The Rheology Handbook. Thomas Mezger

force, the forces of the wind and of the continental drift or the pumping power of the heart.

3.3Flow curves and viscosity functions

      Flow curves are usually measured at a constant measuring temperature, i. e. at isothermal conditions. In principle, flow behavior is combined always with flow resistance, and therefore with an internal friction process occurring between the molecules and particles. In order to perform accurate tests in spite of the resulting viscous heating of the sample, the use of a temperature control device is required, for example in the form of a water bath or a Peltier element (see also Chapter 11.7.6: Temperature control systems).

       Figure 3.1: Preset profile: Time-dependent shear rate ramp in the form of a step-like function

       Figure 3.2: Preset profile: Time-dependent shear rate ramp

       Figure 3.3: Flow curves, overview:

      (1) ideal-viscous, (2) shear-thinning,

      (3) shear-thickening behavior

       Figure 3.4: Viscosity functions, overview:

      (1) ideal-viscous, (2) shear-thinning,

      (3) shear-thickening behavior

3.3.1Description of the test

      Preset

      1 With controlled shear rate (CSR): Profile γ ̇ (t) in the form of a step-like function, see Figure 3.1; or as a shear rate ramp, see Figure 3.2.

      2 With controlled shear stress (CSS): Profile τ(t), similar to Figures 3.1 and 3.2. The shear stress ramp test is the “classic method” to determine the yield point of a sample (see Chapter 3.3.4.1b).

      Measuring result: Flow curve τ(γ) or γ ̇ (τ),

      respectively, see Figure 3.3.

      Usually, flow curves are plotted showing γ ̇ on the x-axis and τ on the y-axis; and rarely reversed. This also applies to curves which are obtained when controlling the shear stress.

      Further results: Viscosity function η( γ ̇ ), see Figure 3.4; or η(τ), respectively.

      Usually, viscosity curves are presented showing γ ̇ on the x-axis and η on the y-axis. This also applies to curves which are obtained when controlling the stress.

      a) Extended test programs (including intervals at rest, for temperature equilibration, and pre-shear)

      Sometimes in industry, test programs are used showing besides shear rate ramps also other intervals without ramps, for example

      1 Rest intervals, presetting constantly γ ̇ = 0 either after a pre-shear interval, or at the start of the test to enable relaxation of the sample after gap setting of the measuring system which may cause a high internal stress particularly when testing highly viscous and viscoelastic samples. Simultaneously, this period is suited to enable temperature equalibration.

      2 Pre-shear intervals, presetting a constant low shear rate to distribute the sample in the shear gap homogeneously, and to equalize or even to reduce possibly still existing pre-stresses deriving from the preparation of the sample.

      Example 1: Testing resins

      Test program consisting of three intervals, preset:

      1 st interval: pre-shear phase (for t = 3 min): at γ ̇ = 5 s-1 = const

      2 nd interval: rest phase (for t = 1 min): at γ ̇ = 0

      3 rd interval: upward shear rate ramp

      (in t = 2min): γ ̇ = 0 to γ ̇ max

      at γ ̇ max = 100 s-1 (or, for a rigid consistency:

      at γ ̇ max = 20 s-1 only)

      Analysis: viscosity value at γ ̇ = 50 s-1 (or at 10 s-1, respectively)

      Example 2: Testing chocolate melts (at the test temperature T = +40 °C)

      Test program consisting of four intervals, preset:

      1 st interval: pre-shear phase (for t = 500 s): at γ ̇ = 5 s-1 = const

      2 nd interval: upward shear rate ramp (in t = 180 s): γ ̇ = 2 to 50 s-1

      3 rd interval: high-shear phase (for t = 60 s): at γ ̇ = 50 s-1 = const

      4 th interval: downward shear rate ramp (in t = 180 s): γ ̇ = 50 to 2 s-1

      Analysis: According to the ICA method (International Confectionery Association), the following two values are determined of the downward curve [3.1] [3.79]:

      1) Viscosity value at γ ̇ = 40 s-1 as the so-called apparent viscosity η40

      2) Shear stress value at γ ̇ = 5 s-1 as the so-called yield stress YS5

      b) Time-dependent effects, steady-state viscosity and transient viscosity

      (at low shear rates)

      When measuring at shear rates of γ ̇ < 1 s-1, it is important to ensure that the measuring point duration is long enough. This is especially true when testing highly viscous and viscoelastic samples at these low-shear conditions. Otherwise start-up effects or time-dependent transition effects are obtained, i. e., values of the transient viscosity function will be determined instead of the desired constant value of steady-state viscosity at each measuring point. Steady-state visco­sity is only dependent on the shear rate (or the shear stress) applied, resulting point by point in the viscosity function η( γ ̇ ) or η(τ), respectively. The values of transient viscosity, however, are dependent on both, shear rate (or shear stress) and passing time. Therefore, they are presented in the form of η+( γ ̇ , t) or η+(τ, t), respectively.

      When performing tests at γ ̇ > 1 s-1, only samples with pronounced viscoelastic properties are still influenced by transient effects. Therefore here, for liquids showing low or medium viscosity values, a duration of t = 5 s is sufficient for each single measuring point in almost all cases. However, transient effects should always be taken into account for polymers when measuring at shear rates of γ ̇ < 1 s-1 (i. e. in the low-shear range).

      As a rule of thumb: The measuring point duration should be selected to be at least as long as the value of the reciprocal shear rate (1/ γ ̇ ).

      Illustration, using the Two-Plates model (see also Figure 2.9, no.5)

      When setting the upper plate in motion at a constant speed, during a certain start-up time not all flowing layers of the sample are already shifted to the same extent along the neighboring layers. Initially, the resulting shear rate is not constant in the entire shear gap then since at first, only those layers are shifted which are close to the moving upper shear area. It takes a certain time until all the other layers are also set in motion, right down to the fixed bottom plate. Of course, this process will take a considerably longer time when presetting a considerably lower velocity to the upper plate.

      The full shear force representing the flow resistance of the whole and homogeneously sheared sample is measured not before the shear rate is reaching a constant