Rheology

1 Introduction ................................................................................................................................ 2

2 Theoretical foundation .................................................................................................................. 2

2.1 Fundamental terms in rheology.............................................................................................. 2

2.2 Linear-viscoelastic behavior ................................................................................................. 4

2.3 Measuring technique ........................................................................................................... 7

2.3.1 Oscillation measurements ........................................................................................ 7

2.3.2 Rotational experiments ............................................................................................ 8

2.3.3 Tension experiment .............................................................................................. 10

2.3.4 Relaxation experiment ........................................................................................... 10

2.4 Borderline behavior of matter and rheological models .............................................................. 10

2.4.1 Elastic behavior ................................................................................................... 11

2.4.2 Plastic behavior .................................................................................................... 12

2.4.3 Viscous behavior .................................................................................................. 13

2.4.4 Viscoelastic behavior ............................................................................................ 14

2.4.5 Characterization by flow and viscosity curves ............................................................ 16

2.5 Time-dependent rheological behavior ................................................................................... 17

2.6 Rheometry (measuring technique) ........................................................................................ 18

3 Experimental ............................................................................................................................ 19

3.1 Conduction of rotational measurements ................................................................................. 19

3.2 Time-dependent change of viscosity ..................................................................................... 20

3.3 Oscillation measurements to determine the viscoelastic behavior ............................................... 20

4 Questions ................................................................................................................................. 21

5 Literature ................................................................................................................................. 21

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1 Introduction

Rheology is the science which describes, explains, quantifies and applies the phenomena appearing

while bodies or liquids are deformed or while they flow. According to Ziabicki [1], the rheological

behavior is responsible for the drawability and thus of fundamental importance for the spinnability of

liquid systems. Further examples of applied rheology are found in various areas in natural science

and engineering. [2-7]

1. Colors and varnish (brushability, storage)

2. Polymer solutions and melts (polymer extrusion and spinning

3. Characterization of polymers (statement about molecular weights and molecular weight

distribution

4. Manufacture of high performance materials (ceramics)

5. Flow behavior of food (ketchup, convenience sauce)

6. Cosmetics and sanitary products (tooth paste, cream, shampoos)

7. Geo-rheology (simulation of volcanic flow)

8. Medicine (hemorheology)

9. Pharmaceutical products

10. Electronics

In the following paragraphs the basic principles of rheology, which are described in literature [1 –

20] are addressed.

2 Theory

2.1 Fundamental terms in rheology

To characterize the flow behavior of substances, they are subjected to defined forces and the

resulting deformations are described in detail in dependence of different parameters. Depending on

the direction of the affecting force, the relevant cases for rheometry are distinguished: elongation,

compression strain and shear strain. The effect occurring during the shear experiment of a liquid and

the associated fundamental terms in rheology can be explained with the aid of a two-plate-model

(Figure 1). In this model a liquid is located between two parallel plates of the area A. The upper plate

is moved relative to the lower static plate with a constant velocity. Thereby the power F needs to be

applied due to the internal friction. This shear strain causes a laminar flow of the velocity v which

linearly decreases from the moving to the static plate.

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Fig.1: Two-plate-model. The resulting shear rate gradient is also called deformation velocity or shear velocity:

γγ==

=

=

dtd

dydx

dtd

dtdx

dyd

dydv

(1)

velocity gradient = shear rate

Deformation: αγ tan=≡dydx

[-] (2)

Deformation velocity: dtdγγ ≡ [1/s] (3)

When the force applied during the shearing experiment is related to the plate area A, the shear stress

τ is obtained, which is connected with the deformation velocity γ by the shear viscosity η.

Shear stress: γητ ⋅==AF

[Pa] (4)

Stationary shear viscosity: γτη

≡ [Pa·s] (5)

According to the dependence of the stationary shear viscosity on the shear rate, flow behavior can be

characterized as Newtonian, shear thinning and shear thickening (dilatant). Newtonian flow

behavior is present, when the viscosity is independent of the shear rate. If the viscosity decreases

with increasing shear rate, the behavior is called shear thinning, this is typical for polymer melts

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and polymer solutions. When the viscosity increases with increasing shear rate the flow behavior is

referred to as shear thickening. Examples of viscosity curves are given in 2.4.5.

For a Newtonian liquid, a direct proportionality exists between shear stress and deformation rate,

whereas for an ideal Hook-type body a direct proportionality between shear stress and deformation is

present, i.e. Hook’s law is in force. The proportionality constant is the modulus of shear G:

Shear stress: γτ ⋅= G [Pa] (6) It should be noted, that also elastic systems exist which to not apply to Hook’s law (e. g. rubbery-

elastic materials). A general definition of elastic behavior is given in 2.4.1.

2.2 Linear-viscoelastic behavior

Many materials do not show exclusively viscous or elastic behavior but a combination of these

characteristics. This is referred to as viscoelastic behavior. The theory of linear viscoelasticity

describes the rheological phenomena of polymer solutions and melts, which is connected to the

preservation of the resting structure/state of the temporary network of entangled molecular chains.

The theory of non-linear viscoelasticity describes viscoelastic phenomena, which are connected with

depletion of the temporary network structure. The rheological material value functions for describing

linear viscoelasticity are determined with the aid of oscillatory experiments. Thereby, the latent state

of the sample is not disturbed, which permits to separately display viscous and elastic behavior. At a

deformation-controlled oscillatory measurement, the sample, which is located in a gap between two

plates, is loaded by a periodic deformation γ(t) and thereby a periodic strain τ(t) is induced, which

shows a displacement of phase δ relative to the preset deformation.

preset deformation resulting strain (response of the system)

}cos{0 t⋅⋅= ωγγ }cos{0 δωττ +⋅⋅= t ω radial frequency of the oscillation [rad/s] 𝜏0 strain amplitude [Pa] 𝛾0 deformation amplitude [-] Based on the displacement of phase δ, rheological behavior can be classified:

• elastic behavior: 0=δ

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• viscous behavior: 2πδ =

• viscoelastic behavior: 20 πδ <<

Fig. 2: Course of strain and deformation during oscillatory measurements. To simplify rheological calculations, complex values are introduced. The transition to complex

values is performed by extending strain and deformation with the respective imaginary part. This

allows the transition from trigonometric functions to the complex e-function, thus simplifying

calculations considerably. The following rheological values are defined:

Complex shear strain:

)}(exp{})sin{}(cos{* 00 δωτδωδωττ +⋅⋅⋅=+⋅⋅++⋅≡ titit (7) Complex deformation:

}exp{})sin{}(cos{* 00 titit ⋅⋅⋅=⋅⋅+⋅≡ ωγωωγγ (8) Complex deformation velocity:

}exp{*)(* 0 tiidtd

⋅⋅⋅⋅⋅=≡ ωγωγγ (9)

Viscoelastic behavior can be described by the complex modulus G*, which is defined as the quotient

of complex strain and complex deformation.

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Complex modulus:

'''}exp{***

0

0 GiGiG ⋅+=⋅⋅=≡ δγτ

γτ

(10)

Here, G’ is the storage modulus and G’’ is the loss modulus. The storage modulus represents the

degree of elastic behavior, i.e. the energy, which is reversibly stored by restoring forces. The loss

modulus represents the amount of viscous behavior, i.e. the energy which irreversibly dissipated due

to viscous flow. For G’ and G’’ applies:

Storage modulus: δγτ cos'

0

0 ⋅=G [Pa] (11)

Loss modulus: δγτ sin''

0

0 ⋅=G [Pa] (12)

The ratio of loss and storage modulus is the dissipation factor 𝑡𝑎𝑛(𝛿):

Dissipation factor: '"tan

GG

≡δ [-] (13)

The dissipation factor is used to estimate, whether the viscous or elastic behavior is dominating. The

following classification is used:

• tan δ < 1: elastic behavior dominates

• tan δ > 1: viscous behavior dominates

Based on equation (10), it accounts for the absolute value of the complex modulus:

0

022 '''*γτ

=+= GGG [Pa] (14)

The absolute value of the complex modulus corresponds to the ratio of stress amplitude and

deformation amplitude.

The viscoelastic behavior may also be described with help of the complex viscosity η*, which is

defined as the quotient of complex sheer stress τ* and complex deformation velocity *γ .

Complex viscosity:

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'''*}exp{***

0

0 ηηω

δγω

τγτη ⋅−=

⋅=⋅⋅

⋅⋅=≡ i

iGi

i (15)

η’ is a measure for the viscose behavior, η’’ describes the elastic behavior.

For η’ and η’’ accounts:

ωδ

ωγτη 'cos''0

0 G=⋅

⋅= [Pa∙s] (16)

ωδ

ωγτη ''sin'0

0 G=⋅

⋅= [Pa∙s] (17)

It results for the absolute value of complex viscosity:

0

0

0

022

22 ''''''*γτ

ωγτ

ωηηη

=

⋅=

+=+=

GG [Pa∙s]

(18) Accordingly, the absolute value of complex viscosity corresponds to the ratio of stress amplitude and

deformation rate amplitude.

2.3 Measuring technique

2.3.1 Oscillation measurements

Oscillation measurements are used to study the linear-viscoelastic behavior. In the rheometers used,

the sample is located in a gap between an upper plate or cone and a lower plate. This setup is also

called plate-plate or cone-plate geometry. (In the following sections, measuring geometries will be

further explained.) In principle, both geometries are suitable for oscillation measurements.

2.3.1.1 Amplitude sweep (= strain sweep and stress sweep)

During the amplitude test, the frequency is held constant and the amplitude of the deformation signal

or the strain signal is varied, depending on whether the following frequency measurement is

supposed to be conducted by deformation control or by strain control. If the amplitude is not too

high, the rheological material value functions (i.e. G‘(ω) and G‘‘(ω)) do not show any dependence

on the amplitude. This measurement range is called region of linear viscoelasticity. In this range, the

idle state of the sample is not disturbed. Starting from a specific amplitude value, the rheological

material functions G‘(ω) and G‘‘(ω) decrease with increasing amplitude. In this range the laws of

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non-linear viscoelasticity are applicable; the idle state of the sample is disturbed. For solutions and

melts of polymers a disentanglement of entangled (verhakt) molecular chains occurs.

2.3.1.2 Frequency sweep

Within the frequency test, the radial frequency ω is varied, whereas the deformation amplitude γ0 is

held constant in case of deformation-controlled oscillation experiments and the strain amplitude τ0 is

held constant for strain-controlled experiments. Concerning an optimum in signal to noise ratio, the

highest possible deformation or strain amplitude is chosen from the rheograms of the previously

performed amplitude tests, which is just in the linear viscoelastic area. Usually, storage modulus

𝐺′(𝜔), loss modulus 𝐺′′(𝜔) and the absolute value of complex viscosity Iη*I are measured and

drawn against radial frequency ω in a double logarithmic reference frame, because the rheological

material value functions change with radial frequency over several orders of magnitude.

2.3.1.3 Time sweep

Time sweep is carried out at constant amplitude γ0 or τ0, respectively and constant angular velocity.

The time-dependent behavior of the rheological material value functions is observed. Thus, changes

in the material properties over time can be recorded by using rheology. One example is the

thickening process in the manufacture of gels or the stability of polymer solutions against gelling.

2.3.1.4 Temperature sweep

A temperature ramp at constant angular frequency and deformation is applied. The temperature

dependent measurement is illustrated by a semi-logarithmic plot of storage and loss modulus as a

function of temperature. With the aid of a temperature sweep, for example, glass transition

temperature and crystallization temperature of polymers can be determined. This technique is often

called dynamic mechanical thermal analysis (DMTA).

2.3.2 Rotational experiments

Rotational experiments offer another possibility to either preset strain or deformation rate. In a

strain-controlled experiment, the resulting deformation rate is received as the answer of the system,

in deformation-controlled experiments, respectively, the resulting strain is obtained. Rotational

experiments are usually conducted with cone/plate geometry, because with this measuring system,

the deformation rate is independent of the distance r to the middle of the plate and thus constant.

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Exclusively rotational experiments are performed to record flow curves (plot of 𝜏 against �̇� ) or

viscosity curves (plot of η against �̇�).

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2.3.3 Tension experiment

This experiment is a rotational experiment in which the time-dependent behavior of rheological

quantities is recorded. Here, a constant deformation rate is preset and the resulting strain signal is

measured as a function of time. In the ideal case of the experiment, the angular frequency escalates

from the idle state to a constant value. Viscoelastic liquids exhibit a delayed increase in shear stress.

If the measured time-dependent shear stress is correlated to the preset constant deformation rate, the

time-dependent (transient) viscosity η+(t) is obtained:

γτ

η

)()( tt ≡+

[Pa·s] (19)

In the case of viscoelastic fluids the transient viscosity approximates a boundary value with

progressing measurement time. This boundary value is called stationary (= time-independent) shear

viscosity η:

)(),(lim γηγη =+

∞→

tt

[Pa·s] (20)

2.3.4 Relaxation experiment

In the relaxation experiment, the sample is stressed by an escalating deformation γo and the resulting

strain signal τ(t), which decreases with time, is measured. Due to its elastic restoring force a strain is

produced by the preset deformation. A relaxation process within the sample takes place by viscous

flow and the generated strain diminishes. If the strain signal is correlated with the preset

deformation, the nonlinear-viscoelastic relaxation modulus is obtained, with is dependent of time and

the existent deformation:

Relaxation modulus: 0

0)(),(

γτγ ttG ≡ [Pa]

τ(t): strain [Pa] γo: deformation [-]

2.4 Borderline behavior of matter and rheological models

In rheometry material-specific dependencies of the above mentioned interactions of applied shear

stress and resulting shear deformation are obtained. Thereby, the material’s behavior is distinguished

by the following properties: viscous, elastic, viscoelastic and plastic behavior. These behaviors of

material are sketched in Figure 3. All liquids can be described with the aid of viscosity.

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Fig. 3: Boundary behavior of matter: (1) elastic (steel), (2) plastic (modelling clay), (3) viscous (water), (4) viscoelastic (silicone rubber).

2.4.1 Elastic behavior

Upon application of strain, which is held constant over a certain period of time, an elastic material

experiences a deformation, which is constant over time, too (Figure 4). In case a strain is applied as a

step function, the resulting deformation shows the same escalating behavior. Solids with this

behavior are defined elastic. If there is an additional directly proportional ratio between applied

strain and the resulting deformation, the solid is called Hookean solids, i.e. Hook’s law is applicable

(see section 2.1, eq. 6). Note that also elastic solids exist, that do not follow Hook’s law, i.e. strain

and deformation are not linearly connected to each other (e. g., materials for which the law of rubber-

elasticity is applicable).

Fig. 4: Definition of elasticity in general: applied strain as a step function and resulting deformation

of escalating behavior.

(1) (2) (3) (4)

t0

t

t t0

γ

t t1

response input

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The behavior of a Hookean solid is described by a spring for which Hook’s law is applicable.

Fig. 5: Spring as the mechanical model for elastic behavior.

2.4.2 Plastic behavior

Plastic behavior is characterized by a flow behavior with an existing flow limit. The flow limit is the

strain value under which no or only elastic deformation occurs. Above this limit a permanent

deformation appears. Plastic behavior is illustrated with the Saint Venant body. This mechanical

model consists of a slider, which only moves if the applied force overcomes the resistance of static

friction.

Fig. 6: Shearing of a plastic body as a consequence of strain; for deformation a certain shear stress is

necessary, then, shear stress is constant.

Fig. 7: Saint Venant body as a mechanical model for plastic behavior.

τ

γ

τ0

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2.4.3 Viscous behavior

Viscous behavior is found for ideal liquids, the so-called Newtonian liquids. For the definition of the

stationary shear viscosity η the previously described two plate model can be used, for which a

laminar flow is induced in the liquid between two plates as a consequence of the applied shear.

Because of the inner friction of the liquid, the layers only move partially against each other.

Assuming that a laminar flow is present, a velocity gradient is formed in the liquid between the two

plates. As described in section 2.1, for Newtonian liquids, there is a direct proportionality between

shear stress and shear rate, where the constant value is called shear viscosity.

Fig. 8: Applied strain as a step function and resulting deformation for Newtonian liquids. The viscous flow behavior of a Newtonian liquid is described by the mechanical model of an

attenuator. At a constant affecting shear force, force and piston speed are proportional. The piston

immediately stops at the position where it was, when the force effect is finished. Therefore the

deformation of the liquid fully persists even when the force is relieved.

Fig. 9: Attenuator as a mechanical model for viscous flow behavior.

t0

input

τ

tt0 t1t1

γ

tt1

response

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2.4.4 Viscoelastic behavior

As described in section 2.2 many materials do not show exclusively viscous or elastic behavior, but a

combination of both properties. Depending on the type of strain that is applied to the material, the

respective components of viscoelastic flow behavior appear more or less pronounced. Rheological

material value functions used for describing viscoelastic flow behavior are given in section 2.2.

Viscoelastic behavior can be described by mechanical models where spring and attenuator are

combined. For describing the behavior of viscoelastic liquids (polymer melts or concentrated

polymer solutions) one or several Maxwell elements are used. A Maxwell element is a series of

connected springs and attenuators. If a force is applied in form of a step function, the result is a

spontaneous deflection (elastic behavior). Then, the effect of the attenuator appears (viscous

behavior). The initial position is not reached again. This model describes the ideal behavior of

viscoelastic liquids.

Fig. 10: Applied strain as a step function and resulting deformation for a simple Maxwell element.

Fig. 11: Maxwell element as a simple mechanical model for viscoelastic liquids.

For many viscoelastic liquids this model does not describe the flow behavior adequately enough.

Only by parallel connection of several Maxwell elements viscoelastic liquids can be described with

satisfactory accuracy. This approach is called generalized Maxwell model.

τ

t t0 t1

γ

t t1 t0

spring

attenuator regression of the spring

input

response

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Fig. 12: Generalized Maxwell model for improved description of the behavior of viscoelastic liquids.

For viscoelastic solids, the viscoelastic behavior is described by the Kelvin Voigt model. Within this

model, spring and attenuator are connected in parallel. The deformation occurs as long as the

straining force is acting with constant intensity. Both components can only be deformed at the same

time and to the same degree, because they are connected by a fixed frame. The spring cannot be

deformed in the same spontaneous way as it would if it was a single spring with liberty of action,

because it is retarded by the attenuator. As a result of the strain period, deformation behavior is

observed as a curved, time-dependent e-function in the γ(t)-graph having deformation values rising

to a certain maximum value. Accordingly, the spring tends to move back to its initial state when the

force is released. This energy effects that both components reach their initial positions. However, this

happens after a certain time. Due to the presence of the attenuator, this is a time-delayed process, too.

Fig. 13: Strain input as a step function and resulting deformation for the Kelvin Voigt model.

input

τ

t t0 t1

γ

t t1 t0

response

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Fig. 14: Kelvin Voigt model as a simple mechanical model for viscoelastic solids.

2.4.5 Characterization by flow and viscosity curves

In the following graphs flow and viscosity curves are summarized, which are used to characterize the

rheological behavior of fluid media.

Fig. 15: Flow curves for the description of rheological behavior.

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Fig. 16: Viscosity curves for the description of rheological behavior. For a shear thinning substance, viscosity is dependent on the extent of shear strain. With increasing

strain, the flow curve exhibits a negative slope, viscosity decreases, respectively. In the consequence

of shearing, a structural change is induced, which results in the decrease of viscosity. For the filled

systems, the arrangement of the particles is in favor of the lowest possible flow resistance. Thereby,

the arrangement significantly relies on the underlying structure of the deformed material.

Fig. 17: Effect of shearing on the structure of shear thinning materials.

2.5 Time-dependent rheological behavior

To study the time-dependency of structure disassembly and assembly, experiments are conducted

during which the deformation rate is preset as a step function and viscosity is measured in

dependence of time. By such measurements it is possible to distinguish between thixotropic

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(structure disassembly) and rheopectic (structure amplification) behavior, whereat these notations

may only be used in case of fully reversible and isothermally occurring processes. If the disassembly

of structure is irreversible, the behavior is denoted non-thixotropic. These time-dependent

deformation phenomena are defined as follows:

Thixotropy:

Thixotropy describes the disassembly of a structure at constant shear strain and complete reassembly

of the structure after a certain period of time. This disassembly/reassembly cycle is a completely

reversible process. Well-known examples for materials with thixotropic behavior are, e.g.,

dispersions like paste, creams, ketchup, lacquer, etc.

Non-thixotropic behavior:

If the reassembly of structure is incomplete or not happening even after a long period of recovery,

the shear strain induces a permanent change in the structure. This effect is sometimes called “unreal”

or “incomplete” thixotropy. A very prominent example for this effect is mixing up yoghurt. After

mixing, the yoghurt is flowing much more than before, even after a long relaxation period.

Rheopecty:

Rheopecty means an increase in structural strength during shear strain, i.e. assembly of structure

during constant shearing and complete disassembly after relaxation. This assembly/disassembly

cycle is a completely reversible process.

2.6 Rheometry (measuring technique)

For conducting rheological studies, rotational rheometers of different geometries can be used. Each

measuring geometry is used for a different value of viscosity. The most common geometries are:

Plate-plate-geometry:

A plate-plate meassuring system consists of two even plates. Ususally the upper plate is the rotor and

thus the movable part of the meassuring geometry (“measuring plate”) und the lower plate is fixed on

the rheometer stand. The geometry is determined by the plate’s radius R. A disadvantage of this

geometry is, that even at a constant rotational speed, the deformation speed – viewed over the entire

plate gap – is not constant but depends on the distance r to the middle of the plate. That is, a radius-

dependent shear rate distribution exists. These non-uniform, non-constant shear conditions are seen

as a disadvantage for scientifically working rheologists, especially when performing exclusively

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rotational experiments. These experiments should be conducted with cone-plate geometry for the

above mentioned reasons. However, this disadvantage is of low relevance when determining

rheological material value constants of linear viscoelasticity (that is G’, G’’ and Iη*I), for this reason,

the plate-plate geometry is often used for performing oscillation measurements, especially when the

sample is analyzed at different temperatures or, if the sample is filled with particles (e. g., filled

polymer melts or dispersions with relatively large particles). Plate-plate geometry allows for larger

gap positions, thus, phenomena which negatively affect the measured values, like thermal expansion

of the measuring tools or friction effects due to incorporated particles in filled systems could be

minimized.

Cone-plate geometry:

A cone-plate measuring system consists of a round measurement body with a slightly tilted, slightly

cone-shaped surface and a plate. Usually, the cone is the rotor and hence, the upper, moveable part of

the measuring geometry and the lower plate is unmovably fixed on the rheometer stand. The

dimensions of the conical surface are determined by the cone’s radius R and the cone angle α. A

major advantage of the cone-plate geometry is that with this measurement system, the deformation

rate is independent of the distance r to the middle of the plate. Because of this relationship, cone-

plate geometry is especially recommended for performing rotational experiments.

Coaxial cylinder geometry:

Coaxial cylinder measuring systems consist of a measurement body (inner cylinder) and a measuring

cup (outer cylinder). Coaxial means that both cylindrical components are located along one identical

rotationally symmetric axis when the system is in working position. These measuring systems are

especially used for studying low viscous liquids. According to the operating mode, two system types

are distinguished. In the Couette system, the outer cylinder is rotating whereas in the Searle system,

it is the inner cylinder.

3 Experimental

All experiments are conducted with a cone-system (Ø=50 mm, cone-plate-geometry). Temperature

control of the plate is conducted by a Peltier element. Unless stated otherwise, all experiments are

carried out at a temperature of T = 25 °C.

3.1 Conduction of rotational measurements

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The following samples should be classified according to their characteristic flow behavior. The

respective flow phenomena and the underlying structure are to be discussed based on the measured

flow and viscosity curves.

Sample 1: Honey

Shear rate: �̇� = 10-1 to 103 1𝑠

Sample 2: 14 wt.-% PVP-solution (H2O) (Mw = 1,300,000 g/mol)

Temperature: T = 20°C

Shear rate: �̇� = 100 to 103 1𝑠

Sample 3: starch/H2O suspension (50 wt.-%)

Shear rate: �̇� = 10-1 to 102 1𝑠

3.2 Time-dependent change of viscosity

Time-dependent measurements at predetermined deformation rates are performed and the

characteristic evolution of the viscosity function depending on time is discussed. The observed effect

is to be discussed with regard to the underlying effects.

Sample 4: Ketchup Measuring program: From t = 0 to 3 s: γ = 0.1 1

𝑠

From t = 3 to 6 s: γ = 100 1𝑠

From t = 6 to 250 s: γ = 0.1 1𝑠

3.3 Oscillation measurements to determine the viscoelastic behavior

Two oscillation experiments are preformed and the measured curves are discussed. The highest

possible deformation amplitude is chosen from the viscoelastic region and used as a constant

parameter (default value) for the following frequency test.

3.3.1 Oscillation measurement by varying the deformation amplitude at a constant angular

frequency (amplitude test)

Sample 5: 20 wt.-% PVP-solution (H2O) (Mw = 360,000 g/mol)

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Temperature: T = 20°C

Measuring program: angular frequency: ω = 10 rad/s

Deformation amplitude from 𝛾𝑜 = 1 % to 1000 %

Illustration of G’, G’’ and |𝜂∗| as a function of the deformation amplitude 𝛾𝑜 and choice of the

deformation amplitude from the measured curves for the subsequent oscillation measurement (from

linear viscoelastic to non-linear viscoelastic behavior).

3.3.2 Oscillation measurement by varying the angular frequency

Temperature: T = 20°C

Measuring program: Use of the deformation amplitude determined in 3.3.1 as a default

Angular frequency from ω = 100 to 0.1 rad/s

Illustration of G’, G’’ and |𝜂∗| as a function of angular frequency. Explain the rheological behavior

based on the depicted curves (viscosity, viscoelasticity and elasticity). Describe the structural events

at the transition between the borderline cases.

4 Questions

1. Term other applied examples for the determination of materials’ viscosity.

2. Sketch the most important flow and viscosity diagrams.

3. Describe the advantages and disadvantages of plate/plate and cone/plate geometry.

5 Literature

1. M. Dragoni, A. Tallarico, J. Volcanol. Geoth. Res. (1994), 59, 241

2. G. Miyamoto, S. Sasaki, Computers & Geosciences (1996), 23, 283

3. G. B. Thurston, Biophys. J. (1972), 12, 1205

4. W.P. Cox, E.H. Merz: J. Polym. Sci. (1958), 28, 619

5. G. Böhme, M. Stenger: Chem. Eng. Technol. (1988), 11, 199

6. G. V. Vinogradov, A. Y. Malkin, Y. G. Yanovsky, E. A. Dzyura V. F. Schumsky, V. G.

Kulichikhin: Rheol. Acta 8 (1969), 490-496

7. G. V. Vinogradov, N. V. Prozorovskaya: Rheol. Acta 3 (1964)

8. G. V. Vinogradov, A. Y. Malkin: J. Polym. Sci. A: Polym. Chem. (1964), 2, 2357

9. H. M. Laun: Progr. Coll. Pol. Sci. (1987), 75, 111

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10. H. M. Laun: Rheol. Acta (1978), 17, 1

11. J. D. Ferry: Viscoelastic properties of polymers, John Wiley & Sons, Inc. (1970)

12. L. E. Nielsen: Polymer Rheology, Marcel Dekker, Inc., New York – Basel (1977)