The Rheology Handbook. Thomas Mezger

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СКАЧАТЬ on the other hand increasing viscosity values (named negative hysteresis). [3.86]

      3.4.2.2.11c) Very simple evaluation methods (for evaluating thixotropic behavior)

      1) Time-dependent viscosity ratio or “thixotropy index” (using a single test interval only)

      Some users evaluate thixotropic behavior by the following simple testing and analysis method: with a single test interval, presetting a constant medium or high rotational speed n = const (or shear rate). Afterwards the thixotropy index (TI) is calculated as follows

      TI = η1(t1) / η2(t2)

      with the time points t1 and t2 [s], (e. g., t1 = 30 s, and t2 = 600 s). For flow behavior independent of time TI = 1, for time-dependent shear-thinning TI > 1, and for time-dependent shear-thickening TI < 1.

      Comment: Here, the term thixotropy index is misleading since this ratio quantifies time-dependent structural decomposition of a material only. Thixotropic behavior, however, can only be quantified if – directly after the break of a material’s superstructure – also the subsequent time-dependent structural recovery under low-shear condition is evaluated (to TI, see also Note 3 in Chapter 3.4.2.2a, and Note 2 in Chapter 3.3.2). Therefore, instead of TI, this ratio should better be called time-dependent viscosity ratio under a constant shear load, or similar.

      2) Bingham build-up (BBU) and rate of build-up (RBU) after a 20-minute gelation test consisting of two test intervals: first high, then low shear load [3.7].

      Some users perform the following simple test and analysis method consisting of two intervals. In the first part, preset is a constantly high rotational speed nH [min-1] for a period of t10 = 10 min, and in the second part a constantly low speed nL for another 10min = t20 (e. g. for ceramic suspensions, with nL = nH /10, for example, at nH = 100 min-1 and at nL = 10 min-1). Please be aware that these η-values are relative viscosity values if the test is performed using a spindle (which is a relative measuring system; see also Chapter 10.6.2). Here, instead of the shear stress often is used dial reading DR (which is the relative torque value Mrel in %), and the viscosity values are calculated then simply as η = DR/n (with the rotational speed n in min-1). Usually here, all units are ignored.

      Bingham build-up (BBU) indicates the change of the relative viscosity values between the end of the second, low-shear interval and the first, high-shear interval.

      Calculation: BBU = ηL (nL, t20) – ηH (nH, t10) = (DRL/nL) – (DRH/nH).

      Example: with nH = 100, nL = 10, DRH = 50, DRL = 40,

      then: BBU = (40/10) – (50/100) = 4 – 0.5 = 3.5

      Rate of build-up (RBU) is the partial change over the first two minutes in the second, low-shear interval related to the total change over the full ten minutes in this interval.

      Calculation: RBU = [η(nL, t12) – η(nH, t10)] / [η(nL, t20) – η(nH, t10)]

      = [(DRL, 12/nL) – (DRH/nH)] / [(DRL/nL) – (DRH/nH)]

      with time point t12 after 12 minutes (or after two minutes in the second interval, resp.)

      Example: with nH, nL, DRH and DRL as above, and DRL, 12 = 30, then:

      RBU = [(30/10) – (50/100)] / [(40/10) – (50/100)] = (3 – 0.5) / (4 – 0.5) = 2.5/3.5

      Thus: RBU = 0.71 = 71 %

      Comment: Using this simple method, usually a too high rotational speed is applied in the low-shear phase to enable regeneration conditions which are related to practice. At these conditions, which are not really simulating low-shear conditions or even the state-at-rest, any regeneration – if at all – is merely possible to a partial, very limited degree.

3.4.3Time-dependent flow behavior of samples

      showing hardening

      Rheological tests are physical tests and usually it is assumed that the chemical structure of the sample does not change during the measurement. However, if it is aimed to determine time-

      dependent flow behavior during a hardening process, e. g. during a chemical curing reaction, then both: shear conditions and measuring temperature should be kept constant (thus testing takes place at isothermal conditions). The shear load should be sufficiently low to ensure an undisturbed hardening or curing process; for example, at a shear rate of γ ̇ = 1 s-1.

      3.1.2.1.1a) Gelation time and gel time, gel point and gelation point

      An η(t)-diagram of a time-dependent hardening material usually shows a course of the viscosity curve as displayed in Figure 3.45. Here, two time points are relevant:

      1 time point tS as start time at the onset of gelation or curing reaction

      2 time point tV when reaching the previously defined viscosity value

      The terms gel time, gelation time, hardening time often are used as synonyms. Examples of measuring curves showing gelation of modified starch are displayed in [3.70]

       Figure 3.45: Time-dependent viscosity function of a sample showing gelation or curing: The

      gelation or curing reaction starts at time point tS and the previously defined viscosity value is reached at time point tV

      3.1.2.1.2Example 1: Testing epoxy resins

      1 Time point at the viscosity minimum (if it occurs): after t = 90 s (e. g. showing ηmin = 60 Pas then)

      2 Gel time (when reaching the pre-defined value of η = 100 Pas): after t = 200 s

      3.1.2.1.3Example 2: The isothermal viscosity development of reactive resin mixtures

      (acc. to DIN 16945)

      After mixing the components for 10 minutes, gelation time is determined as the period required to reach a previously defined upper limiting value of the viscosity (termed η2). The following values are specified for three different consistencies (with η1 as the viscosity directly after mixing):

      1 for η1 ≤ 250 mPas,then:η2 =1500 mPas

      2 for 250 mPas < η1 ≤ 1000 mPas,then:η2 =7500 mPas

      3 for η1 > 1000 mPas,then:η2 =15,000 mPas

      Comparsion: In ISO 2535 is stated for testing unsaturated polyester resins using a rotating bar: The gelation time is reached at the upper limiting viscosity value of 50 Pas.

      3.1.2.1.4Example 3: The gelation time of reaction resins, when reaching the thousandfold viscosity value

      The gelation time tgel is reached if ηgel = 1000 СКАЧАТЬ