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Detailed information on the yield point can be found in Chapter 3.3.4.1 Figure 3.21 presents a possible shape of flow curves explained below in sections b) to e).

a) Bingham :τ = τB + ηB ⋅ γ ̇

Flow curve model function with the “Bingham yield point” τB which occurs at the intersection of “Bingham straight line” and τ-axis in a diagram on a linear scale (see Figure 3.30), and “Bingham viscosity“ηB (according to E. C. Bingham, of 1916 [3.4]). Note: Despite of the denomination, this equation first was proposed by T. Schwedoff already in 1880 [3.12] [3.53].

Note: ηB is not a viscosity value of an investigated sample, since it is not more than a calculated coefficient used for curve fitting (it would be better to speak of the “Bingham flow coefficient”).

Before computers became widely used for analysis of flow curves, the Bingham model was often selected because analysis is very simple via the “Bingham straight line”, merely requiring a ruler. However, the “Bingham yield point” describes the transition from the state of rest to flow rather inaccurately. This model should therefore only be used for very simple QC tests (see also Chapter 3.3.4.2c: Plastic behavior, and Chapter 14.3: 1916, Bingham).

Figure 3.30: Flow curve fitting according to Bingham

Note: Simple evaluation methods (“according to Bingham”)

Some users perform the following simple test and analysis method consisting of two intervals. In the first part, a constantly high rotational speed nH [min-1] is preset 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 the values of τ and η are relative stress and viscosity values if the test is performed with 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 [3.7].