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1Introduction

1.1Rheology, rheometry and viscoelasticity

a) Rheology

Rheology is the science of deformation and flow. It is a branch of physics and physical chemistry since the most important variables come from the field of mechanics: forces, deflections and velocities. The term rheology originates from the Greek: rhei or rheo meaning to flow [1.1]. Thus, rheology is literally flow science. However, rheological experiments do not merely reveal information about flow behavior of liquids but also about deformation behavior of solids. The connection here is that a large deformation produced by shear forces causes many materials to flow.

All kinds of shear behavior, which can be described rheologically in a scientific way, can be viewed as being in between two extremes: flow of ideal-viscous liquids on the one hand and deformation of ideal-elastic solids on the other. Illustrative examples coming close to these two extremes of ideal behaviors are a low-viscosity mineral oil and a rigid steel ball. Viscosity and flow behavior of fluids are explained in Chapter 2. Elasticity and deformation behavior of solids are described in Chapter 4.

Behavior of all real materials is based on the combination of both a viscous and an elastic portion and therefore, it is called viscoelastic. Wallpaper paste is a viscoelastic liquid, for example, and a gum eraser is a viscoelastic solid. Information on viscoelastic behavior can be found in Chapter 5. Complex and extraordinary rheological behavior is presented in Chapter 9 using the example of surfactant systems.

Table 1.1 shows the most important terms, all of which will be covered in this book. This chart can also be found at the beginning of Chapters 2 to 8, with those terms given in bold print being discussed in the chapter in hand.

Table 1.1: Overview on different kinds of rheological behavior
Liquids	Solids
(ideal-) viscousflow behaviorviscosity 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

Rheology was first seen as a science in its own, right not before the beginning of the 20th century. However, scientists and practical users have long before been interested in the behavior of liquids and solids, although some of their methods have not always been very scientific. A list of important facts of the historical development in rheology is given in Chapter 14. Of special interest are here the various attempts to classify all kinds of different rheological behavior, such as the classification of Markus Reiner in 1931 and 1960, and of George W. Scott Blair in 1942; see also [1.2]. The aim of the rheologists’ is to measure deformation and flow behavior of a great variety of matters, to present the obtained results clearly and to explain it.

b) Rheometry

Rheometry is the measuring technology used to determine rheological data. The emphasis here is on measuring systems, instruments, and methods for testing and analysis. Both liquids and solids, but also powders, can be investigated using rotational and oscillatory rheometers. Rotational tests which are performed to characterize viscous behavior are presented in Chapter 3. In order to evaluate viscoelastic behavior, creep tests (Chapter 6), relaxation tests (Chapter 7) and oscillatory tests (Chapter 8) are performed. Chapter 10 contains information on measuring systems (e. g. measuring geometries) and special measuring devices, and Chapter 11 gives an overview on diverse instruments used. Shear experiments on slightly compressed powders and on strongly compressed bulk materials are explained in Chapter 13.

Analog programmers and on-line recorders for plotting flow curves have been on the market since around 1970. Around 1980, digitally controlled instruments appeared which made it possible to store measuring data and to use a variety of analysis methods, including also complex ones. Developments in measuring technology are constantly pushing back the limits. At the same time, thanks to standardized measuring systems (geometries) and procedures, measuring results can be compared world-wide today. Meanwhile, several rheometer manufacturers can offer test conditions to customers in many industrial branches which come very close to simulate even complex process conditions in practice.

A short guideline for rheological measurements is presented in Chapter 12 in order to facilitate the daily laboratory work for practical users.

c) Appendix

Chapter 15 (Appendix) shows all the used signs, symbols and abbreviations with their units. The Greek alphabet and a conversion table for units (SI and CGS system) can also be found there.

More than 500 standards are listed in Chapter 16 (ISO, ASTM, EN and DIN). The refer

ences, publications and books are specified at the end of the respective chapter. They can be identified by the number in brackets (e. g. [12.34] as reference 34 in Chapter 12).

d) Information for “Mr. and Ms. Cleverly”

Throughout this textbook, the reader will find sections for “Mr. and Ms. Cleverly” which are marked with a symbol showing glasses:

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)