The Rheology Handbook E-Book

Thomas Mezger

• Herausgeber: Vincentz Network
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 1360

Veröffentlichungsjahr: 2020

Beschreibung

Already in its 5th edition, this standard work describes the principles of rheology clearly, vividly and in practical terms. The book includes the rheology of additives in waterborne dispersions and surfactant systems. Not only it is a great reference book, it can also serve as a textbook for studying the theory behind the methods. The practical use of rheology is presented in the areas quality control, production and application, chemical and mechanical engineering, materials science and industrial research and development. After reading this book, the reader should be able to perform tests with rotational and oscillatory rheometers and interpret the results correctly.

Leseprobe

Thomas G. Mezger

The Rheology Handbook

For users of rotational and oscillatory rheometers

5th Revised Edition

Cover: Zffoto - stock.adobe.com

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Mezger, Thomas G.

The Rheology Handbook, 5th Revised Edition

Hanover: Vincentz Network, 2020

European Coatings Library

ISBN 3-86630-532-X

ISBN 978-3-86630-536-6

© 2020 Vincentz Network GmbH & Co. KG, Hanover

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European Coatings Library

Thomas G. Mezger

The Rheology Handbook

For users of rotational and oscillatory rheometers

5th Revised Edition

Thomas G. Mezger

The Rheology Handbook

For users of rotational and oscillatory rheometers

5th Revised Edition

Foreword

Why was this book written?

People working in industry are often confronted with the effects of rheology, the science of deformation and flow behavior. When looking for appropriate literature, they find either short brochures which give only a few details and contain little useful information, or highly specialized books overcharged of physical formulas and mathematical theories. There is a lack of literature between these two extremes which reduces the discussion of theoretical principles to the necessary topics, providing useful instructions for experiments on material characterization. This book is intended to fill that gap.

The practical use of rheology is presented in the following areas: quality control (QC), production and application, chemical and mechanical engineering, industrial research and development, and materials science. Emphasis is placed on current testing methods related to daily working practice. After reading this book, the reader should be able to perform useful tests with rotational and oscillatory rheometers, and to interpret the achieved results correctly.

How did this book come into existence?

The first computer-controlled rheometers came into use in industrial laboratories in the mid-1980s. Ever since then, test methods as well as control and analysis options have improved with breath-taking speed. In order to organize and clarify the growing mountain of information, company Anton Paar Germany – and previously Physica Messtechnik – has offered basic seminars on rheology already since 1988, focused on branch-specific industrial application. During the “European Coatings Show” in Nuremberg in April 1999, the organizer and publishing director Dr Lothar Vincentz suggested expanding these seminar notes into a comprehensive book about applied rheology.

What is the target audience for this book? For which industrial branches will it be most interesting?

The Rheology Handbook is written for everyone approaching rheology without any prior knowledge but is also useful to people wishing to update their expertise with information about recent developments. The reader can use the book as a course book and read from beginning to end or as a reference book for selected chapters. The numerous cross-references make connections clear and the detailed index helps when searching. If required, the book can be used as the first step on the ladder towards theory-orientated rheology books at university level. In order to break up the text, there are as well many figures and tables, illustrative examples and small practical experiments, as well as several exercises for calculations. The following list reflects how the contents of the book are of interest to rheology users in many industrial branches.

Polymers:

Solutions, melts, solids; film emulsions, cellulose solutions, latex emulsions, solid films, sheetings (uni-laminar, multi-laminar), laminates; natural resins, epoxies, casting resins; silicones, caoutchouc, gums, soft and hard rubbers; thermoplastics, elastomers, thermosets, blends, foamed materials; uncrosslinked and cross-linked polymers containing or without fillers or fibers; polymeric compounds and composites; solid bars of glass-fiber, carbon-fiber and synthetic-fiber reinforced polymers (GFRP, CFRP, SFRP); polymerization, cross-linking, curing, vulcanization, melting and hardening processes; powder rheology, resin powders, granulates

Adhesives and sealants:

Glues, single and multi-component adhesives, pressure sensitive adhesives (PSA), UV curing adhesives, hotmelts, plastisol pastes (e. g. for automotive underseals and seam sealings), construction adhesives, putties; uncured and cured adhesives; curing process; tack, stringiness

Coatings, paints, lacquers:

Spray, brush, dip coatings; solvent-borne, water-based coatings; metallic effect, textured, low solids, high solids, photo-resists, UV (ultra violet) radiation curing, powder coatings; glazes and stains for wood; coil coatings; reactive fire-protection coatings; solid coating films; powder rheology, powder coatings, colored powders (e. g. titanium dioxide, soot), e. g. for additive manufacturing (AM)

Printing inks and varnishes:

Gravure, letterpress, flexographic, planographic, offset, screen printing inks, UV (ultra violet) radiation curing inks; ink-jet printer inks; writing inks for pens; mill-base premix, color pastes, “thixo-pastes”; liquid and pasty pigment dispersions; printing process; misting; tack; powder rheology: materials for additive manufacturing (AM)

Paper coatings:

Primers and topcoats; immobilization process

Foodstuffs:

Water, vegetable oils, aroma solvents, fruit juices, baby food, liquid nutrition, liqueurs, syrups, purees, thickeners as stabilizing agents, gels, pudding, jellies, ketchup, mayonnaise, mustard, dairy products (such as yogurt, cream cheese, cheese spread, soft and hard cheese, curds, butter), emulsions, chocolate (melt), soft sweets, ice cream, chewing gum, dough, whisked egg, cappuccino foam, sausage meat, sauces containing meat chunks, jam containing fruit pieces, animal feed; bio-technological fluids; gel formation of hydrocolloids (e. g. of corn starch and gelatin); interfacial rheology (e. g. for emulsions, foams); rheology of powders and granulates: milk powder, cocoa powder, coffee powder, coffee whitener, flour, starch powder (e. g. as a binder), powdered sugar, granulated sugar, spices, animal feed (as granulates, pellets), grain, corn, rice, spray-dried products; influence of humidity (e. g. biscuits, cookies, crackers); food tribology (e. g. for creaminess); tack

Cosmetics, beauty care products:

Perfume oils, emulsions (e. g. skin care, hair-dye), lotions, nail polish, roll-on fluids (deodorants), shampoo, shower gels, skin creams, abrasive peeling creams, hair gels, styling waxes, shaving creams, tooth-gels, toothpastes, makeup dispersions, lipstick, mascara, medical adhesives (e. g. for diapers), super-absorbers; hairs, sponges; interfacial rheology (e. g. for emulsions, foams); powder rheology: make-up powders, rouge, deodorant powders, dry shampoo, baby powders, hygienics powders

Pharmaceuticals, medicaments, bio-tech products, health and personal care products

: Cough mixtures, wetting agents, nose sprays, vaccines, blood (hemo-rheology), blood-plasma substitutes, emulsions, saliva, mucus, hydrogels, skin creams, synovia fluid (e. g. for joints), hyaluronan acid (HA), ointments, vaseline, natural and synthetic membranes, silicone pads and cushions, dental molding materials, tooth filling, sponges, contact lenses, medical adhesives (e. g. for skin plasters, dental prothesis), denture fixative creams, hair, bone cement, implants, organic-inorganic compounds (hybrids); “biologically active” suspensions and gels (e. g. microalgae, bacteria); tribolgy: bacterial bio-films, biological cells, tissue engineered medical products (TEMPs), cartilage, catheters; interfacial rheology (e. g. emulsions, foams); powder rheology: tablets, disinfection powders

Agrochemicals:

Plant or crop protection agents, solutions and dispersions of insecticides and pesticides, herbicides and fungicides

Detergents, home care products:

Household cleaning agents, liquid soap, disinfectants, surfactant solutions, dispersions containing viscoelastic surfactants (VES), washing-up liquids, dish washing agents, laundry, fabric conditioners, washing powder concentrate, fat removers; interfacial rheology: emulsions, foams; powder rheology: superabsorbers (e. g. for diapers)

Surface technology:

Polishing and abrasive suspensions; cooling emulsions; powder rheology, tribology: polishing powders, abrasive suspensions

Electrical engineering, electronics industry:

Thick film pastes, conductive, resistance, insulating, glass paste, soft solder and screen-printing pastes; SMD adhesives (for surface mounted devices), insulating and protective coatings, de-greasing agents, battery fluids and pastes, coatings for electrodes

Petrochemicals:

Crude oils, petroleum, solvents, de-icing agents, fuels, mineral oils, light and heavy oils, lubricating greases, paraffines, waxes, petrolatum, vaseline, natural and polymer-modified bitumen (PmB), asphalt binders, distillation residues; from coal and wood: tar and pitch; interfacial rheology (e. g. for emulsions); tribology: lubricating behavior

Ceramics and glass:

Casting slips, kaolin and porcelain suspensions, glass powder and enamel pastes, glazes, plastically deformable ceramic pastes, glass melts, aero-gels, xero-gels, sol/gel materials, composites, organo-silanes (hybrids), basalt melts; powder rheology: ceramic powders (e. g. for additive manufacturing, AM), clay, loam

Construction materials:

Self-levelling cast floors, plasters, mortar, cement suspensions, tile adhesives, dispersion paints, sealants, floor sheeting, natural and polymer-modified bitumen (PmB), and GTR (ground tire rubber) modified asphalt binder (for road pavement); bulk and powder rheology: sand, lime, chalk, gypsum

Metals:

Melts of magnesium, aluminum, steel, alloys, slags; molding process in a semi-solid state (“thixo-forming”, “thixo-casting”, “thixo-forging”), compounds: ceramic fiber reinforced light-weight metals; powder rheology: metal powders (e. g. for additive manufacturing, AM)

Waste industry:

Waste water, sewage sludges, animal excrements (e. g. of fishes, poultry, cats, dogs, pigs, cattle), residues from refuse incineration plants; powder rheology: sludges, filter cakes

Geology, soil mechanics, mining industry:

Sludges from coal, peat, soil, drilling muds; river and lake sediment masses; soil deformation (e. g. due to mining operations, earthwork, canal and drain constructions, operations of vehicles in agriculture); drilling fluids, fracturing fluids (e. g. containing “flow improvers”); melts of volcanic stones (e. g. basalt), lava, magma, salt melts; powder rheology: coal powder, briquet manufacturing

Disaster control:

Foam for fire extinguishers, deformation behavior of burning materials, soil deformation due to floods and earthquakes

Materials for special functions

(e. g. as “smart fluids”): Magneto-rheological fluids (MRF), electro-rheological fluids (ERF), di-electric (DE) materials, self-repairing coatings, materials showing self-organizing superstructures (e. g. surfactants), dilatant fabrics (shock-absorbing, “shot-proof”), mesogenic fluids (MF), liquid crystals (LC), ionic fluids, micro-capsule paraffin wax (e. g. as “phase-change material” PCM), shape-memory materials (SPM); tribology: haptic sensation (when prooving the shape of the whole sample) or tactile sensation (when touching or scanning the surface); systems reacting by a change in shape due to an external excitation (e. g. temperature, light, pressure); powder rheology: materials used for additive manufacturing (AM)

It is pleasing that the first four editions of The Rheology Handbook, published in 2002, 2006, 2011 and 2014 sold out so unexpectedly quickly. It was positive to hear that the books met with approval, not only from laboratory technicians and practically oriented engineers, but also from teachers and professors of schools and colleges of applied sciences. Even at universities, The Rheology Handbook is meanwhile taken as an introductory teaching material for explaining the basics of rheology in lectures and practical courses, and as a consequence, many students worldwide are using it when writing their final paper or thesis. This textbook is also available in German language, and between 2000 and 2016 also here, five editions were published meanwhile (title: Das Rheo­logie Handbuch).

New in this fifth edition is Chapter 13 (shear tests with powders and bulk solids). Further present-day examples have been added resulting as well from contacts to industrial users as well as from corporation with several working groups, e. g. for developing modern standardizing measuring methods for diverse industrial branches. The references and standards have been updated (e. g. in Chapter 15).

I hope that The Rheology Handbook will prove itself a useful source of information for characterizing the above mentioned products in an application-oriented way, assuring their quality and helping to improve them wherever possible.

Stuttgart, June 2020

Thomas G. Mezger

Foreword

1 Introduction

1.1 Rheology, rheometry and viscoelasticity

1.2 Deformation and flow behavior

1.3 References

2 Flow behavior and viscosity

2.1 Introduction

2.2 Definition of terms

2.2.1 Shear stress

2.2.2 Shear rate

2.2.3 Viscosity

2.3 Shear load-dependent flow behavior

2.3.1 Ideal-viscous flow behavior

2.4 Types of flow illustrated by the Two-Plates model

2.5 References

3 Rotational tests

3.1 Introduction

3.2 Basic principles

3.2.1 Test modes-controlled shear rate (CSR) and controlled shear stress (CSS), raw data and rheological parameters

3.3 Flow curves and viscosity functions

3.3.1 Description of the test

3.3.2 Shear-thinning flow behavior

3.3.3 Shear-thickening flow behavior

3.3.4 Yield point

3.3.5 Overview: flow curves and viscosity functions

3.3.6 Fitting functions for flow and viscosity curves

3.3.7 The effects of rheology additives in water-based dispersions

3.4 Time-dependent flow behavior and viscosity function

3.4.1 Test description

3.4.2 Time-dependent flow behavior of samples showing no hardening

3.4.3 Time-dependent flow behavior of samples showing hardening

3.5 Temperature-dependent flow behavior and viscosity function

3.5.1 Test description

3.5.2 Temperature-dependent flow behavior of samples showing no hardening

3.5.3 Temperature-dependent flow behavior of samples showing hardening

3.5.4 Fitting functions for curves of the temperature-dependent viscosity

3.6 Pressure-dependent flow behavior and viscosity function

3.7 References

4 Elastic behavior and shear modulus

4.1 Introduction

4.2 Definition of terms

4.2.1 Deformation and strain

4.2.2 Shear modulus

4.3 Shear load-dependent deformation behavior

4.3.1 Ideal-elastic deformation behavior

4.4 Yield point determination using the shear stress/deformation diagram

4.5 References

5 Viscoelastic behavior

5.1 Introduction

5.2 Basic principles

5.2.1 Viscoelastic liquids according to Maxwell

5.2.2 Viscoelastic solids according to Kelvin/Voigt

5.3 Normal stresses

5.4 References

6 Creep tests

6.1 Introduction

6.2 Basic principles

6.2.1 Description of the test

6.2.2 Ideal-elastic behavior

6.2.3 Ideal-viscous behavior

6.2.4 Viscoelastic behavior

6.3 Analysis

6.3.1 Behavior of the molecules

6.3.2 The Burgers model

6.3.3 Curve discussion

6.3.4 Definition of terms

6.3.5 Data conversion

6.3.6 Determination of the molar mass distribution

6.4 Determination of the yield point via creep tests

6.5 References

7 Relaxation tests

7.1 Introduction

7.2 Basic principles

7.2.1 Description of the test

7.2.2 Ideal-elastic behavior

7.2.3 Ideal-viscous behavior

7.2.4 Viscoelastic behavior

7.3 Analysis

7.3.1 Behavior of the molecules

7.3.2 Curve discussion

7.3.3 Definition of terms

7.3.4 Data conversion

7.3.5 Determination of the molar mass distribution

7.4 References

8 Oscillatory tests

8.1 Introduction

8.2 Basic principles

8.2.1 Ideal-elastic behavior

8.2.2 Ideal-viscous behavior

8.2.3 Viscoelastic behavior

8.2.4 Definition of terms

8.2.5 The test modes controlled shear strain and controlled shear stress, raw data and rheological parameters

8.3 Amplitude sweeps

8.3.1 Description of the test

8.3.2 Limiting value of the LVE range

8.3.3 Determination of the yield point and the flow point by amplitude sweeps

8.3.4 Frequency-dependence of amplitude sweeps

8.3.5 SAOS and LAOS tests, and Lissajous diagrams

8.4 Frequency sweeps

8.4.1 Description of the test

8.4.2 Behavior of uncrosslinked polymers (solutions and melts)

8.4.3 Behavior of crosslinked polymers

8.4.4 Behavior of dispersions and gels

8.4.5 Comparison of superstructures using frequency sweeps

8.4.6 Multiwave test

8.4.7 Data conversion

8.5 Time-dependent behavior at constant dynamic-mechanical and isothermal conditions

8.5.1 Description of the test

8.5.2 Time-dependent behavior of samples showing no hardening

8.5.3 Time-dependent behavior of samples showing hardening

8.6 Temperature-dependent behavior at constant dynamic mechanical conditions

8.6.1 Description of the test

8.6.2 Temperature-dependent behavior of samples showing no hardening

8.6.3 Temperature-dependent behavior of samples showing hardening

8.6.4 Thermoanalysis (TA)

8.7 Time/temperature shift

8.7.1 Temperature shift factor according to the WLF method

8.8 The Cox/Merz relation

8.9 Combined rotational and oscillatory tests

8.9.1 Presetting rotation and oscillation in series

8.9.2 Superposition of oscillation and rotation

8.10 References

9 Complex behavior, surfactant systems

9.1 Surfactant systems

9.1.1 Surfactant structures and micelles

9.1.2 Emulsions

9.1.3 Mixtures of surfactants and polymers, polymers containing surfactant components

9.1.4 Applications of surfactant systems

9.2 Rheological behavior of surfactant systems

9.2.1 Typical shear behavior

9.2.2 Shear-induced effects, shear-banding and “rheo chaos ”

9.3 References

10 Measuring systems

10.1 Introduction

10.2 Concentric cylinder measuring systems (CC MS)

10.2.1 Cylinder measuring systems in general

10.2.2 Narrow-gap concentric cylinder measuring systems according to ISO 3219

10.2.3 Double-gap measuring systems (DG MS)

10.2.4 High-shear cylinder measuring systems (HS MS)

10.3 Cone-and-plate measuring systems(CP MS)

10.3.1 Geometry

10.3.2 Calculations

10.3.3 Conversion between raw data and rheological parameters

10.3.4 Flow instabilities and secondary flow effects in CP systems

10.3.5 Cone truncation and gap setting

10.3.6 Maximum particle size

10.3.7 Filling of the cone-and-plate measuring system

10.3.8 Advantages and disadvantages of cone-and-platemeasuring systems

10.4 Parallel-plate measuring systems(PP MS)

10.4.1 Geometry

10.4.2 Calculations

10.4.3 Conversion between raw data and rheological parameters

10.4.4 Flow instabilities and secondary flow effects in a PP system

10.4.5 Recommendations for gap setting

10.4.6 Automatic gap setting and automatic gap controlusing the normal force control option

10.4.7 Determination of the temperature gradientin the sample

10.4.8 Advantages and disadvantages of parallel-plate measuring systems

10.5 Mooney/Ewart measuring systems(ME MS)

10.6 Relative measuring systems

10.6.1 Measuring systems with sandblasted, profiledor serrated surfaces

10.6.2 Spindles in the form of disks, pins, and spheres

10.6.3 Krebs spindles

10.6.4 Paste spindles and rotors showing pins and vanes

10.6.5 Ball measuring systems (motion along a circular path)

10.6.6 Further relative measuring systems

10.7 Measuring systems for solid torsion bars

10.7.1 Bars showing a rectangular cross section

10.7.2 Bars showing a circular cross section

10.7.3 Composite materials

10.8 Special measuring devices

10.8.1 Special measuring conditions which influence rheology

10.8.2 Rheo-optical measuring devices

10.8.3 Other special measuring devices

10.8.4 Other kinds of testings besides shear tests

10.9 References

11 Instruments

11.1 Introduction

11.2 Short overview: methods for testing viscosity and elasticity

11.2.1 Very simple determinations

11.2.2 Flow on a horizontal plane

11.2.3 Spreading or slump on a horizontal plane after lifting a container

11.2.4 Flow on an inclined plane

11.2.5 Flow on a vertical plane or over a special tool

11.2.6 Flow in a channel, trough or bowl

11.2.7 Flow cups and other pressureless capillary viscometers

11.2.8 Devices showing rising, sinking, falling and rolling elements

11.2.9 Penetrometers, consistometers and texture analyzers

11.2.10 Pressurized cylinder and capillary devices

11.2.11 Simple rotational viscometer tests

11.2.12 Devices with vibrating or oscillating elements

11.2.13 Rotational and oscillatory curemeters (for rubber testing)

11.2.14 Tension testers

11.2.15 Compression testers

11.2.16 Linear shear testers

11.2.17 Bending or flexure testers

11.2.18 Torsion testers

11.3 Flow cups

11.3.1 ISO cups

11.3.2 Other types of flow cups

11.4 Capillary viscometers

11.4.1 Glass capillary viscometers

11.4.2 Pressurized capillary viscometers

11.5 Falling-ball viscometers

11.6 Stabinger viscometer

11.7 Rotational and oscillatory rheometers

11.7.1 Rheometer set-ups

11.7.2 Control loops

11.7.3 Devices to measure torques

11.7.4 Devices to measure deflection angles and rotational speeds

11.7.5 Bearings

11.7.6 Temperature control systems

11.8 References

12 Guideline for rheological tests

12.1 Selection of the measuring system (geometry)

12.2 Rotational tests

12.2.1 Flow and viscosity curves

12.2.2 Time-dependent flow behavior (rotation)

12.2.3 Step tests (rotation): structural decomposition and regeneration (thixotropy)

12.2.4 Temperature-dependent flow behavior (rotation)

12.3 Oscillatory tests

12.3.1 Amplitude sweeps

12.3.2 Frequency sweeps

12.3.3 Time-dependent viscoelastic behavior (oscillation)

12.3.4 Step tests (oscillation): structural decomposition and regeneration (thixotropy)

12.3.5 Temperature-dependent viscoelastic behavior(oscillation)

12.4 Selection of the test type

12.4.1 Behavior at rest

12.4.2 Flow behavior

12.4.3 Structural decomposition and regeneration (thixotropic behavior, e. g. of coatings)

12.5 References

13 Shear tests with powders and bulk solids

13.1 Introduction

13.1.1 Classification of bulk solids according to their fluidizability

13.1.2 Influences on the flow behavior of powder

13.2 Shear test of highly compacted, consolidated bulk solids

13.2.1 Pre-compaction of the bulk solid

13.2.2 Pre-shear of the bulk solid

13.2.3 Shear-to-failure of the bulk solid

13.2.4 Further pre-shear and shear-to-failure cycles

13.2.5 The Mohr´s circles

13.2.6 Further tests with shear cells

13.3 Shear test of slightly compacted bulk solids, using the powder cell

13.3.1 Powder cells

13.3.2 Preparations for powder testing

13.3.3 Preliminary tests for fluidization behavior of powders

13.3.4 Powder testing and the determination of the cohesion strength

13.4 References

14 Rheologists and the historical development of rheology

14.1 Development until the 19 century

14.2 Development between 1800 and 1900

14.3 Development between 1900 and 1949

14.4 Development between 1950 and 1979

14.5 Development since 1980

14.6 References

15 Appendix

15.1 Symbols, signs and abbreviations used

15.2 The Greek alphabet

15.3 Conversion table for units

15.4 References

16 Standards

16.1 ISO standards

16.2 ASTM standards

16.3 DIN, DIN EN, DIN EN ISO and EN standards

16.4 Important standards for users of rotational rheometers

16.5 References

Author

Index

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 references, 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):

The mineral oil is flowing and spreading until it shows a very thin layer finally (

ideal-viscous flow behavior

: see Chapter 2.3.1)

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)

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):

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.

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.

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.

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.

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-) 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

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 to illustrate the velocity distribution of a flowing fluid in the shear gap

Figure 2.2: Laminar flow in the form of planar fluid layers

The sample shows

adhesion

to both plates without any wall-slip effects.

There are

laminar flow

conditions

, i. e. flow can be imagined in the form of layers. Therefore, there is no turbulent flow, i. e. no vortices are appearing.

Accurate calculation of the rheological parameters is only possible if both conditions are met.

Experiment 1: The stack of beer mats

Each one of the individual beer mats represents an individual flowing layer. The beer mats are showing a laminar shape, and therefore, they are able to move in the form of layers along one another (see Figure 2.2). Of course, this process takes place without vortices, thus without showing any turbulent behavior.

The real geometric conditions in rheometer measuring systems (or measuring geometries) are not as simple as in the Two-Plates model. However, if a shear gap is narrow enough, the necessary requirements are largely met and the definitions of the following rheological parameters can be used.

2.2.1Shear stress

Definition of the shear stress:

Equation 2.1

The unit of the shear stress is [Pa], (pascal).

Blaise Pascal (1623 to 1662 [2.1]) was a mathematician, physicist, and philosopher.

Note: [Pa] is also the unit of pressure

Example: In a weather forecast, the air pressure is given as 1070 hPa (hecto-pascal; = 107 kPa).

Some authors take the symbol σ for the shear stress (pronounced: sigma) [2.2][2.3]. However, this symbol is usually used for the tensile stress (see Chapters 4.2.2, 10.8.4.1 and 11.2.14). To avoid confusion and in agreement with the majority of current specialized literature and standards, here, the symbol τ will be used to represent the shear stress (see e. g. ISO 3219-1, ASTM D4092 and DIN 1342-1).

2.2.2Shear rate

Definition of the shear rate:

Equation 2.2

γ̇ (pronounced: gamma-dot); with the velocity v [m/s] and the distance h [m] between the plates, see Figure 2.1.

The unit of the shear rate is [1/s] or [s-1], called “reciprocal seconds”.

Sometimes, the following terms are used as synonyms: strain rate, rate of deformation, shear gradient, velocity gradient.

Previously, the symbol D was often taken instead of γ̇. Nowadays, almost all current standards are recommending the use of γ̇ (see e. g. ISO 3219-1, ASTM D4092). Table 2.1 presents typical shear rate values occurring in industrial practice.

For “Mr. and Ms. Cleverly”

a) Definition of the shear rate using differential variables

Equation 2.3

flowing layers, and the “infinitely” (differentially) small thickness dh of a single flowing layer (see Figure 2.2).

Table 2.1: Typical shear rates of technical processes

Process

Shear rates γ̇ (s-1)

Practical examples

physical aging, long-term creep within days and up to several years

10-8 ... 10-5

solid polymers, asphalt

cold flow

10-8 ... 0.01

rubber mixtures, elastomers

sedimentation of particles

≤ 0.001 ... 0.01

emulsion paints, ceramic suspensions, fruit juices

surface leveling of coatings

0.01 ... 0.1

coatings, paints, printing inks

sagging of coatings, dripping, flow under gravity

0.01 ... 1

emulsion paints, plasters, chocolate melt (couverture)

self-leveling at low-shear conditions in the range of the zero-shear viscosity

≤ 0.1

silicones (PDMS)

mouth sensation

1 ... 10

food

dip coating

1 ... 100

dip coatings, candy masses

applicator roller, at the coating head

1 ... 100

paper coatings

thermoforming

1 ... 100

polymers

mixing, kneading

1 ... 100

rubbers, elastomers

chewing, swallowing

10 ... 100

jelly babies, yogurt, cheese

spreading

10 ... 1000

butter, spreadcheese

extrusion

10 ... 1000

polymer melts, dough,ceramic pastes, tooth paste

pipe flow, capillary flow

10 ... 104

crude oils, paints, juices, blood

mixing, stirring

10 ... 104

emulsions, plastisols,polymer blends

injection molding

100 ... 104

polymer melts, ceramic suspensions

coating, painting, brushing, rolling, blade coating (manually)

100 ... 104

brush coatings, emulsion paints, wall paper paste, plasters

spraying

1000 ... 104

spray coatings, fuels, nose spray aerosols, adhesives

impact-like loading

1000 ... 105

solid polymers

milling pigments in fluid bases

1000 ... 105

pigment pastes for paints and printing inks

rubbing

1000 ... 105

skin creams, lotions, ointments

spinning process

1000 ... 105

polymer melts, polymer fibers

blade coating (by machine), high-speed coating

1000 ... 107

paper coatings, adhesive dispersions

lubrication of engine parts

1000 ... 107

mineral oils, lubricating greases

Figure 2.3: Velocity distribution and shear rate in the shear gap of the Two-Plates model

b) Calculation of shear rates occurring in technical processes

The shear rate values which are given below are calculated using the mentioned formulas and should only be seen as rough estimations. The main aim of these calculations is to get merely an idea of the dimension of the relevant shear rate range.

1) Coating processes: painting, brushing, rolling or blade-coating

Examples

1a) Painting with a brush:

1b) Buttering bread:

1c) Applying emulsion paint with a roller

1d) Blade-coating of adhesive dispersions (e. g. for pressure-sensitive adhesives PSA):

Table 2.2: Shear rates of various kinds of blade-coating processes for adhesive emulsions

Coating process

Application rateAR [g/m2]

Coating velocityv [m/min]

Coating velocityv [m/s]

Layer thicknessh [µm]

Approx. shear rate range γ̇ [s-1]

metering blade

2 to 50

up to 250

up to 4.2

2 to 50

80,000 to 2 mio.

roller blade

15 to 100

up to 100

up to 1.7

15 to 100

10,000 to 100,000

lip-type blade

20 to 100

20 to 50

0.33 to 0.83

20 to 100

3000 to 50,000

present maximum

2 to 100

700

12

2 to 100

120,000 to 6 mio.

future plans

up to 1500

up to 25

250,000 to 12.5 mio.

2) Flow in pipelines, tubes and capillaries

Assumptions: horizontal pipe, steady-state and laminar flow conditions (for information on laminar and turbulent flow see Chapter 3.3.3), ideal-viscous flow, incompressible liquid. According to the Hagen/Poiseuille relation, the following holds for the maximum shear stress τw and the maximum shear rate γ̇w in a pipeline (index w for “at the wall”):

Equation 2.4

Equation 2.5

With the pipe radius R [m]; the pressure difference Δp [Pa] between inlet and outlet of the pipe or along the length L [m] of the measuring section, respectively (Δp must be compensated by the pump pressure); and the volume flow rateV̇ [m3/s]. This relation was named in honor to Gotthilf H. L. Hagen (1797 to 1848) [2.6] and Jean L. M. Poiseuille (1799 to 1869) [2.7].

Examples

2a) Pipeline transport of automotive coatings[2.8][2.9]

2b) Drinking water supply, transport in pipelines [2.10]

2c) Filling bottles using a filling machine (e. g. drinks in food industry):

2d) Squeezing an ointment out of a tube (e. g. pharmaceuticals):

2e) Filling ointment into tubes using a filling machine (e. g. medicine):

2f) Transport process of a stucco gypsum suspension during production of architectural plates [2.11]

3) Sedimentation of particles in suspensions

Assumptions: fluid in a state-at-rest; the particles are almost suspended and therefore they are sinking very, very slowly in a steady-state process (laminar flow, at a Reynolds number Re ≤ 1; more about Re numbers: see Chapter 10.2.2.4b); spherical particles; the values of the weight force FG [N] and the flow resistance force FR [N] of a particle are approximately equal in size.

According to Stokes’ law (Georges G. Stokes, 1819 to 1903 [2.12]):

Equation 2.6

Equation 2.7

with the thickness h of the boundary layer on a particle surface, which is sheared when in motion against the surrounding liquid (the shear rate occurs on both sides of the particle). This equation is valid only if there are neither interactions between the particles, nor between the particles and the surrounding dispersion fluid.

Examples

3a) Sedimentation of sand particles in water

3b) Sedimentation of sand particles in water containing a thickener

Note 1: Calculation of a too high settling velocity if interactions are ignored

Stokes’ sedimentation formula only considers a single particle sinking, undisturbed on a straight path. Therefore, relatively high shear rate values are calculated. These values do not mirror the real behavior of most dispersions, since usually interactions are occurring. The layer thickness h is hardly determinable. We know from colloid science: It depends on the strength of the ionic charge on the particle surface, and on the ionic concentration of the dispersion fluid (interaction potential, zeta-potential) [2.28][2.29]. Due to ionic adsorption, a diffuse double layer of ions can be found on the particle surface. For this reason, in reality the result is usually a considerably lower settling velocity. Therefore, and since the shear rate within the sheared layer is not constant: It is difficult to estimate the corresponding shear rate values occurring with sedimentation processes.

Note 2: Particle size of colloid dispersions, and nano-particles

In literature, as medium diameters of colloid particles are mentioned different specifications: between 10-9 m and 10-6 m (or 1 nm to 1 µm) [2.14][2.25], or between 10-9 m and 10-7 m (or 1 nm to 100 nm) [2.13], or between 10-8 m and 10-6 m (or 10 nm to 1 µm) [2.26]. In ISO 80004-1 of 2015 is stated: Nano-scaled particles are in the range of approximately 1 nm to 100 nm [2.27]. Due to Brownian motion, the nano-particles usually are remaining in a suspended state and do not tend to sedimentation. Above all, the limiting value of the settling particle size depends on the density difference of particles and dispersing fluid.

End of the Cleverly section

2.2.3Viscosity

For all flowing fluids, the molecules are showing relative motion between one another, and this process is always combined with internal frictional forces. Therefore, for all fluids in motion, a certain flow resistance occurs which may be determined in terms of the viscosity. All materials which clearly show flow behavior are referred to as fluids (thus: liquids and gases).

a) Shear viscosity

For ideal-viscous fluids measured at a constant temperature, the value of the ratio of shear stress τ and corresponding shear rate γ̇ is a material constant. Definition of the shear viscosity, in most cases just called “viscosity“:

Equation 2.8

η (eta, pronounced: etah or atah), the unit of the shear viscosity is [Pas], (pascal-seconds).

For low-viscosity liquids, the following unit is usually used:

Sometimes, for highly viscous samples the following units are used:

Sometimes, the term dynamic viscosity is used for η (as in DIN 1342-1). However, some people use the same term to describe either the complex viscosity determined by oscillatory tests, or to mean just the real part of the complex viscosity (the two terms are explained in Chapter 8.2.4b). To avoid confusion and in agreement with the majority of current international authors, here, the terms viscosity or shear viscosity will be used for η. Table 2.3 lists viscosity values of various materials.

The inverse value of viscosity is referred to as fluidityΦ (phi, pronounced: fee or fi) [2.17]. However today, this parameter is rarely used. The following holds:

Equation 2.9

For “Mr. and Ms. Cleverly”

Note 1: Usually, samples with high viscosity values are viscoelastic

Many rheological investigations showed that at values of η > 10 kPas, the elastic portion should no longer be ignored. These kinds of samples should no longer be considered simply viscous only, but visco-elastic (see also Chapter 5).

Note 2: Shear viscosity η and extensional viscosity ηE

End of the Cleverly section

b) Kinematic viscosity

Definition of the kinematic viscosity:

Equation 2.10

ν (ny, pronounced: nu or new), with the density ρ [kg/m3], (rho, pronounced: ro).

Example

Conversion of the values of kinematic viscosity and shear viscosity

Usually, kinematic viscosity values are measured by use of flow cups, capillary viscometers, falling-­ball viscometers or Stabinger viscometers (see Chapters 11.3 to 11.6).

2.3Shear load-dependent flow behavior

Figure 2.4: Double-tube test

Experiment 2: The double-tube test, or the contest of the two fluids (see Figure 2.4)

In the beginning, fluid F1 is flowing faster than fluid F2. With decreasing fluid level, F1 shows reduced flow velocity. F2, however, continues to flow with a hardly visible change in velocity. Therefore finally, F2 empties its tube before F1 does. F1, a wallpaper paste, is an aqueous methylcellulose solution, and F2 is a mineral oil. Flow behavior of polymer solutions such as the wallpaper paste is explained in Chapter 3.3.2.1: shear-thinning flow behavior.

2.3.1Ideal-viscous flow behavior

a) Viscosity law

Formally, ideal-viscous flow behavior is described by the viscosity law:

Equation 2.11

Isaac Newton (1643 to 1727) wrote in 1687 in his textbook Principia [2.18] in a quite inaccurate form about the flow resistance of liquids (“defectus lubricitatus”; see also Chapter 14.1: 1687). Therefore, and especially in English spoken countries, ideal-viscous flow behavior often is also called Newtonian flow behavior. In rheology, both terms have the same meaning. Based on later research on fluid dynamics by D. Bernoulli (in 1738, Hydrodynamica [2.19]), L. Euler (in 1739/1773, Scientia Navalis, and Construction des vaisseaux [2.20]), Joh. Bernoulli (in 1740, Hydraulica [2.21]), and C. L. M. H. Navier (in 1823 [2.22]), finally G. G. Stokes (in 1845 [2.12]) stated the modern form of what was called later Newton’s viscosity law. Therefore sometimes, the viscosity law is also termed the “Newton/Stokes law” [2.23].

Examples of ideal-viscous materials

Low-molecular liquids (and this means here: with a molar mass below 10,000 g/mol) such as water, solvents, mineral oils (without polymer additives), silicone oils, viscosity standard fluids (of course!), blood plasma; but also pure and clean bitumen (without associative superstructures, and at a sufficiently high temperature).

Flow behavior is illustrated graphically by flow curves (previously sometimes also called rheograms) and viscosity curves. Flow curves are showing the interdependence of shear stress τ and shear rate γ̇ . Usually, γ̇ is presented on the x-axis (abscissa), and τ on the y-axis (ordinate). However, τ might also be displayed on the x-axis and γ̇ on the y-axis, but this is meanwhile rarely used in industrial laboratories.

Viscosity curves are derived from flow curves. Usually, η is presented on the y-axis and γ̇ on the x-axis. Alternatively, the function η(τ) can be shown with η on the y-axis and τ on the x-axis, however, this is less frequently carried out in industrial labs.

Figure 2.5: Flow curves of two ideal-viscous fluids

Figure 2.6: Viscosity curves of two ideal-viscous fluids

The values of the shear viscosity of ideal-viscous fluids or Newtonian fluids are independent of the degree and duration of the shear load applied.

Viscosity values of ideal-viscous liquids are often measured using flow cups, capillary viscometers, falling-ball viscometers or Stabinger viscometers (see Chapters 11.3 to 11.6). However, when using these simple devices, the results do not accurately mirror the more complex behavior of non-Newtonian liquids (see for example Chapter 11.3.1.2c: change of shear rates in capillaries).

For “Mr. and Ms. Cleverly”

Figure 2.7: The dashpot model to illustrate ideal-viscous behavior

Figure 2.8: A shock absorber which can be loaded from both sides [2.24]

b) The dashpot model

The dashpot model is used to illustrate the behavior of ideal-viscous fluids or Newtonian liquids, respectively (see Figure 2.7). Mechanically similar examples are gas or liquid shock absorbers (see Figure 2.8).

Ideal-viscous flow behavior, explained by the behavior of a dashpot

1) When under load

Under a constant force, the piston is moving continuously as long as the force is applied, pressing the dashpot fluid (e. g. an oil) through the narrow annular gap between the piston and the cylinder wall of the dashpot. When applying forces of differing strength to the dashpot, it can be observed in all cases: The resulting velocity of the piston is proportional the driving force. The proportionality factor corresponds to the internal friction of the fluid within the dashpot, and therefore, to the fluid’s flow resistance or viscosity, respectively.

2) When removing the load

As soon as the force is removed, the piston immediately stops to move and remains in the position reached.

Summary: Behavior of the dashpot model

Under a constant load, the dashpot fluid is flowing at a constant velocity or deformation rate. After removing the load, the deformation applied to the fluid remains to the full extent. In other words: After a load-and-removal cycle, an ideal-viscous fluid completely remains in the deformed state. This kind of fluids shows absolutely no sign of elasticity.

Comparison: Dashpot fluid and viscosity law

For a dashpot the force/velocity law or flow resistance law holds according to Newton:

Here: F corresponds to the shear stress τ, CN corresponds to the viscosity η, v or ṡ correspond to the shear rate γ̇, and s corresponds to the deformation γ.

Note: Viscous behavior, viscous shear-heating, and lost deformation energy

Deformation energy acting on a fluid leads to relative motion between the molecules. As a consequence, in flowing fluids frictional forces are occurring between the molecules, causing frictional heating, also called viscous heating. For fluids showing ideal-viscous flow behavior, the applied deformation energy is completely used up and can be imagined as deformation work. A part of this thermal energy may heat up the fluid itself and another part may be released as heat to the surrounding environment. During a flow process, the applied deformation energy is used up completely by the fluid, and therefore, it is no longer available for the fluid afterwards, i. e., it is lost. Scientists explain this process as energy dissipation: Here, all the applied deformation energy is lost (dissipated), as it is completely transformed into heat energy.

When the load is removed, the state of deformation which was reached finally by the fluid is remaining to the full extent. Not even a partial elastic re-formation effect can be observed. Therefore here, an irreversible process has taken place since the shape of the sample remains permanently changed finally, after the load is released from the fluid.

If fluids are showing ideal-viscous flow behavior, there are absolutely no or at least no significant interactions between their mostly small molecules or particles. Examples are pure solvents, oils and water; and there might be also some diluted polymer solutions and dispersions, however, only if they show a really very low concentration. Since this kind of fluids does not show any visco-elastic gel-like structure, they may tend to separation, and therefore, effects like sedimentation or flotation may occur in mixtures of fluids and in dispersions.

End of the Cleverly section

2.4Types of flow illustrated by the Two-Plates model

Figure 2.9 illustrates seven different types of laminar flow which may occur in a shear gap: (1) state-at-rest; (2) homogeneous laminar flow, showing a constant shear rate (see also Chapter 2.2); (3) wall-slip, the sample displays very pronounced cohesion while slipping along the walls without adhesion; (4) “plastic behavior”, only a part of the sample is sheared homogeneously (see also Chapter 3.3.4.2c); (5) transient behavior,showing a start-up effect as time-dependent transition until a steady-state viscosity value is reached (occurring above all at low shear rates; see also Chapter 3.3.1b); (6) shear-banding,exhibiting here pronounced cohesion of the medium band (see also Chapter 9.2.2); (7) shear-banding, showing here three different flow velocities or viscosities, respectively (see also here Chapter 9.2.2)

Figure 2.9: Different appearances of laminar flow in a shear gap, illustrated by use of the Two-Plates model

2.5References

[2.1]Pascal, B., Récit de la grande éxperience de l’équilibre des liqueurs, 1649; Traités de l’équilibre des liqueurs et de la pesenteur de la masse de l’air, Paris, 1663

[2.2]Barnes, H. A., Hutton, J. F., Walters, K., An introduction to rheology, Elsevier, Amsterdam, 1989; Barnes, H. A., A handbook of elementary rheology, Univ. of Wales Inst. Non-Newtonian Fluid Mechanics, Aberystwyth, 2000;