be extended further until good test conditions are achieved. Sometimes, however, even shorter times as t = 1/ γ ̇ are sufficient (see also the Note in Chapter 3.3.1b and Figure 2.9, no. 5: transient behavior).

      Note 2: Which mode of testing is more useful – shear rate or shear stress control?

      If the instrument is able to control very rapid changes in shear rates, then controlled shear rate (CSR) tests are often preferable to controlled shear stress (CSS) tests. The reason is that the process of structural decomposition and regeneration is directly dependent on the degree of the shear rate or deformation, respectively. Shear stress in fact is causing this deformation, but it is the deformation itself leading to the change in the structural strength. This is correct since the visco­sity value is only changing if the acting shear force indeed produces a sufficiently high deformation. As a result of this interrelation, in most cases, measuring results obtained from CSR tests are more reproducible.

      Optional methods to analyze structural regeneration

      A number of options to analyze thixotropic behavior are given below, many users prefer evaluation according to method M4.

      M1) The thixotropy value as difference between the minimum and maximum values of viscosity

      The extent of thixotropic behavior is determined in terms of the viscosity change Δη, which is the difference between the maximum viscosity after structural regeneration and the minimum visco­sity after structural decomposition. With ηmin at the time point t2 and ηmax at the time point t3 the following holds (see Figure 3.41):

      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.

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