EN ISO 3219-2:2021

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)

Le présent document spécifie les principes généraux de la rhéométrie rotative et oscillatoire.
Des informations détaillées sont fournies dans l’Annexe A. D’autres informations de base sont couvertes dans les parties suivantes de la série ISO 3219, qui sont actuellement en préparation.

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

General Information

• Status: Published
• Publication Date: 25-May-2021
• Withdrawal Date: 29-Nov-2021
• ICS: 83.080.01 - Plastics in general
• Technical Committee: CEN/TC 139 - Paints and varnishes
• Drafting Committee: CEN/TC 139 - Paints and varnishes
• Current Stage: 6060 - Definitive text made available (DAV) - Publishing
• Start Date: 26-May-2021
• Completion Date: 26-May-2021
• Ref Project: SIST EN ISO 3219-2:2021 - Rheology - Part 2: General principles of rotational and oscillatory rheometry (ISO 3219-2:2021)

Relations

• Replaces: EN ISO 3219:1994 - Plastics - Polymers/resins in the liquid state or as emulsions or dispersions - Determination of viscosity using a rotational viscometer with defined shear rate (ISO 3219:1993)
• Effective Date: 08-Jun-2022

Overview

EN ISO 3219-2:2021 - "Rheology - Part 2: General principles of rotational and oscillatory rheometry (ISO 3219-2:2021)" is a CEN-adopted international standard that specifies the general principles for performing rotational and oscillatory rheometry. The document defines measurement concepts, symbols and terminology, and the main elements of a measuring assembly. Detailed information is provided in Annex A, and further background is covered in other parts of the ISO 3219 series (in preparation).

Keywords: ISO 3219-2:2021, rheology standard, rotational rheometry, oscillatory rheometry, measuring geometries, viscosity measurement.

Key topics and technical requirements

The standard sets out foundational requirements and definitions used across rotational and oscillatory rheometry:

• Scope and normative references: builds on ISO 3219-1 (terms and definitions).
• Terms and definitions: clear definitions such as measuring gap, gap width, no-slip condition, wall slip, absolute and relative measuring geometries.
• Symbols and units: standardized symbols for shear stress, shear strain, complex viscosity, complex shear modulus, torque, angular velocity and more.
• Measuring principles:
  • Rotational rheometry: torque-angular velocity relationships and viscosity evaluation.
  • Oscillatory rheometry: strain, stress, complex modulus and phase relationships.
• Measuring assembly and accessories:
  • Temperature control systems and thermal covers.
  • Measuring geometries: absolute geometries (e.g., cone‑plate, coaxial cylinders) and relative geometries (including plate‑plate), with guidance on gap width and flow-field coefficients.
  • Optional items: covers, solvent traps, stepped plates and others.
• Annex A (informative): information on rheometry and flow-field patterns for practical understanding.

Practical applications

This standard is used to ensure consistency, reproducibility and comparability of rheological measurements in:

• Quality control and R&D for polymers, paints, coatings, varnishes and other complex fluids.
• Characterization of viscosity, shear stress, shear rate, storage and loss moduli using rotational and oscillatory tests.
• Instrument selection, method development and reporting of rheological data.

Keywords: viscosity measurement, shear rate, complex modulus, rheometer calibration, measuring geometry.

Who should use this standard

• Test laboratories and quality control teams in polymer, coatings and chemical industries.
• Rheometer manufacturers and instrument engineers.
• Research scientists performing rheological characterization.
• Standards committees and regulatory bodies harmonizing test methods.

Related standards

• ISO 3219-1 (terms and definitions) - normative reference.
• Additional parts of the ISO 3219 series (under development) provide expanded test methods and background.

This standard provides the essential, standardized framework for rotational and oscillatory rheometry, improving measurement reliability across industry and research.

Standards Content (Sample)

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

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.

Contents Page
European foreword . 3

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.
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
ISO 3219-2:2021(E)
© 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: [phone]
Email: [e-mail]
Website: www.iso.org
Published in Switzerland
ii © ISO 2021 – All rights reserved

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 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

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
h
H
cc
H
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 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.
cp
ISO 3219-2:2021(E)
3.3
flow field coefficient
geometric factor
k
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:
M
η=⋅k
Ω
−3
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
k
γ
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.
−1
Note 3 to entry: The strain factor k has units of reciprocal radians (rad ).
γ
3.9
shear stress factor
k
τ
proportionality factor between the torque M and the shear stress τ for absolute measuring geometries
(3.7)
−3
Note 1 to entry: The shear stress factor k has units of reciprocal cubic metres (m ).
τ
2 © ISO 2021 – All rights reserved

ISO 3219-2:2021(E)
4 Symbols
Table 1 — Symbols and units
Meaning Symbol Unit
*
Absolute value of the complex shear modulus Pa
G
Absolute value of the complex viscosity * Pa·s
η
−2
ϕ
Acceleration of the angular deflection rad·s
Amplitude of the angular deflection of the motor * rad
ϕ
M,0
*
Amplitude of angular deflection of torque transducer rad
ϕ
D,0
Amplitude of the angular deflection rad
ϕ
−1
Amplitude of the angular velocity ϕ rad·s
−1
Amplitude of the shear rate  s
γ
Amplitude of the shear strain γ 1
Amplitude of the shear stress τ Pa
Amplitude of the torque M N·m
−2
*
Angular acceleration of motor rad·s
ϕ
M
−2
*
Angular acceleration of torque transducer rad·s

ϕ
D
Angular deflection φ rad
*
Angular deflection of motor rad
ϕ
M
Angular deflection of sample * rad
ϕ
P
*
Angular deflection of torque transducer rad
ϕ
D
−1 −1
Angular frequency ω rad·s or s
−1
Angular velocity across the measuring gap ω(r) rad·s
−1
Angular velocity (presented in brackets: as the time derivative of the angular Ω,  ϕ rad·s
()
deflection)
−1
*
Angular velocity of motor rad·s
ϕ
M
−1
Angular velocity of torque transducer * rad·s

ϕ
D
Coefficient of bearing friction D N·m·s
L
Coefficient of friction D N·m·s
*
Complex angular deflection rad
ϕ
*
Complex shear modulus Pa
G
Complex torque * N·m
M
*
Complex viscosity Pa·s
η
Cone angle α ° or rad
Deflection path s m
tanζ
Drive loss factor 1
Drive phase angle ζ rad
Face factor c 1
L
−3
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 3219-2:2021(E)
Table 1 (continued)
Meaning Symbol Unit
Gap width h m
Gap width defined by the coaxial cylinders geometry H m
cc
Gap width defined by the cone-plate geometry H m
cp
−1
Geometry compliance C rad·(N·m)
G
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
M
P
Shear force F N
Shear loss modulus, viscous shear modulus G′′ Pa
Shear modulus G Pa
Shear plane A m
−1
Shear rate factor rad
k

γ
−1

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
−3
Shear stress factor m
k
τ
Shear viscosity η Pa·s
−1
Strain factor k rad
γ
Temperature T °C or K
Time t s
Torque M N·m
*
Torque applied by motor N·m
M
M
*
Torque caused by bearing friction N·m
M
L
*
Torque caused by transducer inertia N·m
M
I
*
Torque measured by transducer N·m
M
m
−1
Torsional compliance of the measurement system C rad·(N·m)
−1
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

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):
F
τ = (1)
A
where
τ is the shear stress, in pascals;
F is the shear force, in newtons;
A is the shear plane, in square metres.
v

γ = (2)
h
where

γ
is the shear rate, in reciprocal seconds;
v is the velocity, in metres per second;
h is the gap width, in metres.
ISO 3219-2:2021(E)
Based on the Newtonian law of viscosity, the shear viscosity can be calculated using Formula (3):
τ
η= (3)

γ
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):
s
γ = (4)
h
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

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 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).
τ
′
G = cosδ (9)
γ
τ
G″= sinδ (10)
γ
The quotient of the shear loss modulus G′′ and shear storage modulus G′ is the dimensionless loss
factor tanδ, see Formula (11):
G″
tanδ = (11)
G′
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):
*
G
*
η = (12)
ω
*
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

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 3219-2:2021(E)
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,
droplets, air bubbles) are considered. 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 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. Derivations of the basic flows for the absolute measuring geometries are presented in A.2.
6.3.2 Absolute measuring geometries
6.3.2.1 Coaxial cylinders measuring geometry
6.3.2.1.1 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.
Key
1 measuring cup (outer cylinder)
2 measuring bob (inner cylinder)
3 sample chamber
Figure 5 — Schematic drawing of a coaxial cylinders measuring geometry
10 © ISO 2021 – All rights reserved

ISO 3219-2:2021(E)
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.3.2. 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.
6.3.2.1.2 Calculation methods

Calculations of the shear stress τ and shear rate γ 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 6.3.3.2.
ISO 3219-2:2021(E)
This document confines itself solely to Formula (13):
ττ+
ττ== (13)
rep
where
τ is the shear stress at the outer radius of the inner cylinder, in pascals;
τ is the shear stress at the inner radius of the outer cylinder, in pascals;
Formula (14) applies for the representative shear stress:
1+δ 1
τ ==kM⋅ ⋅ ⋅M (14)
rep τ
2 2
2⋅δπ2 ⋅⋅LR ⋅c
1 L
where
k is the shear stress factor for the conversion of torque into shear stress, in reciprocal cubic metres;
τ
R is the outer radius of the inner cylinder, in metres;
δ is the ratio of the inner radius of the outer cylinder and outer radius of the inner cylinder;
L is the length of the inner cylinder, in metres;
M is the torque, in newton multiplied by metres;
c is the face factor, dimensionless.
L
The face factor depends on the measuring geometry and on the rheological properties of the sample
and shall be determined experimentally.
Formula (15) applies to the representative shear rate, γ :
rep
2 2
1+δ 1+δ

γ ==kn⋅⋅⋅ΩΩ= 2π⋅ (15)

rep γ
2 2
δ −1 δ −1
where
k is the shear rate factor for the conversion of angular velocity into shear rate, in reciprocal radians;

γ
n is the rotational speed, in reciprocal seconds;
Ω is the angular velocity, in radians per second.
This results in the following for a standard geometry with δ = 1,084 7, given in Formulae (16) and (17):
M
τ =⋅0,0446 (16)
rep
R

γ =⋅77,46 n (17)
rep
12 © ISO 2021 – All rights reserved

ISO 3219-2:2021(E)
Key
1 sample
R radius of the shaft
R outer radius of the inner cylinder
R inner radius of the outer cylinder
β opening angle of the face on the bottom of the inner cylinder
L length of the inner cylinder
L′ distance between the lower edge of the inner cylinder and the bottom of the outer cylinder
L′′ immersed shaft length
Figure 7 — Standard measuring geometry for coaxial cylinders
For the standard measuring geometry for coaxial cylinders shown in Figure 7, the face factor c (drag
L
coefficient for the face surface correction that takes into account the torque acting at the end surfaces
of the measuring geometry) was determined experimentally and has a value of c = 1,1 for samples
L
with Newtonian flow behaviour for ratios given in Formula (18). Deviations from 1,1 are possible and
require experimental determination of the face factor.
For the standard measuring geometry for coaxial cylinders, the following ratios apply:
R R
′
L L L″
0 2
==31,,,==10,,31δβ== ,,0847 =°120 (18)
R R R R R
11 1 1 1
where
L′ is the distance between the lower edge of the inner cylinder and the bottom of the outer cylin-
der, in metres;
L′′ is the immersed shaft length, in metres;
R is the radius of the shaft, in metres;
R is the inner radius of the outer cylinder, in metres;
β is the opening angle of the face on the bottom of the inner cylinder, in degrees.
ISO 3219-2:2021(E)
6.3.2.1.3 Advantages and disadvantages
— Advantages:
— determination of absolute measured values;
— handling errors due to overfilling and underfilling are smaller than for cone-plate and plate-
plate measuring geometries;
— depending on the gap width, also suitable for coarsely dispersed samples (rule of thumb: gap at
least 10 times larger than the diameter of the dispersed material, e.g. particles, droplets);
— almost no evaporation influence due to small boundary surface compared to the sample volume;
— viscosity range from low to high viscosities can be covered by varying the dimensions of the
coaxial cylinders measuring geometry;
— low distribution of shear rates in the measuring gap compared to the plate-plate measuring
geometry.
— Disadvantages:
— depending on the sensitivity of the measuring device and the measuring geometry that is used,
a larger sample volume is required than with cone-plate and plate-plate measuring geometries;
— generally higher mass inertia compared to cone-plate and plate-plate measuring geometries;
— more laborious cleaning compared to cone-plate and plate-plate measuring geometries;
— more severe damage to the sample structure when inserting the rotor into the sample compared
to the plate-plate measuring geometry with gap setting controlled by normal force;
— lower heating and cooling rates can be realized and therefore longer temperature control times
are required due to the larger sample volume and the larger dimensions of the measuring
geometry compared to cone-plate and plate-plate measuring geometries;
— danger of air bubble entrapment when inserting the rotor into the sample.
6.3.2.2 Double-gap measuring geometry
6.3.2.2.1 Description of the measuring geometry
The measuring geometry is a variant of a coaxial measuring geometry and consists of a measuring
cup with an inner insert and a hollow cylinder that are positioned coaxially relative to one another, as
shown in Figure 8.
With the double-gap measuring geometry, the shear stress τ and shear rate γ in the measuring gap are
not constant, but instead decrease from the inside to the outside. The calculation assumes a
representative measured value within the measuring gap.
14 © ISO 2021 – All rights reserved

ISO 3219-2:2021(E)
Key
1 measuring cup with inner insert
2 hollow cylinder with vent holes
3 sample chamber
Figure 8 — Schematic drawing of a double-gap measuring geometry
ISO 3219-2:2021(E)
6.3.2.2.2 Calculation method
Key
1 sample
L effective length of the hollow cylinder
R outer radius of the inner insert
R inner radius of the hollow cylinder
R outer radius of the hollow cylinder
R inner radius of the measuring cup
Figure 9 — Double-gap measuring geometry
For the double-gap measuring geometry, the following ratios apply based on Figure 9:
R R
2 4
δ == ≤11, 5 (19)
R R
1 3
L
≥3 (20)
R
The following applies for the representative shear stress:
1+δ
τ = ⋅M (21)
rep
2 2 2
4πδ⋅+LR Rc⋅
()
3 2 L
The representative shear rate is calculated analogously to the coaxial cylinders measuring geometry:
2 2
1+δ 1+δ

γ = ⋅=Ω ⋅⋅2π n (22)
rep
2 2
δ −1 δ −1
where
16 © ISO 2021 – All rights reserved

ISO 3219-2:2021(E)
δ is the radius ratio;
L is the effective length of the hollow cylinder, in metres;
R is the outer radius of the inner insert, in metres;
R is the inner radius of the hollow cylinder, in metres;
R is the outer radius of the hollow cylinder, in metres;
R is the inner radius of the measuring cup, in metres;
c is the face factor, dimensionless.
L
This face factor depends on the measuring geometry and on the rheological properties of the sample
and shall be determined experimentally.
6.3.2.2.3 Advantages and disadvantages
See 6.3.2.1.3. Additionally, or as deviations, the following applies.
— Advantages:
— extension of the achievable measuring range for low-viscosity samples due to the larger
measuring area compared to the coaxial cylinders measuring geometry;
— more suitable for oscillatory measurements as the inertia moment of the double-gap measuring
geometry is significantly lower than that of the cylinder measuring geometry for the same outer
diameter of the measuring bob.
— Disadvantages:
— a filling error has a greater impact compared to the coaxial cylinders measuring geometry;
— only suitable for low-viscosity samples.
6.3.2.3 Cone-plate measuring geometry
6.3.2.3.1 Description of the measuring geometry
The measuring geometry consists of a cone and plate (see Figure 10).
ISO 3219-2:2021(E)
Key
1 sample chamber
2 cone
3 plate
Figure 10 — Schematic drawing of a cone-plate measuring geometry
The angle between the cone and the plate (cone angle) shall be as small as possible, and under no
circumstances greater than 5°. The influence of friction between the cone tip and plate is avoided by
the flattened cone tip (truncated cone). The flattened cone tip and angle create the specified measuring
gap for the individual cone. See Figure 11 for details. The extent to which the cone tip decreases, i.e. the
distance between the flattened cone tip and the plate, has an impact on the measuring result.
NOTE There are also cone geometries with non-flattened cone tips.
Key
1 sample
R radius of the cone
α cone angle
H distance between flattened cone tip and plate
cp
Figure 11 — Cone-plate measuring geometry
6.3.2.3.2 Calculation method
The derivation of shear stress or shear rate for this cone-plate measuring geometry is presented
in A.3.3. For cone angles > 3°, the exact formulae in A.3.3 and Formulae (23) and (24) shall be used.
18 © ISO 2021 – All rights reserved

ISO 3219-2:2021(E)
If α ≤ 0,05 rad (i.e. α ≤ 3°), Formulae (23) and (24) can be used for calculating the shear stress and shear
rate:
3M
τ = (23)
2πR
where
M is the torque, in newton multiplied by metres;
R is the radius of the cone, in metres.
Ω

γ= (24)
α
where
α is the angle between the cone and plate, in radians;
Ω is the angular velocity, in radians per second.
6.3.2.3.3 Advantages and disadvantages
— Advantages:
— determination of absolute measured values;
— for smaller cone angles, the shear strain or shear rate in the cone gap can be considered to be
sufficiently constant;
— faster cleaning compared to coaxial cylinders and double-gap measuring geometries;
— lower filling amount than with coaxial cylinders measuring geometries;
— viscosity range from low to high viscosities can be covered by varying the dimensions of the
cone-plate measuring geometry;
— low inertia moment compared to coaxial cylinders measuring geometries, i.e. better detection
of short-term effects, e.g. in oscillatory, creep and relaxation experiments;
— shorter temperature control times and higher heating and cooling rates compared to coaxial
cylinders and double-gap measuring geometries.
— Disadvantages:
— gap width significantly smaller than with coaxial cylinders measuring geometries, which limits
the maximum size of the dispersed material (e.g. particles, droplets);
— may be used in dispersed systems only if the diameter of the dispersed material (e.g. particles,
droplets) is a maximum of 1/10 of the distance between flattened cone tip and plate, H (see
cp
Figure 11);
— strong influence of potential solvent evaporation due to a larger boundary surface relative to
the sample volume (the use of a solvent trap minimizes the effect);
— higher impact due to underfilling and overfilling compared to coaxial cylinders and double-gap
measuring geometries;
— high influence on the sample structure is possible through trimming;
ISO 3219-2:2021(E)
— greater influence of a change of the gap width through temperature changes;
— greater influence of changes in the surface roughness, e.g. through abrasive samples or wrong
cleaning procedure;
— unsuitable for sedimenting samples;
— emptying of the measuring gap is possible.
6.
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