PowerPoint-Präsentation - Anton Paar Rheology

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22 Φεβ 2014 (πριν από 3 χρόνια και 6 μήνες)

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-
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Rheology

of food materials

2

Food products: life cycle

Food
products

Rheological characterization

Formulation

--

Composition,
additives and
stabilizers

Viscosity and flow behavior of
formulation

Production


Flow behavior, viscosity, elasticity

Storage


Sedimentation stability, thermal
stability

Application (usage)



Flow behavior under shear
conditions,
Thixotropy

3

Rheology road

Rheology road and measuring system

4

-

Measuring systems for rotational and oscillatory rheometers

-

Flow and viscosity curves in a wide shear rate range


Examples: Water; Polymer solutions (polysaccharide); Emulsions; Binder solutions

-

Special measuring systems: measuring with the ball measuring system


Examples: Marmalade, Bolognese sauce with meat chunks

-

Yield point in flow curves (via rotational tests)


Examples: Creams; Ketchups

-
Yield point as the limiting value of the linear
-
elastic deformation range (via rotational tests)


Example: Ketchup

-
Structure at rest as G’ value (via oscillatory tests: amplitude and frequency sweeps)


Examples: 1) Butter; 2) Starch gels; 3) Pudding; 4) Milk drinks; 5) Emulsions

-

Structure regeneration of coatings, leveling, sagging behavior and layer thickness

-

Step tests (oscillatory and rotational tests)


Example: Ketchup

-

Temperature
-
dependent behavior during heating, softening, melting, cooling, solidification,


crystallization (using rotational and oscillatory tests)


Examples: Chocolate; Ice creams; Spreading cheese and melting cheese

-
Gel formation (using time
-
dependent and temperature
-
dependent rotational and oscillatory tests)


Examples: Corn starch; Gelatin

Overview

5

Typical shear rates







Process

Shear rate range [s
-
1
]

Examples of application

Sedimentation

(fine particles in
a suspension)

10
-
6

to 10
-
4

Salad dressing, fruit juice

Leveling



-

due to surface tension

10
-
2

to 10
-
1


Coatings, printing inks,
lacquers, chocolate

Dip coating

1 to 10
0


Chewing
,
swallowing

Pouring from a bottle

10 to 100

Cheese, yogurt, chocolate


Transport in tubes, pipe flow,
pumping, filling into
containers

1 to 10
4

Blood, crude oils, paints, juices

Mixing
,
stirring


10 to 10
4


Emulsion,
plastisol
, polymer
blends

Brushing
,
painting
,
spraying
,
blade coating

100 to 10
4

Brush coating, tooth paste,
butter

6

Materials

Shear viscosity



Gases / air

0.01 to 0.02 / 0.018
mPas

Water at 20
°
C

(at 0 / 40 / 60 / 80 / 100
°
C)

1.0
mPas

(1.8 / 0.65 / 0.47 / 0.35 / 0.28
mPas
)

Milk,
coffee

creams

2 to 10 mPas

Olive oil

approx. 100
mPas

Glycerin

1480
mPas

Polymer melts (T=+100 to +200
°
C

and at shear rates of 10 to 1000 1/s)

10 to 10 000 Pas

Polymer melts (zero
-
shear viscosity)

1
kPas

to 1MPas

Bitumen (T = +80 / +60 / +40 /


+20 / +0
°
C)

200 Pas / 1
kPas

/ 20
kPas

/

0.5
MPas

/ 1
MPas

Viscosity values

7

Typically used measuring systems

Cone
-

plate and plate
-

plate systems

Use

sandblasted

or

profiled

measuring

systems

for

oily

and

fatty

substances

!

Viscoelastic, high
viscous
, caution to particles and
structures sizes

Paste like, sticky and almost not flowing


Viscoelastic, medium
viscosity

(f
ree

flowing and

significantly above 100
mPas

(1000mPas)

(larger
particles

or

super
structures

)

Low
viscosity

CP75
-
0,5

CP50
-
1

PP50

CP25
-
1, CP25
-
2,
CP25
-
2

PP25

Gel
-
like

samples

G
‘ > G‘‘
and

temperature

tests

Profiled geometries for
mozarrella

type of cheeses,

sandblasted for cream cheese



Viscoelastic, medium
viscosity

(f
ree

flowing and

significantly above 100
mPas

(1000mPas)

Flowing liquid but larger super
-
structures (CP50
-
2)

8

Cone with truncation:

CPxx
: Cone & Plate

Cone truncation

+ Shear rate and shear strain constant

+ Easy to clean

-

Measurement of friction if particles are below the tip of the cone

Standards: ISO 3219, DIN53019, DIN53018

Crash!!

Name

Cone

Truncation

-

[µm]

CP25
-
1

50

CP25
-
2

105

CP25
-
3

170

CP35
-
3

240

CP50
-
0.5

50

CP50
-
1

100

CP50
-
2

210

CP50
-
3

345

CP60
-
0.5

60

CP60
-
1

120

CP60
-
2

250

CP75
-
1

150

CP75
-
2

315

cone truncation

=

measuring gap

9

Double Cone BI
-
C60
-
1
°

Applications: Food, Cosmetics,
Pharma

modular

Bi
-
cone

for inset
-
Peltier


precise determination of melting and crystallization temperature


homogenous heating and cooling


low temperature measurements without condensation (inert, dry)


no evaporation of water or solvents

Peltier basis
-
c
ontrol by conduction

Peltier
-
hood


heating & cooling


by convection


and radiation

N
2

10

PTD


Peltier Temperature Device

Excellent temperature control from the bottom to the top


unique
combination of

radiation
,
convection
(frost protection) &
conductive heating & cooling


homogenous
heating and cooling


low
temperature measurement without having


condensation (inert, dry)


frost formation

Peltier
-
Hood

Heating

/
Cooling


by

Convection


and

Radiation

Peltier Basis
Temp.
-
Control

by

Conduction

optional

evaporation

blocker

11

Sealing the Gap: PP & CP

Applications: Food, cosmetics, coatings

2
-

guard ring

oil

(10 mPas Si
-
Oil
)



evaporation of solvent / water ?



skin formation ?


12

Sealing the Gap: PP & CP

Applications: Food, cosmetics, coatings



evaporation of solvent / water ?



skin formation ?


1a
-

solvent trap

sample

solvent

13

Typically used measuring systems

Concentric cylinders systems

Standards: ISO 3219, DIN53019, DIN53018


Easy to prevent sample from drying
-
out (oil film on top of sample)


No trimming


Good solution for all kind of liquids in rotational mode


CC: not recommended for oscillation; DG: also recommended for oscillation


CC: Helical groove if phase separation or vertical profiling to prevent slippage

Above 10mPas and below 100mPas with super
-
structures


DG27 (same dimensions like CC27), gap size = 1mm

Above 1000mPas (100mPas)


CC27


Above 10mPas and below 1000mPas


CC39

Below 10mPas und homogenous, small structure


DG26.7, gap size = 0.4mm

14

0.1

1

10

mPas

0.01

0.1

1

10

1000

mPa

1

10

100

s
-
1



DG 42

(double gap MS)

T = +20
°
C





Double
-
gap

measuring

systems

are

special

systems

designed


for

low

-

viscosity

liquids
.

constant viscosity

water

lg


lg
t

lg

Flow
Behavior
:
ideally

viscous

behavior

15



A special measuring system
for:

E.g. natural yoghurt

Natural Food Products

Measure natural product without destroying the initial structure
by cutting into the sample structure

Advantages:


allows
measurement of
brittle, natural materials


excellent penetration characteristics


dimensions similar to standard CC27


alternative: combination with flexible cup holder
-

>


ST22
-
4V
-
40 measuring system


aluminum cup


or stainless steel cup

16

Coarse disperse materials




Building materials



Slurries



Food (Yoghurt)

Special Geometries

CC
with

Surface

Treatment
or

Vanes
,
Stirrers
, Propellers



Better grip



No slip


More Stirrers on request:



-

User defined



-

Brookfield Spindels



-

Krebs Stormer
Spindels



-

...

17

All these stirrers are

relative
measuring systems

Special
Geometries (Relative
Values)

Helix 1

Helix 2

Stirrer for

Building Materials

Starch

Stirrer

Blade

Anchor

Ball Measuring System

18

Rheometry with special Geometries


Ball Measuring System (BMS)

for dispersions containing

coarse
-
grained particles

(showing a diameter up to 10mm)

Example: Marmalade

containing fruit pieces

19

Rheometry

with

special

Geometries

Ball
Measuring

System (BMS)

1
10
100
1,000
Pa
1
10
100
1,000
Pa·s
0.1
1
10
100
1/s
Shear Rate

.
Flow- and Viscosity Curves of Jams at 23 °C
Measured with the Ball Measuring System
Anton Paar GmbH
blueberry
KMS-3 /Q1; d=0 mm
Shear Stress
Viscosity
lemon
KMS-3 /Q1; d=0 mm
Shear Stress
Viscosity
Flow and Viscosity Curves of two
Marmalade
Preparations

20

Rheometry

with

special

Geometries


Ball
Measuring

System (BMS)

Flow and Viscosity Curves of a

Sauce Bolognese


10

0

10

1

10

2

10

3

Pa

t

10

0

10

1

10

2

10

3

10

4

Pa∙s



10

-
4

10

-
3

10

-
2

10

-
1

10

0

10

1

10

2

1/s

Shear rate





.



Copyright (C) 1999 Physica Meßtechnik GmbH

meat sauce

KMS
-
1M

t

shear stress



viscosity

meat sauce (new sample)

KMS
-
1M

t

shear stress



viscosity


Spaghetti Sauce

containing meat pieces

(testing reproducibility)

21

Further measuring systems/ temperature
control systems


Starch (pressure) measuring cell


Tribology

cell


Penetration measurements


Interfacial rheology (IRS)


Sentmanat

extensional rheology(SER)


Flexible
Toolholder


Rheo
-
Microscopy

22

Flow
Behavior

Rheo

-

Microscopy

Size and shape

of the droplets

are depending

on shear rate

and

“shear history”.

water / oil emulsion

dispersions


lg



23

Shear
-
Thinning flow
B
ehavior

Suspension 1:

Orientation of particles

(needle shaped)



Suspension 2:

Agglomerated particles

Break
-
up of agglomerates




Emulsion:

Deformation and break
-
up of
droplets

high
viscosity

low viscosity

rest

high shear rates

24

Shear
-
Thickening flow
B
ehavior

At low shear load:

The rod inclines slowly.

Low viscosity

At high shear load:

Solidification of the liquid
due to shear thickening.

High viscosity

25

Suspensions


shear
-

thickening


of suspensions at



-

high solid concentrations

-

high shear loads

Flow
Behavior

Shear
-
thickening

Behavior

1

f


... volume fraction of solid particles

dispersions

26

Flow Curves on a

linear
scale


Yield

Point
as

a
limiting

value

of

the

shear

stress

1
without

a yield point

2
having

a yield point
t
y

2

1

t
y

Flow
Behavior

Yield

Point

Break
of

the

structure

-

at

-

rest
.

Super
-

structure

by

a
chemical

-

physical

network

via
interactive

forces
.





t

The applied force is
higher than the
structural force

Low stress

…no movement

High stress

…sample starts moving

t
1

t
2

Examples
: Pastes, concentrated dispersions, suspensions, ketchups, mayonnaises, chocolate
melts, butter, gels


27

0

500


1000


1500


2000


2500



Pa

t

0

200

400

600

1000

s
-
1

shear rate



Ketchup

t

shear stress



Yield point can hardly be
read
-
off

Flow curve

showing a
yield point

(on a
linear scale
)

Flow behavior: yield point

28

10

100

1000

10
4

Pa

1

10

100

1000

s
-
1



Ketchup

Flowcurve

showing

a
Yield

Point

(on a
logarithmic

scale
)



yield point
t
y

= 48 Pa

food

Flow
Behavior

Yield

Point,
comparison

lin

/ log
diagrams

(2)

lg
t

lg

29

Flow curves on a
logarithmic scale

t
y



Flow behavior: yield point

Yield point analysis

in the low
-
shear range,

e.g.
read off


at = 0.01 s
-
1

t
y

Yield point analysis

in the low
-
shear range,

e.g.
read off


on the
t
-
=
慸楳

30

Mathematical curve fitting


for flow curves on a
linear scale

(approximation, "regression")

other often used models:

-

Casson

blood,
food


-
Herschel /
Bulkley

materials with a yield

stress and shear thinning or shear
thickening behavior

Flow behavior: yield point

Bingham
:

flow curve of a
material with a yield stress

and a constant viscosity

(
food

or cosmetics
)



t
B

-


y
ield point

acc. to

Bingham“


B
-

“Bingham viscosity“

Windhab
:
chocolate

and
other cocoa products


t
0

-

y
ield point

t
1

-

linear
y
ield point





-

“high
-
shear

viscosity“


examples:

models

according to


31

0
200
400
600
800
1,200
Pa
t
0
50
100
1/s
Cream 1
t
Shear Stress
Cream 2
t
Shear Stress
Cream 1 Herschel -Bul kl ey
tau0 = 705.01 Pa; b = 11.503; p = 0.84742
t
Shear Stress
Cream 2 Herschel -Bul kl ey
tau0 = 31.224 Pa; b = 4.7648; p = 0.94538
t
Shear Stress
Analysis
using

Approximation
Functions

for

Flow
Curves

here
:

according

to

Casson

(OICC 1973),

and

Windhab

(IOCCC 2001 / ICA)

0
50
100
150
200
250
300
Pa
0
10
20
30
40
50
1/s
Scherrate

.
Anton Paar GmbH
Zartbitter 2
Schubspannung
Weiße 1
;
A4...A4
Schubspannung
Vollmilch
;
A4...A4
Schubspannung
Chocolate

Melts

(T = +40
°
C)


Bitter



White




Whole Milk



Analysis


Casson


Windhab



t
0

(
Pa
)


t
0
(
Pa
)

Bitter



15



18



White



19


25

Whole

Milk


21


23

shear

rate

food

Summary
:


Yield

Points
are

not
material
constants
,

since

they

are

depending

on
the

measuring

method

and

on
the

analysis

method
.

t

Flow
Behavior

Yield

Point

32

Viscoelastic
Behavior

Yield

Point (
using

a


/

t

-

Diagram
)

Testing

with

controlled

shear

stress

Yield

point

as

the


limiting

value


of

the

shear

stress
:

The sample
starts

to

flow

not
before

the

external

forces

are

exceeding

the

network
-
of
-
forces

of

the


internal

structure
.


Below

the

yield

point

there

is


elastic

deformation
.

yield

point

t
y

using

the


best

fit
straight

line

(


tangent

)

in
the

linear
-
elastic

deformation

range

yield

point

t
y

using

the



tangent

crossover


method

lg
t

lg



lg


lg
t

33

10
-
2

10
0

10
2

10
4

10
6

%

lg



0.1

1

10

100

1000

Pa

shear

stress
lg

t



without binder

yield point 13.5 Pa

with binder

yield point 114 Pa

Comparison

of

two

Ketchups

deformation

food

Viscoelastic
Behavior

Yield

Point (
using

a


/

t

-

Diagram
)

34

Introduction

Viscoelastic
Behavior

liquid
-

like

structure

„at the gel
point“

gel
-

like


structure

G
''

>> G
'

G
''

> G
'

G'' = G'

G' > G''

G
'

>> G
''


tan
d

㸾=1
=



=

tan
d

㸠1
=

tan
d

=

1


tan
d

㰠1
=
瑡t
d

㰼=1
=


0

with

tan
d

=

G'' / G'


viscous



viscoelastic



elastic

35

Application

Shear

Modulus



Material
Stiffness

and

Shear

Moduli


Example
:
different
types

of

cheese


cheese


type

example

shear modulus

(around)

1
cream

Philadelphia

1
kPa

2 soft

French

Camembert

10
kPa

3 semi
-
hard

Holland Gouda
(young)

0.1
MPa

4 hard

Swiss

Emmentaler

0.5
MPa


5 extra hard

Italian

Parmigiano

1
MPa

5

1

2

4

36

100

1000

10,000

Pa


1

0.1

1

10

100

%



Gel Strength
, Dependence on the Binder
-

Concentration

15 w
-
%

10 w
-
%

7.5 w
-
%

5% w
-
%

0.1



10



Viscoelastic
Behavior


Amplitude
Sweeps

ω = 10 rad/s

T = +23
°
C

loss factor

tan
d

= G‘‘ / G‘


Starch Gel

(in water)

Summary:

Gel strength

is dependent

on the binder

concentration

First check in the LVE range:

tan
d

< 1
for all samples
( = gel structure) ?
Yes !

food

lg tan
d

lg

G'

strain lg


37




0.01


0.1


1


10

MPa

0.01

0.1

1

10

%



ω = 10 rad/s

Temperature

Dependence

of

Butter

Viscoelastic
Behavior

Amplitude
Sweeps

Summary:

cold butter shows
brittle break
,

hence


poor spreadability

T = +10
°
C

T = +23
°
C

food

lg

G'

lg G''

strain lg


38

10
2
10
3
10
4
10
5
Pa
G'
G''
10
0
10
1
10
2
10
3
Pa
0,001
0,01
0,1
1
10
100
%
Deformation

am03014
Margarine css
CP 50-2; d=0,05 mm
G'
Speichermodul
G''
Verlustmodul
Schubspannung
10
2
10
3
10
4
10
5
Pa
G'
G''
10
-1
10
0
10
1
10
3
Pa
0,001
0,01
0,1
1
10
100
%
Deformation

am03014
Margarine CSD
CP 50-2; d=0,05 mm
G'
Speichermodul
G''
Verlustmodul
Schubspannung
Amplitude
Sweep

/CSD /CSS

Margarine
as

semi
-
solid material
with

flow

point

CSD

CSS

39

Application

Sedimentation, Long
-
term

Storage
Stability


in the beginning

Stability of Dispersions

Example:
Salad Dressings

after 15min

Behavior in the low
-
shear range or at rest, respectively

dispersions

40

Frequency

Sweep

Stability

of

suspensions

t = 1 /
omega

Time
dependent

structural

strength



G’
decreasing


-

Long
term

behavior

=
Fluid
-
like

-

Strength

of

the

structure

G’
decreases

-

Good

flow

characteristics


-

Low
stability




G’
constant
,
light

decreasing


-

Long time
structural

strength

G‘

-

Bad
flow

characteristics


-

High
stability


1

1

2

w
=1/
Time

G‘‘

2

G‘

1

2

41

Milk:
Geometry

DG26.7*


Pure milk


Chocolate Milk
Plus


Chocolate Milk
Budget


Ca

enriched

Mill

Mechanical

storage

stability


Amplitude
Sweep

Sedimentation
-
Stability

42

Amplitude
Sweep


Structural

strength

G
´

as

function

of

stress

TAU
LVE

=
Yield

stress =
External

force

to

overcome

the

structure

at

rest

Shear

stress




t
=
*)
Strain
-
Test
,
plottet
as

function

of

strain

10

-
4

10

-
3

10

-
2

10

-
1

Pa

G'

0,0001

0,001

0,01

0,1

Pa

Pure Milk (
no

G‘ )





t
LVE

t
LVE

t
LVE

CA Milk

CHOC
budget

CHOC plus

43

Measurement
of

structural

strength

at

rest

or

mechanical

stability

of

milk

Frequency

Sweep

Sedimentation
Stability

10

-
4

10

-
3

10

-
2

10

-
1

10

0

Pa

G'

0,1

1

10

100

1/s




w

Pure milk

DG 26.7

G'

Choc milk,
plus

DG 26.7

G'

Choc

milk,
Std.

DG 26.7

G'

CA
-
Milk

DG 26.7

G'

44

Spread

cheese



Temperature

behavior



Flow
point

=
Spreadability

as

crossover

point

at

G‘ = G“

Spread

cheese

5
°
C

G'

G''

Spread

cheese

20
°
C

G'

G''

Spread

cheese

36
°
C

G'

G''

10

3

10

4

10

5

Pa

G'

G''

10

2

10

3

10

4

Pa



t
=
5
°
C

20
°
C

36
°
C

Amplitude
Sweep


Representation

as

function

of

stress
to

determine

the

flow

points

45

Penetration measurements

Soft cheese


Presetting

0.3N
contact

pressure


Temperature

60
°
C


Temperature

of

cheese

before

test

ca
. 25
°
C


0
2
4
6
10
mm
d
0
10
20
30
40
60
°C
T
0
2
4
6
8
10
12
14
min
Zeit

t
Penetration Test
Anton Paar GmbH
Start

End

Depth

Time

46

-1
-0,5
0
0,5
1
2
N
F
N
-2.000
-1.500
-1.000
-500
0
500
1.000
2.000
µm/s
v
0
5
10
15
20
25
s
Zeit

t
Penetration
measurement


Margarine


Presetting
: Penetration
velocity

down/
up

= 2000µm/s


Alternatively
: Normal
force

controlled

testing

stop

up

down

Time

47

Flow
Behavior

Temperature

-

dependent

Behavior

softening

and

melting
,

or

solidification

and

crystallization

preset
:
constant

shear

conditions


(
shear

rate
or

shear

stress)


result
:
viscosity

/
temperature

curve


with

steadily

decreasing

or

increasing


viscosity

values
,
respectively

gel

formation

and

curing


preset
:
constant

shear

conditions


(
shear

rate
or

shear

stress)


result
:
viscosity

/
temperature

curve


showing

a
viscosity

minimum





T

T


min

48

0

2

4

6

8

10

Pas



20

25

30

35

40

°
C

temperature
T



Chocolate

Melt

Flow
Behavior

Temperature

-

dependent

Behavior



Cooling

process
:

Crystallization

Temperature


of

Cocoa

Butter

food




crystallization

49

Starch gelling


Electrical heated cell


Watercooling


Fast heating and cooling
rate


Stirrer acts against
sedimentation of particles

50

melting

or

crystallization

process


preset
:
constant

shear

conditions

(
amplitude

and

frequency
)


(
with

an
amplitude

in
the

LVE
-
range
,
and

mostly

with

ω = 10 rad/s)

T
k

... crystallization temperature

result
:

steep decrease or increase, resp.,

in a
narrow

temperature range

Viscoelastic
Behavior

Temperature

-

dependent

Behavior

51

preset:



= 0
.
02 %

ω = 10 rad/s

T = T(t)

Viscoelastic
Behavior

Temperature

-

dependent

Behavior

food

melting



10

2

10

3

10

4

10

5

10

6

10

8

Pa

-
20

-
15

-
10

-
5

0

5

10

°
C

temperature

T



Advantages of icecream 2:

1) better separable at

20
°
C

2) less cold
-

feel when melting

3) creamier feel at molten state

lg G'

lg G''

1

2

Comparison of two Ice Creams

1 Old Freezer

2 New Freezer

52

10
-1
10
0
10
1
10
2
Pa
G'
G''
30
35
40
45
50
55
60
65
70
75
°C
T
0
20
40
60
80
100
min
Time

t
Anton Paar GmbH
Vegetable Fat 10%
G'
Storage Modulus
G''
Loss Modulus
T
Temperature

=1 %
w
=10 1/s

Crystallization of a Vegetable Fat

Rheo
-
Microscopy

53

Different Behavior of two Ketchup Samples

fast


structure recovery

slow

structure recovery

Viscoelastic
Behavior

Time
-

dependent

Structure

Recovery

for coatings:

high wet
-
layer thickness,


good film stability

for coatings:

small wet
-
layer thickness,
good levelling

54

Viscoelastic

Behavior

Time
-

dependent

Structure

Recovery

preset:

1 low
-

shear conditions

(strain in the LVE
-
range, oscillation)

2 high
-

shear conditions (rotation)

3 low
-

shear conditions

(strain in the LVE
-
range, oscillation)


measuring result:

1 state of rest

2 structure decomposition

3 structure regeneration

Step test with 3 intervals, as oscillation / rotation / oscillation


(measuring „thixotropic behavior“)

2
nd

test interval:

liquid, at high shear rates


1
st

& 3
rd

test interval:

G‘ > G‘‘ („gel
-
like structure“ at rest)

www.anton
-
paar.com

10

100

1000

Pa

G'

G''

0.4

0.6

0.8

1.0

Pas


=
0

50

100

150

200

250

s

time



t

Ketchup

G'

G''




1

=

3

= 0.3 %

ω = 10 rad/s


=
㄰〠s
-
1


T = +23
°
C

Step test: oscillation / rotation / oscillation



Viscoelastic behavior: time
-

dependent
structure recovery

56

Interfacial

Rheology System (IRS)

MCR Rheometer +
Interfacial

Rheology System (IRS)

H
1

= 22,5
mm

H
2

= 45
mm

R = 40
mm

R
2

= 34,14
mm

2


= 10
°

P. Erni et. al.

J.Rev.Sci.Instr.
,

74(11)
, 4916
-
4924 (2003)


57

IRS: Film
Formation
of

a Coffee Sample
at

different
Concentrations



0.1% strain, frequency 1Hz



0.05g, 0.15g, and 0.3g coffee powder / 114ml double distilled water

10
-6
10
-5
10
-4
10
-3
10
-2
10
0
Pa·m
G
i
'
G
i
''
0
200
400
600
800
min
Time

t
G
i
´
= 3*10
-
5
Pa
*m