The Rheology Handbook. Thomas Mezger

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 of shear-thickening behavior. However, this effect is often occurring due to a reduction of the average droplet size, caused by droplet subdivision during a continued dispersing process due to the shear forces. Here, corresponding increase of the volume-specific surface (which is the ratio of droplet surface and droplet volume) and, as a consequence, the resulting increase in the interactions between the now smaller droplets may lead to higher values of the flow resistance (more on emulsions: see also Chapter 9.1.2 and [3.21] [3.22].

      Example: Creaming effect of pharmaceuticals and cosmetic products

      The “creaming effect” is a result of this continued dispersion process. When spreading and rubbing corresponding emulsions such as creams, lotions and ointments, on the skin, a “whitening effect” may occur which is often leading to tacky, and even stringy, behavior, therefore causing of course an unpleasant skin sensation.

      Note 2: Observation and visualization of flowing emulsions using a rheo-microscope

      Using special measuring devices, flow behavior of emulsions at defined shear conditions can be observed simultaneously as well in the form of the measured viscosity function as well as visually, for example, in order to observe the onset of breaking up the droplets. This process can be recorded via digital photography or video, measuring point by measuring point. (See also Chapters 10.8.2.2 and 10.8.2.5: Rheo-optics, microscopy and SALS).

      Note 3: Difference between dilatancy and dilatation

      Sometimes, also due to historic reasons, these two terms are used falsely as synonyms (see Chapter 14.2, 1883 Reynolds). In proper science, however, there should be made a difference: On the one hand, dilatant or shear-thickening behavior is a rheological effect. On the other hand, dilatation may occur with a shear deformation on bulk materials including relatively coarse particles, e. g. such as dry and humid sand (see Chapter 13.2.2: Pre-shear of powder or bulk solids). Example: The following can be seen when setting one foot after another in humid sand during a stroll along the seaside. The area around the feet seems to dry immediately. This happens due to the compression stress onto the sand grains and the resulting deformation. Initially there was a highly ordered cubic closest ball packing of the sand grains, showing therefore a higher density. When this state is disarranged, as a consequence, the surrounding water is sucked rapidly into the now enlarged amount of hollow space between the particles. Imagine a volume element within this bulk material, this process leads to a certain volume increase finally. This effect may be even stronger, if besides the compression there is also a shear load acting on the sand grains, and if some particles have to move across other ones. Dilatation describes a change of the

      geometrical shape and volume.

      Summary: There should be made a clear difference between the two terms (rheological) dilatance and (volumetric) dilatation, since both of them are specifying clearly different physical phenomena. Both effects may occur simultaneously, however, mostly this is not the case. In order to prevent any confusion, some authors even recommend to use for the rheological thickening