These sections are written for those readers who wish to go deeper into the theoretical side and who are not afraid of a little extra mathematics and fundamentals in physics. However, these “Cleverly” explanations are not required to understand the information given in the normal text of later chapters, since this textbook is also written for beginners in the field of rheology. Therefore, for those readers who are above all interested in the practical side of rheology, the “Cleverly” sections can simply be ignored.
1.2Deformation and flow behavior
We are confronted with rheological phenomena every single day. Some experiments are listed below to demonstrate this point. The examples given will be discussed in detail in the chapters mentioned in brackets.
Experiment 1: Behavior of mineral oil , plasticine, and steel
Completely different types of behavior can be seen when the following three subjects hit the floor (see Figure 1.1):
1 The mineral oil is flowing and spreading until it shows a very thin layer finally (ideal-viscous flow behavior: see Chapter 2.3.1)
2 The plasticine will be deformed when it hits the floor, and afterwards, it remains deformed permanently (inhomogeneous plastic behavior outside the linear viscoelastic deformation range: see Chapter 3.3.4.2c)
3 The steel ball bounces back, and exhibits afterwards no deformation at all (ideal-elastic behavior: see Chapter 4.3.1)
Figure 1.1: Deformation behavior after hitting the floor:
a) mineral oil, b) plasticine, c) steel ball
Experiment 2: Playing with “bouncing putty ” (some call it “Silly Putty”)
The silicone polymer (uncrosslinked PDMS) displays different rheological behaviors depending on the period of time under stress (viscoelastic behavior of polymers: see Chapter 8.4, frequency sweep):
1 When stressed briefly and quickly, the putty behaves like a rigid and elastic solid: If you mold a piece of it to the shape of a ball and throw it on the floor, it is bouncing back.
2 When stressed slowly at a constantly low force over a longer period of time, the putty shows the behavior of a highly viscous, yielding and creeping liquid: If it is in the state of rest, thus, if you leave it untouched for a certain period of time, it is spreading very slowly under its own weight due to gravity to show an even layer with a homogeneous thickness finally.
Experiment 3: Do the rods remain in the position standing up straight?
Three wooden rods are put into three glasses containing different materials and left for gravity to do its work.
1 In the glass of water , the rod changes its position immediately and falls to the side of the glass (ideal-viscous flow behavior: see Chapter 2.3.1).
Additional observation: All the air bubbles which were brought into the water when immersing the rod are rising quickly within seconds.
1 In the glass containing a silicone polymer (uncrosslinked PDMS), the rod moves very, very slowly, reaching the side of the glass after around 10 minutes (polymers showing zero- shear viscosity: see Chapters 3.3.2.1a).
Additional observation concerning the air bubbles which were brought into the polymer sample by the rod: Large bubbles are rising within a few minutes, but the smaller ones seem to remain suspended without visible motion. However, after several hours even the smallest bubble has reached the surface. Therefore, indeed long-term but complete de-aeration of the silicone occurs finally.
1 In the glass containing a hand cream , the rod still remains standing straight in the initial position even after some hours (yield point and flow point: see Chapters 3.3.4, 4.4 and 8.3.4).
Additional observation concerning the air bubbles: All bubbles, independent of their size, remain suspended, and therefore here, no de-aeration takes place at all.
Summary
Rheological behavior depends on many external influences. Above all, the following test conditions are important:
Type of loading (preset of deformation, velocity or force; or shear strain, shear rate or shear stress, respectively)
Degree of loading (low-shear or high-shear conditions)
Duration of loading (the periods of time under load and at rest)
Temperature (see Chapters 3.5 and 8.6)
Further important parameters are, for example:
Concentration (e. g. of solid particles in a suspension: see Chapter 3.3.3; of polymer molecules in a solution: see Chapter 3.3.2.1a; of surfactants in a dispersion: see Chapter 9). Using an immobilization cell, the amount of liquid can be reduced under controlled conditions (e. g. when testing dispersions such as paper coatings: see Chapter 10.8.1.3).
Ambient pressure (see Chapter 3.6)
pH value (e. g. with surfactant systems: see Chapter 9)
Strength of a magnetic or an electric field when investigating magneto-rheological fluids or electro-rheological fluids (MRF, ERF), respectively (see Chapters 10.8.1.1 and 2).
UV radiation curing (e. g. of resins, adhesives and inks: see Chapter 10.8.1.4).
Air humidity (see Chapter 10.8.1.5)
Amount of air, flowing through a fluidized mixture of powder and air (see Chapter 13.3)
Degree of solidification in a powder or compressed bulk material (e. g. granulate; see Chapter 13.2)
1.3References
[1.1]Beris, A. N., Giacomin, A. J., Panta rhei – everthing flows, J. Appl. Rheol. 24 (2014) 52918
[1.2] McKinley, G., A hitchhikers guide to complex fluids, Rheol. Bull., 84(1), (2015)
2Flow behavior and viscosity
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 | ||
2.1Introduction
Before 1980 in industrial practice, rheological experiments on pure liquids and dispersions were carried out almost exclusively in the form of rotational tests which enabled the characterization of flow behavior at medium and high flow velocities. Meanwhile since measurement technology has developed, many users have expanded their investigations on deformation and flow behavior performing measurements which cover also the low-shear range.
2.2Definition of terms
Figure 2.1: The Two-Plates model for shear tests