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1) Speed-dependent viscosity ratio (VR) and shear-thinning index

Some users still perform the following simple test and analysis method which consists of two intervals. In the first part a constantly low rotational speed n1 [min-1] is preset, and in the second part a constantly high speed n2 (usually with n2 = 10 ⋅ n1, for example, at n1 = 3 min-1 and n2 = 30 min-1). Afterwards the “viscosity ratio” (VR) is calculated as follows [3.6]:

VR = η1(n1)/η2(n2).

Sometimes this ratio is called the shear-thinning index (ASTM D2196). For ideal-viscous (Newtonian) flow behavior VR =1, for shear-thinning VR > 1, and for shear-thickening VR < 1.

Example: with η1 = 250 mPas at n1 = 3 min-1, and η2 = 100 mPas at n2 = 30 min-1, results:

VR = 250/100 = 2.5

In order to avoid confusion, this ratio should better be called “speed-dependent (or shear rate-

dependent) viscosity ratio”. Sometimes in out-of-date literature, this speed-dependent ratio is named thixotropy index, TI (ASTM D2556: as thixotropic index). But this term is misleading, since VR quantifies non-Newtonian behavior independent of time, but not thixotropic behavior which is a time-dependent effect. For TI, see also Note 3 in Chapter 3.4.2.2a, and Chapter 3.4.2.2c.

2) Pseudoplastic index (PPI)

Some users still use the following simple test and analysis method consisting of two intervals, presetting in the first part 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 10 min until reaching time point t20 = 20 min (e. g. when testing ceramic suspensions, with nL = nH/10, for example, at nH = 100 min-1 and nL = 10 min-1). Afterwards the pseudoplastic index (PPI) is calculated as follows [3.7]:

PPI = [lg ηL(nL, t20) – lg ηH(nH, t10)] / (lg nL – lg nH)

For ideal-viscous (Newtonian) flow behavior PPI = 0, for shear-thinning (pseudoplastic) PPI < 0, and for shear-thickening (dilatant) PPI > 0.

Example: with ηH = 0.3 Pas at nH = 100 min-1, and ηL = 1.2 Pas at nL = 10 min-1, then:

PPI = (lg 1.2 – lg 0.3) / (lg 10 – lg 100) = [0.0792 – (–0.523)] / (1 – 2) = 0.602 / (–1) ≈ –0.6

Please be aware that 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 taken the dial reading DR which is the relative torque value Mrel in %. Then, the viscosity value is calculated simply as η = DR/n (with the rotational speed n in min-1). Usually here, all units are ignored.

Thus, here: PPI = [lg (DRL/nL) – lg (DRH/nH)] / (lg nL – lg nH)

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

PPI = [lg (40/10) – lg (50/100)] / (lg 10 – lg 100) = (lg 4 – lg 0.5) / (1 – 2)

PPI = [0.602 – (–0.301)] / (–1) ≈ –0.9

Comment: Both determinations, as well VR as well as PPI are not scientific methods.