The Rheology Handbook. Thomas Mezger

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      Applications: Shock-proof, stab-proof and bullet-proof protective clothing as a combination of this “nano-dispersion” with synthetic technical textile fabrics; reinforced technical polymers for special functions (e. g. as “nano-composite” STF-Kevlar”) [3.17].

      For “Mr. and Ms. Cleverly”

      Note 5: Increased flow resistance due to flow instabilities and turbulence

      Increased flow resistance can also occur due to hydrodynamic flow instabilities which may lead to secondary flow effects and even to turbulent flow behavior showing vortices at high shear rates. In this case, flow curves and viscosity curves will display as well higher values for shear stress and viscosity as well as higher curve slope values compared to curves measured at regular (i. e. laminar) flow conditions, therefore giving at the first glance an impression of shear-thickening behavior.

      When performing tests on liquids using concentric cylinder measuring geometries with a rotating inner cylinder (Searle method, see Chapter 10.2.1.2a) there is a critical upper limit between laminar and turbulent flow conditions in the circular gap. Exceeding this limit, secondary flow effects may occur for the reason of centrifugal forces or inertial forces due to the mass of the fluid. The critical limiting value can be calculated in the form of a Taylor number (Ta). The range of turbulent flow is also reached when the critical Reynolds number (Re) is exceeded. Re numbers represent the ratio between the forces of inertia and flow resistance. (More about Ta number and Re number: see Chapters 10.2.2.4 and 11.3.1.3.)

      Example 6: Turbulent flow of water

      Water was measured at different temperatures using a double-gap measuring geometry. The limiting value of the shear rate range of ideal-viscous flow behavior was found at

       γ ̇ = 1300 s-1 at T = +10 °C showing η = 1.3 mPas

       γ ̇ = 1000 s-1 at T = +20 °C showing η = 1.0 mPas

       γ ̇ = 800 s-1 at T = +30 °C showing η = 0.80 mPas

      In each viscosity curve at the mentioned upper limit of the shear rate a clear bend was observed, followed by a distinctive increase in the slope of the viscosity curve, indicating the begin of the turbulent flow range.

      Note 6: Observation and visualization of turbulent behavior

      Using a special measuring device, flow behavior of dispersions at defined shear conditions can be observed simultaneously as well in the form of a measured viscosity function as well as visually, for example, in order to observe the onset of vortex formation. This process can be recorded via digital photography or video, measuring point by measuring point. (See also Chapter 10.8.2.3: Rheo-optics, velocity profile of a shear flow field, for example, using a measuring cell particle imaging velocimetry PIV, or particle tracking velocimetry PTV).

      End of the Cleverly section

      Note 7: Daniel wet point (WP), flow point (FP) , and dilatancy index [3.18] [3.19]

      The Daniel WP and FP technique used for millbase premix pigment pastes (pigment powder and vehicle), dispersions, paints and other coatings with a high pigment concentration. It is a simple hand-mixing method for characterizing two consistency stages in the take-up of vehicle (mixture of solvent and binder) by a bed of pigment particles. WP is defined as the stage in the titration of a specified amount of a pigment mass (e. g. 20 g) with vehicle, where just sufficient vehicle as incorporated by vigorous kneading with a glass rod or a spatula is present to form a soft, coherent paste-like mass showing a putty-like consistency. FP is determined by noting what further vehicle is required to produce a mixture that just drops, flows or falls off under its own weight from a horizontally held spatula. Between WP and FP, the mass hangs on a spatula with no sign of flow. The unit of WP and FP is volume of vehicle per mass (weight) of pigment [cm3/g].

      “Daniel dilatancy index” (DDI) is defined as DDI (in %) = [(FP – WP)/WP] ⋅ 100 %. This is the proportion of the additional vehicle required to reach the FP from the WP. A DDI of 5 to 15 % is considered strongly dilatant, does not disperse well although fluid, showing no tack; a DDI = 15 to 30 % is considered moderately to weakly dilatant, an excellent dispersion, showing some tack; and a DDI > 30 % is considered substantially non-dilatant, a dispersion obtained but with difficulty, showing tacky behavior.

      Comment: These three test methods WP, FP and DDI are not scientific since this is a very simple and manually performed technique, and the result depends on the subjective evaluation of the testing person. Even for a given pigment mixture as well WP as well FP obtained may vary significantly if the same pigment paste is used.

       3.3.3.1Structures of uncrosslinked polymers showing

      shear-thickening behavior

      When shearing polymer melts and highly concentrated solutions of chemically uncrosslinked polymers, shear-thickening flow behavior may occur due to mechanical entanglements between the molecule chains, particularly if they are branched and therefore often relatively inflexible. The higher the shear load (shear rate or shear stress, respectively), the more the molecule chains may prevent relative motion between neighbored molecules.

       3.3.3.2Structures of dispersions showing shear-thickening behavior

      Usually with highly filled suspensions during a process at increasing shear rates, the particles may more and more come into contact to one another, and particularly softer and gel-like particles may become more or less compressed. In this case, flow resistance will be increased. Here, the particle shape plays a crucial role. Due to the shear gradient which occurs in each flowing liquid, the particles are rotating as they move into shear direction [3.10] [3.20] [3.83]. Even rod-like particles and fibers are showing now and then rotational motion (photographic images e. g. in [3.14].

      Illustration, using the Two-Plates model (see Figure 2.1)

      Rotation of a particle occurs clockwise when using a Two-Plates model with a fixed lower plate and the upper plate moving to the right. Cube-shaped particles are requiring of course more space when rotating compared to the state-at-rest. As a consequence, between the particles there is less free volume left for the dispersion liquid. On the other hand, spherical particles require the same amount of volume when rotating or when at rest; these kinds of dispersions are less likely to show shear-thickening. A material’s ability to flow can be improved by increasing the amount of free volume available between the particles. This can be achieved by changing the shape of the particles, – and of course also by adding more dispersion liquid.

      Note 1: Droplet subdivision when testing emulsions

      When shearing emulsions, with increasing shear rates sometimes sloping up of the viscosity curve can be observed. This may be assumed to be an indication СКАЧАТЬ