Rheology - Part 2: General principles of rotational and oscillatory rheometry (ISO 3219-2:2021)

This document specifies the general principles of rotational and oscillatory rheometry.
Detailed information is presented in Annex A. Further background information is covered in subsequent
parts of the ISO 3219 series, which are currently in preparation.

Rheologie - Teil 2: Allgemeine Grundlagen der Rotations- und Oszillationsrheometrie (ISO 3219-2:2021)

Dieses Dokument legt die allgemeinen Grundlagen der Rotations- und Oszillationsrheometrie fest.
Detaillierte Informationen sind im Anhang A enthalten. Weitere Hintergrundinformationen werden in Folgeteilen der Normenreihe ISO 3219, die aktuell in Vorbereitung sind, enthalten sein.

Rhéologie - Partie 2: Principes généraux de la rhéométrie rotative et oscillatoire (ISO 3219-2:2021)

Reologija - 2. del: Splošna načela za rotacijsko in oscilacijsko reometrijo (ISO 3219-2:2021)

General Information

Status
Published
Public Enquiry End Date
02-Apr-2020
Publication Date
14-Jun-2021
Technical Committee
Current Stage
6060 - National Implementation/Publication (Adopted Project)
Start Date
07-Jun-2021
Due Date
12-Aug-2021
Completion Date
15-Jun-2021

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SLOVENSKI STANDARD
SIST EN ISO 3219-2:2021
01-julij-2021
Nadomešča:
SIST EN ISO 3219:1997

Reologija - 2. del: Splošna načela za rotacijsko in oscilacijsko reometrijo (ISO 3219

-2:2021)

Rheology - Part 2: General principles of rotational and oscillatory rheometry (ISO 3219-

2:2021)

Rheologie - Teil 2: Allgemeine Grundlagen der Rotations- und Oszillationsrheometrie

(ISO 3219-2:2021)

Rhéologie - Partie 2: Principes généraux de la rhéométrie rotative et oscillatoire (ISO

3219-2:2021)
Ta slovenski standard je istoveten z: EN ISO 3219-2:2021
ICS:
83.080.01 Polimerni materiali na Plastics in general
splošno
SIST EN ISO 3219-2:2021 en,fr,de

2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

---------------------- Page: 1 ----------------------
SIST EN ISO 3219-2:2021
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SIST EN ISO 3219-2:2021
EN ISO 3219-2
EUROPEAN STANDARD
NORME EUROPÉENNE
May 2021
EUROPÄISCHE NORM
ICS 83.080.01 Supersedes EN ISO 3219:1994
English Version
Rheology - Part 2: General principles of rotational and
oscillatory rheometry (ISO 3219-2:2021)

Rhéologie - Partie 2: Principes généraux de la Rheologie - Teil 2: Allgemeine Grundlagen der

rhéométrie rotative et oscillatoire (ISO 3219-2:2021) Rotations- und Oszillationsrheometrie (ISO 3219-

2:2021)
This European Standard was approved by CEN on 9 March 2021.

CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this

European Standard the status of a national standard without any alteration. Up-to-date lists and bibliographical references

concerning such national standards may be obtained on application to the CEN-CENELEC Management Centre or to any CEN

member.

This European Standard exists in three official versions (English, French, German). A version in any other language made by

translation under the responsibility of a CEN member into its own language and notified to the CEN-CENELEC Management

Centre has the same status as the official versions.

CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia,

Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway,

Poland, Portugal, Republic of North Macedonia, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and

United Kingdom.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION
EUROPÄISCHES KOMITEE FÜR NORMUNG
CEN-CENELEC Management Centre: Rue de la Science 23, B-1040 Brussels

© 2021 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 3219-2:2021 E

worldwide for CEN national Members.
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SIST EN ISO 3219-2:2021
EN ISO 3219-2:2021 (E)
Contents Page

European foreword ....................................................................................................................................................... 3

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SIST EN ISO 3219-2:2021
EN ISO 3219-2:2021 (E)
European foreword

This document (EN ISO 3219-2:2021) has been prepared by Technical Committee ISO/TC 35 "Paints

and varnishes" in collaboration with Technical Committee CEN/TC 139 “Paints and varnishes” the

secretariat of which is held by DIN.

This European Standard shall be given the status of a national standard, either by publication of an

identical text or by endorsement, at the latest by November 2021, and conflicting national standards

shall be withdrawn at the latest by November 2021.

Attention is drawn to the possibility that some of the elements of this document may be the subject of

patent rights. CEN shall not be held responsible for identifying any or all such patent rights.

This document supersedes EN ISO 3219:1994.

According to the CEN-CENELEC Internal Regulations, the national standards organizations of the

following countries are bound to implement this European Standard: Austria, Belgium, Bulgaria,

Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland,

Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Republic of

North Macedonia, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and the

United Kingdom.
Endorsement notice

The text of ISO 3219-2:2021 has been approved by CEN as EN ISO 3219-2:2021 without any

modification.
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SIST EN ISO 3219-2:2021
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SIST EN ISO 3219-2:2021
INTERNATIONAL ISO
STANDARD 3219-2
First edition
2021-05
Rheology —
Part 2:
General principles of rotational and
oscillatory rheometry
Rhéologie —
Partie 2: Principes généraux de la rhéométrie rotative et oscillatoire
Reference number
ISO 3219-2:2021(E)
ISO 2021
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SIST EN ISO 3219-2:2021
ISO 3219-2:2021(E)
COPYRIGHT PROTECTED DOCUMENT
© ISO 2021

All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may

be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting

on the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address

below or ISO’s member body in the country of the requester.
ISO copyright office
CP 401 • Ch. de Blandonnet 8
CH-1214 Vernier, Geneva
Phone: +41 22 749 01 11
Email: copyright@iso.org
Website: www.iso.org
Published in Switzerland
ii © ISO 2021 – All rights reserved
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SIST EN ISO 3219-2:2021
ISO 3219-2:2021(E)
Contents Page

Foreword ........................................................................................................................................................................................................................................iv

1 Scope ................................................................................................................................................................................................................................. 1

2 Normative references ...................................................................................................................................................................................... 1

3 Terms and definitions ..................................................................................................................................................................................... 1

4 Symbols .......................................................................................................................................................................................................................... 3

5 Measuring principles ....................................................................................................................................................................................... 4

5.1 General ........................................................................................................................................................................................................... 4

5.2 Rotational rheometry ........................................................................................................................................................................ 5

5.3 Oscillatory rheometry ....................................................................................................................................................................... 6

6 Measuring assembly ......................................................................................................................................................................................... 8

6.1 General ........................................................................................................................................................................................................... 8

6.2 Temperature control systems .................................................................................................................................................... 9

6.3 Measuring geometries ...................................................................................................................................................................... 9

6.3.1 General...................................................................................................................................................................................... 9

6.3.2 Absolute measuring geometries ......................................................................................................................10

6.3.3 Relative measuring geometries ........................................................................................................................20

6.4 Selected optional accessories ..................................................................................................................................................24

6.4.1 Cover with or without solvent trap ...............................................................................................................24

6.4.2 Passive and active thermal covers .................................................................................................................25

6.4.3 Stepped plates .................................................................................................................................................................26

Annex A (informative) Information on rheometry and flow field patterns ..............................................................27

Bibliography .............................................................................................................................................................................................................................45

© ISO 2021 – All rights reserved iii
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SIST EN ISO 3219-2:2021
ISO 3219-2:2021(E)
Foreword

ISO (the International Organization for Standardization) is a worldwide federation of national standards

bodies (ISO member bodies). The work of preparing International Standards is normally carried out

through ISO technical committees. Each member body interested in a subject for which a technical

committee has been established has the right to be represented on that committee. International

organizations, governmental and non-governmental, in liaison with ISO, also take part in the work.

ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of

electrotechnical standardization.

The procedures used to develop this document and those intended for its further maintenance are

described in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the

different types of ISO documents should be noted. This document was drafted in accordance with the

editorial rules of the ISO/IEC Directives, Part 2 (see www .iso .org/ directives).

Attention is drawn to the possibility that some of the elements of this document may be the subject of

patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of

any patent rights identified during the development of the document will be in the Introduction and/or

on the ISO list of patent declarations received (see www .iso .org/ patents).

Any trade name used in this document is information given for the convenience of users and does not

constitute an endorsement.

For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and

expressions related to conformity assessment, as well as information about ISO's adherence to

the World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT), see

www .iso .org/ iso/ foreword .html.

This document was prepared by Technical Committee ISO/TC 35, Paints and varnishes, Subcommittee

SC 9, General test methods for paints and varnishes, in collaboration with the European Committee for

Standardization (CEN) Technical Committee CEN/TC 139, Paints and varnishes, in accordance with the

Agreement on technical cooperation between ISO and CEN (Vienna Agreement), and in cooperation

with ISO/TC 61, Plastics, SC 5, Physical-chemical properties.

This document cancels and replaces ISO 3219:1993, which have been technically revised. The main

changes compared to the previous editions are as follows:
— plate-plate measuring geometry has been added;
— relative measuring geometries have been added;
— oscillatory rheometry has been added.
A list of all parts in the ISO 3219 series can be found on the ISO website.

Any feedback or questions on this document should be directed to the user’s national standards body. A

complete listing of these bodies can be found at www .iso .org/ members .html.
iv © ISO 2021 – All rights reserved
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SIST EN ISO 3219-2:2021
INTERNATIONAL STANDARD ISO 3219-2:2021(E)
Rheology —
Part 2:
General principles of rotational and oscillatory rheometry
1 Scope

This document specifies the general principles of rotational and oscillatory rheometry.

Detailed information is presented in Annex A. Further background information is covered in subsequent

parts of the ISO 3219 series, which are currently in preparation.
2 Normative references

The following documents are referred to in the text in such a way that some or all of their content

constitutes requirements of this document. For dated references, only the edition cited applies. For

undated references, the latest edition of the referenced document (including any amendments) applies.

ISO 3219-1, Rheology — Part 1: General terms and definitions for rotational and oscillatory rheometry

3 Terms and definitions

For the purposes of this document, the terms and definitions given in ISO 3219-1 and the following

apply.

ISO and IEC maintain terminological databases for use in standardization at the following addresses:

— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at http:// www .electropedia .org/
3.1
measuring gap
space between the boundary surfaces of the measuring geometry
3.2
gap width
distance between the boundary surfaces of the measuring geometry

Note 1 to entry: The symbol h refers to a gap width that can be varied (e.g. plate-plate measuring geometry); the

symbol H refers to a gap width which is not variable and which is defined by the relevant measuring geometry.

H is the gap width of the coaxial-cylinders geometry. H is the gap width of the cone-plate geometry.

cc cp

Note 2 to entry: The distance between the boundary surfaces is given by the difference in the radii (coaxial

cylinders), the cone angle (cone-plate) or the distance between the two plates.

Note 3 to entry: In cone-plate measuring geometries, the gap width varies as a function of the radius across the

measuring geometry. The value H is the distance between the flattened cone tip and the plate.

© ISO 2021 – All rights reserved 1
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SIST EN ISO 3219-2:2021
ISO 3219-2:2021(E)
3.3
flow field coefficient
geometric factor
quotient of the shear stress factor (3.9) k and the strain factor (3.8) k
τ γ

Note 1 to entry: The flow field coefficient k relates the angular velocity Ω and torque M to the shear viscosity η of

the fluid as given by the following formula:
η=⋅k

The flow field coefficient k is expressed in radians per cubic metre (rad·m ). It can be calculated from the shape

and dimensions of an absolute measuring geometry (3.7).
3.4
no-slip condition

presence of a relative velocity of zero between a boundary surface and the immediately adjacent fluid

layer
3.5
wall slip

presence of a non-zero relative velocity between a boundary surface and the immediately adjacent fluid

layer
3.6
relative measuring geometry

measuring geometry for which the flow profile and thus the rheological parameters cannot be

calculated

Note 1 to entry: For relative measuring geometries, the viscosity shall not be given in pascal multiplied by

seconds (Pa⋅s) except in the case of plate-plate measuring geometries if the correction referred to in 6.3.3.1.2 is

used.
3.7
absolute measuring geometry

measuring geometry for which the flow profile and thus the rheological parameters can be calculated

exactly for the entire sample, regardless of its flow properties
3.8
strain factor

proportionality factor between the angular deflection φ and shear strain γ for absolute measuring

geometries (3.7)

Note 1 to entry: The absolute value of the strain factor corresponds to the absolute value of the shear rate factor.

The latter is the proportionality factor between the shear rate γ and the angular velocity Ω.

Note 2 to entry: This factor is called the shear rate factor in the rotation test and the strain factor in the oscillatory

test.
Note 3 to entry: The strain factor k has units of reciprocal radians (rad ).
3.9
shear stress factor

proportionality factor between the torque M and the shear stress τ for absolute measuring geometries

(3.7)

Note 1 to entry: The shear stress factor k has units of reciprocal cubic metres (m ).

2 © ISO 2021 – All rights reserved
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SIST EN ISO 3219-2:2021
ISO 3219-2:2021(E)
4 Symbols
Table 1 — Symbols and units
Meaning Symbol Unit
Absolute value of the complex shear modulus Pa
Absolute value of the complex viscosity * Pa·s
ϕ
Acceleration of the angular deflection rad·s
Amplitude of the angular deflection of the motor * rad
M,0
Amplitude of angular deflection of torque transducer rad
D,0
Amplitude of the angular deflection rad
Amplitude of the angular velocity ϕ rad·s
Amplitude of the shear rate  s
Amplitude of the shear strain γ 1
Amplitude of the shear stress τ Pa
Amplitude of the torque M N·m
Angular acceleration of motor rad·s
ϕ
Angular acceleration of torque transducer rad·s
Angular deflection φ rad
Angular deflection of motor rad
Angular deflection of sample * rad
Angular deflection of torque transducer rad
−1 −1
Angular frequency ω rad·s or s
Angular velocity across the measuring gap ω(r) rad·s

Angular velocity (presented in brackets: as the time derivative of the angular Ω,  ϕ rad·s

deflection)
Angular velocity of motor rad·s
Angular velocity of torque transducer * rad·s
Coefficient of bearing friction D N·m·s
Coefficient of friction D N·m·s
Complex angular deflection rad
Complex shear modulus Pa
Complex torque * N·m
Complex viscosity Pa·s
Cone angle α ° or rad
Deflection path s m
tanζ
Drive loss factor 1
Drive phase angle ζ rad
Face factor c 1
Flow field coefficient, geometric factor k rad·m
Frequency f Hz

NOTE The parameters marked with an * refer to complex-valued parameters whose real part is denoted by ′ and

imaginary part by ′′.
© ISO 2021 – All rights reserved 3
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SIST EN ISO 3219-2:2021
ISO 3219-2:2021(E)
Table 1 (continued)
Meaning Symbol Unit
Gap width h m
Gap width defined by the coaxial cylinders geometry H m
Gap width defined by the cone-plate geometry H m
Geometry compliance C rad·(N·m)
Imaginary part of the complex viscosity η′′ Pa·s
Imaginary unit i 1
Loss angle, phase angle δ rad
Loss factor tanδ 1
Moment of inertia I N·m·s
Real part of the complex viscosity η′ Pa·s
−1 −1
Rotational speed n s or min
Sample torque * N·m
Shear force F N
Shear loss modulus, viscous shear modulus G′′ Pa
Shear modulus G Pa
Shear plane A m
Shear rate factor rad
Shear rate, shear deformation rate γ s
Shear storage modulus, elastic shear modulus G′ Pa
Shear strain, shear deformation γ 1 or %
Shear stress τ Pa
Shear stress factor m
Shear viscosity η Pa·s
Strain factor k rad
Temperature T °C or K
Time t s
Torque M N·m
Torque applied by motor N·m
Torque caused by bearing friction N·m
Torque caused by transducer inertia N·m
Torque measured by transducer N·m
Torsional compliance of the measurement system C rad·(N·m)
Velocity v m·s

NOTE The parameters marked with an * refer to complex-valued parameters whose real part is denoted by ′ and

imaginary part by ′′.
5 Measuring principles
5.1 General

There are rotational tests, oscillatory tests and various step tests. The different tests can be combined

with one another.
4 © ISO 2021 – All rights reserved
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SIST EN ISO 3219-2:2021
ISO 3219-2:2021(E)

These can be carried out using various measuring types: controlled deformation (CD), controlled rate

(CR) or controlled stress (CS).
5.2 Rotational rheometry

In the basic rotational test, the sample is subjected to constant or variable loading in one direction.

The shear viscosity η is calculated from the measured data. The corresponding mechanical input

and response parameters are listed in Tables A.1 and A.3. The basic parameters of the test can be

represented schematically in terms of the two-plates model. An infinitesimal element of the measuring

geometry is considered in this subclause (see Figure 1). The two-plates model consists of two parallel

plates, each with a surface area A and with a gap width h, between which the sample is located. The

velocity of the lower plate is zero (v = 0). The upper plate is moved by a defined shear force F, which

results in a velocity v. It is assumed that the sample between the plates consists of layers that move at

different velocities of between v = 0 and v.
Key
1 sample
v velocity
A shear plane
h gap width
F shear force

Figure 1 — Two-plate model with a simplified schematic representation of the basic parameters

of a rotational test

With this model, the following parameters are calculated using Formulae (1) to (3):

τ = (1)
where
τ is the shear stress, in pascals;
F is the shear force, in newtons;
A is the shear plane, in square metres.
γ = (2)
where
is the shear rate, in reciprocal seconds;
v is the velocity, in metres per second;
h is the gap width, in metres.
© ISO 2021 – All rights reserved 5
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SIST EN ISO 3219-2:2021
ISO 3219-2:2021(E)

Based on the Newtonian law of viscosity, the shear viscosity can be calculated using Formula (3):

η= (3)
where η is the shear viscosity, in pascal multiplied by seconds.
5.3 Oscillatory rheometry

In the basic oscillatory test, the sample is stimulated with an angular deflection or torque amplitude at

a given oscillation frequency. The resulting response oscillates with the same frequency and is

characterized by an amplitude and phase shift. The corresponding mechanical input and response

parameters are listed in Tables A.2 and A.3. Parameters such as the shear storage modulus G′ (elastic

shear modulus), the shear loss modulus G′′ (viscous shear modulus), the absolute value of the complex

viscosity η and the loss factor tan δ can be calculated from the measured data in order to characterize

the viscoelastic behaviour. The mathematical principles are presented in A.3. The basic parameter of

the test can be represented schematically in terms of the two-plates model (see Figure 2).

Key
1 sample
s deflection path
φ deflection angle
A shear plane
h gap width
F shear force

Figure 2 — Two-plate model with a simplified schematic representation of the basic parameters

of an oscillatory test
With this model, the following parameters can be calculated using Formula (4):
γ = (4)
where
γ is the shear strain, dimensionless;
s is the deflection path, in metres;
h is the gap width, in metres.
6 © ISO 2021 – All rights reserved
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SIST EN ISO 3219-2:2021
ISO 3219-2:2021(E)

In the oscillatory test, the shear strain γ varies sinusoidally as a function of time t, see Figure 3. The

associated shear stress τ is shifted within the viscoelastic range by the loss angle δ at the same angular

frequency ω. Formulae (5) and (6) apply:
γγ()tt= sin()ω (5)
where
γ is the amplitude of the shear strain, dimensionless;
ω is the angular frequency, in radians per second;
t is the time, in seconds.
ττtt=+sin ωδ (6)
() ()
where
τ is the amplitude of the shear stress, in pascals;
δ is the loss angle, in radians.
Key
γ shear strain
τ shear stress
ω angular frequency
t time
δ loss angle

Figure 3 — Schematic representation of the shear strain and shear stress functions for an

oscillatory test

NOTE Degrees (°) are commonly used in practice as the unit for the loss angle δ. The following conversion

applies: 2π rad = 360°.

In the case of ideal elastic behaviour (in accordance with Hooke’s law), the loss angle has a value

of δ = 0°, i.e. the shear strain and shear stress are always in phase. In the case of ideal viscous behaviour

(in accordance with Newton’s law), the loss angle has a value of δ = π/2 = 90°, i.e. the shear stress curve

is 90° ahead of the shear strain curve.
© ISO 2021 – All rights reserved 7
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SIST EN ISO 3219-2:2021
ISO 3219-2:2021(E)

Using Hooke’s elasticity law, the complex shear modulus G* and its absolute value G can be calculated

using Formulae (7) and (8):
τ t
G = (7)
γ ()t
* 22
GG=+′″G (8)
where
G* is the complex shear modulus, in pascals;
G′ is the shear storage modulus, in pascals;
G′′ is the shear loss modulus, in pascals;
G* describes the overall viscoelastic behaviour.

This can be separated into an elastic component G′ (shear storage modulus) and a viscous component G′′

(shear loss modulus) using Formulae (9) and (10).
G = cosδ (9)
G″= sinδ (10)

The quotient of the shear loss modulus G′′ and shear storage modulus G′ is the dimensionless loss

factor tanδ, see Formula (11):
tanδ = (11)

The ratio of the absolute value of the complex shear modulus G* and the angular frequency ω is the

absolute value of the complex viscosity η*, see Formula (12):
η = (12)

where η is the absolute value of the complex viscosity, in pascal multiplied by seconds.

6 Measuring assembly
6.1 General

The rheological properties are investigated using a measuring system consisting of a measuring device

(viscometer or rheometer) and a measuring geometry (e.g. cone-plate).

The viscometer can only measure the viscosity in rotation (viscometry). This means that the viscosity

function of the sample can be determined as a function of the parameters of time, temperature, shear

rate, shear stress and others such as pressure.

With a rheometer, it is possible to carry out all basic tests in rotation and oscillation (rheometry).

Alongside the viscosity function, the viscoelastic properties can be determined, e.g. shear storage

modulus and shear loss modulus.
8 © ISO 2021 – All rights reserved
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SIST EN ISO 3219-2:2021
ISO 3219-2:2021(E)

A measuring assembly, consisting of a measuring device, a measuring geometry and optional

accessories, is shown in Figure 4. The measuring device and individual components, such as the

temperature control system, can be computer-controlled.
Figure 4 — Example of a measuring assembly

The sample to be investigated is located in a measuring gap where a defined flow profile is generated

in the sample. A necessary prerequisite for this is a sufficiently small gap width. When viscometers

or rheometers are used, they shall be able to impose or detect torque or rotational speed/angular

deflection. The imposed parameter shall be adjustable both in time-dependent and time-independent

manners.

For viscometric measurements, all viscometers are principally suitable, regardless of how the drive

and/or detection unit are supported. For measurements in oscillation, rheometers shall be used that

have the lowest possible internal friction in the drive or detection unit.

To cover the broadest possible range of applications, the viscometer or rheometer shall be able to work

with different measuring geometries. The range of the torques or angular deflections, that result and

the measuring range that can be achieved, depend on the measuring system. The type of measuring

device and measuring geometry to be selected depends on the sample.
6.2 Temperature control systems

A temperature control system consists of one or more temperature control components for heating and/

or cooling, including the required media (e.g. air, water, liquid nitrogen) and the necessary connections

(e.g. hoses and insulation for these hoses).

The rheological properties of the sample are temperature-dependent. As a result, measures such as

controlling of the sample temperature and its measurement with one or more temperature sensors in

the immediate vicinity of the sample are required.

The temperature of the sample shall be kept constant as a function of time during the measurement

period.
6.3 Measuring geometries
6.3.1 General

A measuring geometry consists of two parts that form a sample chamber where the sample is located. A

measuring geometry consists of a rotor and a stator or of two rotors.
© ISO 2021 – All rights reserved 9
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SIST EN ISO 3219-2:2021
ISO 3219-2:2021(E)
The meas
...

SLOVENSKI STANDARD
oSIST prEN ISO 3219-2:2020
01-marec-2020
[Not translated]

Rheology - Part 2: General principles of rotational and oscillatory rheometry (ISO/DIS

3219-2:2020)

Rheologie - Teil 2: Allgemeine Grundlagen der Rotations- und Oszillationsrheometrie

(ISO/DIS 3219-2:2020)

Rhéologie - Partie 2: Principes généraux de la rhéométrie rotative et oscillatoire(ISO/DIS

3219-2:2020)
Ta slovenski standard je istoveten z: prEN ISO 3219-2
ICS:
83.080.01 Polimerni materiali na Plastics in general
splošno
oSIST prEN ISO 3219-2:2020 en,fr,de

2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

---------------------- Page: 1 ----------------------
oSIST prEN ISO 3219-2:2020
---------------------- Page: 2 ----------------------
oSIST prEN ISO 3219-2:2020
DRAFT INTERNATIONAL STANDARD
ISO/DIS 3219-2
ISO/TC 35/SC 9 Secretariat: BSI
Voting begins on: Voting terminates on:
2020-01-20 2020-04-13
Rheology —
Part 2:
General principles of rotational and oscillatory rheometry
Rhéologie —
Partie 2: Principes généraux du rhéométrie rotational et oscillatoire
ICS: 83.080.01
Member bodies are requested to consult relevant national interests in ISO/TC
61/SC 5 before casting their ballot to the e-Balloting application.
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oSIST prEN ISO 3219-2:2020
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Contents Page

Foreword ......................................................................................................................................................................... iv

1 Scope ....................................................................................................................................................................1

2 Normative references ....................................................................................................................................1

3 Terms and definitions ....................................................................................................................................1

4 Measuring principles ......................................................................................................................................3

4.1 General ................................................................................................................................................................3

4.2 Rotational rheometry .....................................................................................................................................3

4.3 Oscillatory rheometry ....................................................................................................................................4

5 Measuring assembly .......................................................................................................................................7

5.1 Measuring device .............................................................................................................................................7

5.2 Temperature control systems .....................................................................................................................8

5.3 Measuring geometries ...................................................................................................................................9

5.3.1 General ................................................................................................................................................................9

5.3.2 Absolute measuring geometries ................................................................................................................9

5.3.3 Relative measuring geometries ............................................................................................................... 20

5.4 Selected optional accessories ................................................................................................................... 25

5.4.1 Cover with or without solvent trap ........................................................................................................ 25

5.4.2 Passive and active thermal covers ......................................................................................................... 26

5.4.3 Stepped plates ................................................................................................................................................ 27

Annex A (normative) Information on rheometry and flow field patterns ............................................ 28

A.1 Rheological input and response parameters for rotation and oscillation ............................... 28

A.2 Flow field patterns ....................................................................................................................................... 29

A.2.1 General ............................................................................................................................................................. 29

A.2.2 Coaxial cylinders measuring geometry ................................................................................................ 29

A.2.3 Cone-plate measuring geometry ............................................................................................................. 34

A.2.4 Plate-plate measuring geometry ............................................................................................................. 36

A.3 Oscillatory rheometry ................................................................................................................................. 38

A.3.1 General ............................................................................................................................................................. 38

A.3.2 Calculation basis ........................................................................................................................................... 42

A.3.3 Working equations for different device types ................................................................................... 43

A.4 Symbols and units ......................................................................................................................................... 47

Bibliography ................................................................................................................................................................. 50

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Foreword

ISO (the International Organization for Standardization) is a worldwide federation of national

standards bodies (ISO member bodies). The work of preparing International Standards is normally

carried out through ISO technical committees. Each member body interested in a subject for which a

technical committee has been established has the right to be represented on that committee.

International organizations, governmental and non-governmental, in liaison with ISO, also take part in

the work. ISO collaborates closely with the International Electrotechnical Commission (IEC) on all

matters of electrotechnical standardization.

The procedures used to develop this document and those intended for its further maintenance are

described in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the

different types of ISO documents should be noted. This document was drafted in accordance with the

editorial rules of the ISO/IEC Directives, Part 2 (see www.iso.org/directives).

Attention is drawn to the possibility that some of the elements of this document may be the subject of

patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of

any patent rights identified during the development of the document will be in the Introduction and/or

on the ISO list of patent declarations received (see www.iso.org/patents).

Any trade name used in this document is information given for the convenience of users and does not

constitute an endorsement.

For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and

expressions related to conformity assessment, as well as information about ISO's adherence to the

World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT), see

www.iso.org/iso/foreword.html.

This document was prepared by Technical Committee ISO/TC 35, Paints and varnishes, Subcommittee

SC 9, General test methods for paints and varnishes, in cooperation with ISO/TC 61, Plastics, SC 5,

Physical-chemical properties.

This document cancels and replaces ISO 3219:1993, ISO 2884-1:1999 und ISO 2884-2:2003, which have

been technically revised. The main changes compared to the previous editions are as follows:

 Plate-plate measuring geometry has been added;
 Relative measuring geometries have been added;
 Oscillatory rheometry has been added;

 The information on cone-and-plate viscometer operated at a high rate of shear (ISO 2884-1:1999)

and on disc or ball viscometer operated at a specified speed (ISO 2884-2:2003) has been integrated

in the ISO 3219 standards series.
A list of all parts in the ISO 3219 series can be found on the ISO website.

Any feedback or questions on this document should be directed to the user’s national standards body. A

complete listing of these bodies can be found at www.iso.org/members.html.
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oSIST prEN ISO 3219-2:2020
DRAFT INTERNATIONAL STANDARD ISO/DIS 3219-2:2020(E)
Rheology — Part 2: General principles of rotational and
oscillatory rheometry
1 Scope

This document specifies the general principles of rotational and oscillatory rheometry. Detailed

information is presented in Annex A.
2 Normative references

The following documents are referred to in the text in such a way that some or all of their content

constitutes requirements of this document. For dated references, only the edition cited applies. For

undated references, the latest edition of the referenced document (including any amendments) applies.

ISO 3219-1, Rheology — Part 1: General terms and definitions for rotational and oscillatory rheometry

3 Terms and definitions

For the purposes of this document, the terms and definitions given in ISO 3219-1 and the following

apply.

ISO and IEC maintain terminological databases for use in standardization at the following addresses:

 ISO Online browsing platform: available at http://www.iso.org/obp
 IEC Electropedia: available at http://www.electropedia.org/
3.1
measuring gap
space between the boundary surfaces of the measuring geometry
3.2
gap width
h, H , H
cc cp
distance between the boundary surfaces of the measuring geometry

Note 1 to entry: The symbol h refers to a gap width that can be varied (e.g. plate-plate measuring geometry); the

symbol H refers to a gap width defined by the relevant measuring geometry (cc – coaxial cylinders, cp – cone-

plate).

Note 2 to entry: The distance between the boundary surfaces is given by the difference in the radii (cc), the cone

angle (cp) or the distance between the two plates.

Note 3 to entry: In cone-plate measuring geometries, the gap width varies as a function of the radius across the

measuring geometry. The value H is the distance between the flattened cone tip and the plate.

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3.3
flow field coefficient
geometric factor
quotient of the shear stress factor k and the strain factor k
τ γ

Note 1 to entry: The flow field coefficient k relates the angular velocity Ω and torque M to the shear viscosity η of

the fluid as given by the following equation:
𝑀𝑀
η =𝑘𝑘∙

The flow field coefficient k is expressed in radians per cubic metre (rad·m ). It can be calculated from the shape

and dimensions of an absolute measuring geometry.
3.4
no-slip condition

presence of a relative velocity of zero between a boundary surface and the immediately adjacent fluid

layer
3.5
wall slip

presence of a non-zero relative velocity between a boundary surface and the immediately adjacent fluid

layer
3.6
relative measuring geometry

measuring geometry for which the flow profile and thus the rheological parameters cannot be

calculated

Note 1 to entry: For relative measuring geometries, the viscosity shall not be given in pascal multiplied by

seconds (Pa⋅s) except in the case of plate-plate measuring geometries if the correction referred to in 5.3.3.1.2 is

used.
3.7
absolute measuring geometry

measuring geometry for which the flow profile and thus the rheological parameters can be calculated

exactly for the entire sample, regardless of its flow properties
3.8
strain factor

proportionality factor between the angular deflection φ and shear strain γ for absolute measuring

geometries

Note 1 to entry: The absolute value of the strain factor corresponds to the absolute value of the shear rate factor.

The latter is the proportionality factor between the shear rate 𝛾𝛾̇ and the angular velocity Ω.

Note 2 to entry: This factor is called the shear rate factor in the rotation test and the strain factor in the

oscillatory test.
Note 3 to entry: The strain factor k has units of reciprocal radians (rad ).
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3.9
shear stress factor

proportionality factor between the torque M and the shear stress τ for absolute measuring geometries

Note 1 to entry: The shear stress factor k has units of reciprocal cubic metres (m ).

4 Measuring principles
4.1 General

There are rotational tests, oscillatory tests and various step tests. The different tests can be combined

with one another.

These can be carried out using various measuring types: controlled deformation (CD), controlled rate

(CR) or controlled stress (CS). The material behaviour is described by several measurement points. The

prerequisites for recording the individual measuring points are described in detail in ISO 3219-3 [2].

Error analysis is described in ISO 3219-4 [3] and ISO 3219-5 [4].
4.2 Rotational rheometry

In the basic rotational test, the sample is subjected to constant or variable loading in one direction. The

shear viscosity 𝜂𝜂 is calculated from the measured data. The corresponding mechanical input and

response parameters are listed in Tables A.1 and A.3. The basic parameters of the test can be

represented schematically in terms of the two-plates model. An infinitesimal element of the measuring

geometry is considered here (Figure 1). The two-plates model consists of two parallel plates, each with

a surface area A and with a gap width h, between which the sample is located. The velocity of the lower

plate is zero (v = 0). The upper plate is moved by a defined shear force F, which results in a velocity v. It

is assumed that the sample between the plates consists of layers that move at different velocities of

between v = 0 and v.
Key
v velocity
A shear plane
h gap width
F shear force

Figure 1 — Two-plates model with a simplified schematic representation of the basic

parameters of a rotational test

With this model, the following parameters are calculated using Formulae (1) to (3):

𝐹𝐹
(1)
𝜏𝜏 =
𝐴𝐴
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where
τ is the shear stress, in pascals;
F is the shear force, in newtons;
A is the shear plane, in square metres.
𝑣𝑣
𝛾𝛾̇= (2)
where
𝛾𝛾̇ is the shear rate, in reciprocal seconds;
𝑣𝑣 is the velocity, in metres per second;
h is the gap width, in metres.

Based on the Newtonian law of viscosity, the shear viscosity can be calculated using Formula 3:

𝜏𝜏
η =
(3)
𝛾𝛾̇
where
η is the shear viscosity, in pascal multiplied by seconds.
4.3 Oscillatory rheometry

In the basic oscillatory test, the sample is stimulated with an angular deflection or torque amplitude at a

given oscillation frequency. The resulting response oscillates with the same frequency and is

characterized by an amplitude and phase shift. The corresponding mechanical input and response

parameters are listed in Tables A.2 and A.3. Parameters such as the shear storage modulus 𝐺𝐺 (elastic

shear modulus), the shear loss modulus 𝐺𝐺 (viscous shear modulus), the absolute value of the complex

viscosity |𝜂𝜂 | and the loss factor tan 𝛿𝛿 can be calculated from the measured data in order to characterize

the viscoelastic behaviour. The mathematical principles are presented in A.3. The basic parameter of

the test can be represented schematically in terms of the two-plates model (Figure 2).

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Key
s deflection path
ϕ deflection angle
h gap width
F shear force

Figure 2 — Two-plates model with a simplified schematic representation of the basic

parameters of an oscillatory test
With this model, the following parameters can be calculated using Formula 4:
𝑠𝑠
𝛾𝛾 =
(4)
where
γ is the shear strain, dimensionless;
s is the deflection path, in metres;
h is the gap width, in metres.

In the oscillatory test, the shear strain γ varies sinusoidally as a function of time t, see Figure 3. The

associated shear stress 𝜏𝜏 is shifted within the viscoelastic range by the loss angle δ at the same angular

frequency 𝜔𝜔. Formulae 5 and 6 apply:
𝛾𝛾(𝑡𝑡) = 𝛾𝛾 sin(𝜔𝜔 𝑡𝑡) (5)
𝜏𝜏(𝑡𝑡) = 𝜏𝜏 sin(𝜔𝜔 𝑡𝑡 +𝛿𝛿) (6)
where
𝛾𝛾 is the amplitude of the shear strain, dimensionless;
𝜏𝜏 is the amplitude of the shear stress, in pascals;
𝛿𝛿 is the loss angle, in radians;
ω is the angular frequency, in radians per second;
t is the time, in seconds.
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Key
γ shear strain
𝜏𝜏 shear stress
ω angular frequency
t time
𝛿𝛿 loss angle

Figure 3 — Schematic representation of the shear strain and shear stress functions for an

oscillatory test

NOTE Degrees (°) are commonly used in practice as the unit for the loss angle 𝛿𝛿. The following conversion

applies: 2𝜋𝜋 rad = 360°.

In the case of ideal elastic behaviour (in accordance with Hooke’s law), the loss angle has a value

of 𝛿𝛿 = 0≡ 0°, i.e. the shear strain and shear stress are always in phase. In the case of ideal viscous

behaviour (in accordance with Newton’s law), the loss angle has a value of 𝛿𝛿 =𝜋𝜋/2≡ 90°, i.e. the shear

stress curve is 90° ahead of the shear strain curve.

Using Hooke’s elasticity law, the complex shear modulus G* and its absolute value |𝐺𝐺 | can be calculated

using Formulae 7 and 8:
𝜏𝜏(𝑡𝑡)
𝐺𝐺 = (7)
𝛾𝛾(𝑡𝑡)
2 2
(8)
|𝐺𝐺 | = 𝐺𝐺′ + 𝐺𝐺′′
where
G* is the complex shear modulus, in pascals;
G‘ is the shear storage modulus, in pascals;
G‘‘ is the shear loss modulus, in pascals.
G* describes the overall viscoelastic behaviour.

This can be separated into an elastic component G‘ (shear storage modulus) and a viscous

component G‘‘ (shear loss modulus) using Formulae 9 and 10.
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𝜏𝜏
𝐺𝐺 = cos𝛿𝛿
(9)
𝛾𝛾
𝜏𝜏
𝐺𝐺 = sin𝛿𝛿
(10)
𝛾𝛾

The quotient of the shear loss modulus G‘‘ and shear storage modulus G‘ is the loss factor tan𝛿𝛿, see

Formula 11:
𝐺𝐺′′
(11)
tan𝛿𝛿 =
𝐺𝐺′
where
tan𝛿𝛿 is the loss factor, dimensionless.

The ratio of the absolute value of the complex shear modulus G* and the angular frequency 𝜔𝜔 is the

absolute value of the complex viscosity 𝜂𝜂 , see Formula 12:
|𝐺𝐺 |
(12)
| |
𝜂𝜂 =
𝜔𝜔
where
| |

𝜂𝜂 is the absolute value of the complex viscosity, in pascal multiplied by seconds;

𝜔𝜔 is the angular frequency, in radians per second.
5 Measuring assembly
5.1 Measuring device

The rheological properties are investigated using a measuring device (viscometer or rheometer).

The viscometer can only measure the viscosity in rotation (viscometry). This means that the viscosity

function of the sample can be determined as a function of the parameters of time, temperature, shear

rate, shear stress and others such as pressure.

With a rheometer, it is possible to carry out all basic tests in rotation and oscillation (rheometry).

Alongside the viscosity function, the viscoelastic properties can be determined, e.g. shear storage

modulus and shear loss modulus.

A measuring assembly, consisting of a measuring device, a measuring geometry and optional

accessories, is shown in Figure 4. The measuring device and individual components, such as the

temperature control system, can be computer-controlled.
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Figure 4 — Example of a measuring assembly

The sample to be investigated is located in a measuring gap where a defined flow profile is generated in

the sample. A necessary prerequisite for this is a sufficiently small gap width (see also ISO 3219-4).

When viscometers or rheometers are used, they shall be able to impose or detect torque or rotational

speed/angular deflection. The imposed parameter shall be adjustable both in time-dependent and time-

independent manners.

For viscometric measurements, all viscometers are principally suitable, regardless of how the drive

and/or detection unit are supported. For measurements in oscillation, rheometers shall be used that

have the lowest possible internal friction in the drive or detection unit.

To cover the broadest possible range of applications, the viscometer or rheometer shall be able to work

with different measuring geometries. The range of the torques or angular deflections, that result and

the measuring range that can be achieved, depend on the measuring system. The type of measuring

device and measuring geometry to be selected depends on the sample; see ISO 3219-3 for further

information.
5.2 Temperature control systems

A temperature control system consists of one or more temperature control components for heating

and/or cooling, including the required media (e.g. air, water, liquid nitrogen) and the necessary

connections (e.g. hoses and insulation for these hoses).

NOTE There are different temperature control systems available, e.g. Peltier elements, liquid thermostats,

cryostats, convection or radiation temperature chambers; see ISO 3219-3 for further information.

The rheological properties of the sample are temperature-dependent. As a result, measures such as

controlling of the sample temperature and its measurement with one or more temperature sensors in

the immediate vicinity of the sample are required.

The temperature of the sample shall be kept constant as a function of time during the measurement

period; see ISO 3219-4 and ISO 3219-5 for further information.
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5.3 Measuring geometries
5.3.1 General

A measuring geometry consists of two parts that form a sample chamber where the sample is located. A

measuring geometry consists of a rotor and a stator or of two rotors.

The measuring geometry shall be selected in such a way that its dimensions are suitable for the

expected viscosity range and viscoelastic properties of the sample. With regard to its gap width, the

measuring geometry shall also be selected in such a way that possible heterogeneities in the sample

(e.g. particles, drops, air bubbles) are considered; see ISO 3219-4. The magnitude of these

heterogeneities is to be determined in advance using suitable methods (e.g. microscopy, laser

diffraction, sieving or determination of fineness of grind). The application range, advantages and

disadvantages of each measuring geometry are described in more detail in ISO 3219-3.

The absolute and relative measuring geometries of a rotational viscometer or rheometer are described

below.

Coaxial cylinders, double-gap and cone-plate measuring geometries are absolute measuring geometries.

All the others are relative measuring geometries.

In the case of an absolute measuring geometry, the flow profile within the complete sample can be

calculated exactly, regardless of its flow properties. This applies under the condition of laminar flow

and without slip (wall slip or slip between flow layers).

In the case of relative measuring geometries apart from plate-plate measuring geometries, calculation

of the flow profile is only possible if the flow properties of the sample are known.

In practice, approximations are also used for absolute measuring geometries and thus corrections are

carried out. The influence of these corrections on the measured values is negligible relative to the total

measurement error, see ISO 3219-4 and ISO 3219-5.

Derivations of the basic flows for the absolute measuring geometries are presented in A.2.

5.3.2 Absolute measuring geometries
5.3.2.1 Coaxial cylinders measuring geometry
5.3.2.1.1 Description of the measuring geometry

The measuring geometry consists of a measuring cup (i.e. the outer cylinder) and a measuring bob (i.e.

the inner cylinder with shaft, as shown in Figure 5). The measuring bob can serve as a rotor and the

measuring cup as a stator (Searle principle), or vice versa (Couette principle); see Figure 6. If not

indicated otherwise, the Searle principle is assumed below.
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Key
1 measuring cup (outer cylinder)
2 measuring bob (inner cylinder)
3 sample chamber
Figure 5 — Schematic drawing of a coaxial cylinders measuring geometry
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a) Couette principle b) Searle principle
Key
1 measuring cup (outer cylinder)
2 measuring bob (inner cylinder)
3 sample chamber
4 drive
5 measuring sensor
Figure 6 — Searle and Couette principles

The flow profile occurring in the measuring gap of the cylinder measuring geometry is calculated

according to A.2.2. The measuring gap is the space between the shell surface of the measuring bob with

a radius R and the lateral surface of the measuring cup with a radius R and the same length L; see

1 2
Figure 7.
5.3.2.1.2 Calculation methods

Calculations of the shear stress τ and shear rate 𝛾𝛾̇ are ideally based on representative values that do not

occur at the inner radius of the outer cylinder R or outer radius of the inner cylinder R of the

2 1

measuring geometry but at a particular geometric position within the measuring gap. τ is defined as

rep

the arithmetic mean of the shear stresses at the outer cylinder τ and inner cylinder τ , which is a good

1 2

approximation for the given ratio of radii (δ ≤ 1,1). For larger values and thus for relative measuring

geometries see 5.3.3.2.
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This document confines itself solely to this approximation:
𝜏𝜏 +𝜏𝜏
1 2
𝜏𝜏 =𝜏𝜏 = (13)
rep
The following applies for the representative shear stress:
1 +𝛿𝛿 1
𝜏𝜏 =𝑘𝑘 ∙𝑀𝑀 = ∙ ∙𝑀𝑀 (14)
rep τ
2 2
2 ∙ 𝛿𝛿
2 𝜋𝜋∙𝐿𝐿∙𝑅𝑅 ∙𝑐𝑐
The following applies for the representative shear rate:
2 2
1 +𝛿𝛿 1 +𝛿𝛿
(15)
𝛾𝛾̇=𝑘𝑘 ∙Ω = ∙Ω = ∙ 2𝜋𝜋∙𝑛𝑛
rep 𝛾𝛾̇2 2
𝛿𝛿 − 1 𝛿𝛿 − 1
This results in the following for a standard geometry with δ = 1,084 7:
𝑀𝑀
𝜏𝜏 = 0,044 6∙
(16)
rep
𝑅𝑅
𝛾𝛾̇= 77,46 ∙𝑛𝑛
(17)
rep
where, taking Figure 7 into account,

k is the shear stress factor for the conversion of torque into shear stress, in reciprocal cubic

metres;
𝑘𝑘 is the shear rate factor for the
...

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