The Rheology Handbook. Thomas Mezger

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[2.7]Poiseuille, J. L. M., Recherches expérimentales sur le mouvement des liquides dans les tubes de très petits diamètres, Acad. Sci., Paris, 1840; Experimentelle Untersuchungen über die Bewegung der Flüssigkeiten in Röhren von sehr kleinen Durchmessern. Pogg. Ann., 1843

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[2.12]Stokes, G. G., Report on the recent researches in hydrodynamics, Report Brit. Assoc., 1846; On some cases of fluid motion, Trans. Cambridge Philos. Soc., 1849 (1843); On the theories of the internal friction of fluids in motion and of the equilibrium and motion of elastic solids, ibid., 1849 (1845); On the effect of the internal friction of fluids on the motion of pendulums, ibid., 1851 (1850)

[2.13]Wörterbuch der Chemie, composed by B. Frunder, E. Hillen, U. Rohlf, dtv, München, 1995

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3Rotational tests

      In this chapter are explained the following terms given in bold:

Liquids		Solids
(ideal-) viscous flow behavior viscosity law(according to Newton)	viscoelasticflow behaviorMaxwell model	viscoelasticdeformation behaviorKelvin/Voigt model	(ideal-) elasticdeformation behaviorelasticity law(according to Hooke)
flow/viscosity curves	creep tests, relaxation tests, oscillatory tests

3.1Introduction

      In Chapter 2 using the viscosity law, the rheological background of fluids showing ideal-viscous flow behavior was explained. Chapter 3 concentrates on rheometry: The performance of rotational tests to investigate the mostly more complex, non-Newtonian flow behavior of liquids, solutions, melts and dispersions (suspensions, emulsions, foams) used in daily practice in industry will be described here in detail. Typical measuring geometries or measuring systems, respectively, are described in Chapter 10.

3.2Basic principles

       3.2.1Test modes-controlled shear rate (CSR) and controlled shear stress (CSS), raw data and rheological parameters

      a) Tests with controlled shear rate (CSR tests)

      When performing CSR tests, the rotational speed or shear rate, respectively, is preset and controlled by the rheometer (see Table 3.1). This test method is called a “controlled shear rate test”, or briefly, “CSR test” or “CR test”.

      The test method with controlled shear rate is usually selected if the liquid to be investigated shows self-leveling behavior (i. e. no yield point), and if viscosity should be measured at a desired flow velocity or shear rate, respectively. This is the case, if certain process conditions have to be simulated, for example, occurring with pipe flow, or when painting and spraying. Shear rates which are occurring in industrial practice are listed in Table 2.1 (see Chapter 2.2.2).

Table 3.1: Raw data and rheological parameters of rotational tests with controlled shear rate (CSR)
Rotation CSR	Test preset	Results
raw data	rotational speed n [min -1]	torque M [mNm]
rheological parameters	shear stress γ ̇ [s-1]	shear stress τ [Pa]
viscosity calculation		η = τ / γ ̇ [Pas]

Table 3.2: Raw data and rheological parameters of rotational tests with controlled shear stress (CSS)
Rotation CSS	Test preset	Results
raw data	torque M [mNm]	rotational speed n [min -1]
rheological parameters	shear stress τ [Pa]	shear stress γ ̇ [s-1]
viscosity calculation		η = τ / γ ̇ [Pas]

      ISO 3219 standard of 1993 recommended to measure and to compare viscosity values preferably at defined shear rate values (i. e., no longer using specifications of rotational speeds, e. g. in rpm). For this purpose, the following two alternative series are specified. Dividing or multiplying these values by 100 provides further γ ̇ -values.

      1) 1.00/2.50/6.30/16.0/40.0/100/250 s-1. This geometric series shows a multiplier of 2.5

      2) 1.00/2.50/5.00/10.0/25.0/50.0/100 s-1

      b) Tests with controlled shear stress (CSS tests)

      When performing CSS tests, the torque or shear stress, respectively, is preset and controlled by the rheometer (see Table 3.2). This test method is called a “controlled shear stress test”, or briefly, “CSS test” or “CS test”.

      This is the classic method to determine yield points of dispersions, pastes or gels (see also Chapter 3.3.4.1b). In nature, almost all flow processes are shear stress controlled, since any motion – creep or flow – is mostly a reaction to an acting force.

      Examples from nature

      Rivers, avalanches, glaciers, landslides, ocean waves, the motion of clouds or of leaves