Rheology
The relationship between rheological
response and material structure
Márta Berka
University of Debrecen
Dept of Colloid and Environmental Chemistry
http://dragon.unideb.hu/~kolloid/
Introduction
The consistency of shower gels and the mouth-feel of yogurt and fruit juice are all
controlled by their rheology - how these everyday colloidal products flow and
deform when in use.
Rheology plays a major role in manufacturing these products well before they reach
supermarket shelves. The rheology of these colloids must be optimum during
mixing, stirring, pumping, coating, spraying or extrusion processes. It follows that
chemists and technologists working in areas as diverse as paints, inks, foods,
agricultural chemicals, pharmaceuticals, electronics and petroleum recovery need to
understand the relationship between the rheology of their products and their
composition.
In turn, the flow behaviour of these products is controlled by their microstructure - the
way in which the constituent colloidal particles interact and self-assemble.
Physicochemical principles of pharmacy, Alexander Taylor Florence,D. Attwood
(internet)
Rheological measurements
In general, rheological measurements on pharmaceutical and cosmetic
materials are performed for the following reasons:
1) to understand the fundamental nature of a system;
2) for quality control of raw materials, final products, and
manufacturing processes such as mixing, pumping, packaging, and
filling;
3) to study the effect of different parameters such as formulation,
storage time, and temperature on the quality and acceptance of a final
product.
Principle
Rheology (from the Greek, panta rhei = all things flows) is the science of
the deformation and flow of matter. Different materials deform differently
under the same state of stress.
Deformation is defined as the relative displacement of points in a body and it
can be divided into two types:
1. Flow is the irreversible part of the deformation: when the stress is removed the
material does not revert into its original configuration. Hence, work is converted
into heat.
2. Elasticity is the reversible part of deformation: removing the stress the applied
work is largely recovered and the body retains its original configuration.
3 main concepts such as force, deformation and time.
Irreversible flows, reversible elastic deformations or their combination
(viscoelasticity) can describe a rheological phenomenon.
Sometimes dynamic characterization such as creep, relaxation tests and
the material response to sinusoidal oscillatory motion is needed.
States of matter
Solids: keep their shape and do not flow. Elastic deformation.
Liquids: it take the shape of the container. Flow if it forces are applied on
it. (Shear deformation with constant speed on liquid – flow)
The states of matter is the question of time scale and the magnitude of
exerted forces. Small forces during very short times – elastic deformation.
Large forces during very long times – flow (mountains). Deborah number.
Intermediate times and forces – viscoelasticity (viscoelastic liquid -liquid like
behaviour, viscoelastic solid - solid like behaviour)
? Cream, butter, ketchup … liquids or solids? Keep their shape if the forces
are weaker than cohesive interaction, semisolids.
relaxation time
>> 1
observation time
Viscous liquid
relaxation time
<< 1
observation time
Elastic solids
relaxation time
~1
observation time
Viscoelasticity
removing the stress the applied work is largely recovered and the body retains its original configuration
Different forces and deformations
•
If a material is subjected to a constant force, it is called static loading. If the loading
of the material is not constant but instead fluctuates, it is called dynamic or cyclic
loading.
elongation
Different way as the forces are applied
Shear can be applied for any condition
gaseous, liquid, solid
Ideal and complex rheological bodies
1. Ideal elastic: Hooke (only reversible deformation, linear relation: stress
and strain)
2. Ideal viscous: Newtonian fluids (continuous irreversible deformation,
flow)
3. Ideal plastic: (no permanent deformation below the yield stress, and
continuous shear rate is at the yield stress.)
Complex rheology
(1 and 2) viscoelastic materials as: elastic fluids (macromolecular
solution) and elastic solids (macromolecular solids)
(2 and 3) real plastic materials
Elastic deformation, ideal elastic body
stress
A
Δl
l0
=ε
Linear relation: strain = constant×stress
ε relative deformation or strain
τ
=E
ε
τ= force/unit area, N/m2
τ = εE
Hooke’s law
Young Modulus, E is a material property that describes the stiffness
of an isotropic elastic material (N/m2)
( rubber E: 0.01 GPa; steel: E 200 GPa)
Elasticity is the reversible part of deformation: removing the stress the
applied work is largely recovered and the body retains its original
configuration.
Giga 109
Shear deformation
Force, deformation and time
stress
area
τ= tangential force/unit
Shear deformation with constant speed on liquid
flow
Linear relation: shear stress = constant×shear rate
τ = ηγ&
Newtonian viscosity
dx/dt = v
γ` (or D) shear rate
x
s-1
v
dx / dy dx / dt dv
γ `=
=
=
dy
dt
dy
γ& ≡ D
strain
γ=
dx
dy
y
Symbol depends on the literature
A shear stress, is applied to the top of the square
while the bottom is held in place. This stress results
in a strain, or deformation, changing the square
into a parallelogram.
Ideal viscous materials
Definition of viscosity: Flow resistance to an external force applied
to a fluid sample
Shear rate is proportional to the stress (force) – linear Newtonian liquid
η = vis cos ity =
Pas
D
shear stress τ
=
shear rate
D
η
τ =ηD
tg alfa: η
τ,
τ
s-1
flow
Pa
α
interchangeable
plotting
β
D
resistance
tg alfa: η
β
α
τ Pa
γ` or D shear rate
D s-1
Ideal Plastic materials
•
Ideal plastic material almost does not exist. Ideal viscosity
with a yield value, τ0
τ = τ 0 +η D
A minimum shear stresses, τ0 required to cause flow. A mechanical analogue to
plastic deformation is the frictional resistance to sliding of a block on a plane. No
displacement occurs until the applied stress reaches the frictional resistance.
τ0
sliding of a block on a plane
η=
τ −τ 0
D
Real materials
Combination of viscous, elastic and plastic properties
Viscoelastic, real plastic materials
If a sample is sheared it may start to break down , therefore we use tiny
perturbation to measure the viscoelastic structure, so called dynamic
measurements:
τ oscillating
small constant τ
small single deformation
Non-Newtonian behaviour
Most dispersion (also blood)
Viscosity depends on the shear rate.
Viscosity is a material function because of the complexity of the micro structure
system. Structural changes due to the forces – changes in viscosity. Rheology
can be used to learn about the microstructure of dispersions.
Rheology and viscosity curves
Where τ shear stress, η viscosity, γ` or D shear rate
Weissenberg hatás
Weissenberg effect
Newtonian fluid
Viscoelastic fluid
High viscosity
? olaj, méz, tészta ?
Low viscosity
Shear thickening fluid
Influences on viscosity
time
concentration
Apparent viscosity
τ −τ 0 )
(
η* =
n
D
If the shear rate changes
during an application, the
internal structure of the
sample will change and the
change in stress or
viscosity can then be seen.
Shape, orientation, attraction
between particles
Shear thinning behaviors
Structural changes due to the forces – changes in viscosity: order
Effect of anisometry and time!
τ)
(
η=
D
n
n<1
Shear thickening behaviours
Structural changes due to the forces – changes in viscosity, disorder
τ)
(
η=
n>1
n
D
Wet sand or
mixture of water
and cornstarch
Corn starch is a shear thickening
non-Newtonian fluid meaning that
it becomes more viscous when it is disturbed
http://video.google.com/videoplay?docid=-4684348427588167444&ei=4JfVStqgI86z-AbYhtGrCg&hl=hu#
Yield stress
Where τ shear stress, η viscosity, γ` or D shear rate
Thixotropy
D, s-1
Rheology curve
viscosity curve
τ, Pa
τ −τ 0 )
(
η* =
n
D
House of card
Below the yield value the sample keeps
its shape behaves as a solid body above
the yield value the structure breaks down
and sample start to flow. The yield value
shows how strong the structure is.
Explanation of Yield value. Gel structure
The height of the barrier indicates how stable the system is.
Vmax>>kT kinetically stabil sol
sol
V sec < 1~2 kT
Thixotropic
gel
~ yield value
Week floc ~gel
In a “secondary minimum” a much weaker and potentially
reversible adhesion between particles exists in a gel structure. These
weak flocs are sufficiently stable not to be broken up by Brownian
motion, but may dissociate under an externally applied force such
as vigorous agitation
sol
Dynamic measurements:
Thixotropy
Time-dependent flow measures the increase or decrease in viscosity with
time, while a constant shear is applied.
The flow is called thixotropic if viscosity decreases
with time, or rheopetic if it increases. Thixotropic
behavior describes a degradation of the structure
during the loaded phase, particles will change to align
with the flow direction.
Viscosity (or stress) during the ramp-down period will
be lower than that in the ramp-up shearing period. In
general, shear thinning measures how easily the
structure can be broken and the loop area indicates the
recovery extent of that broken structure during the
experimental time.
degradation
recovering
J yield value
Determination of Yield stress
The concept of yield stress, the minimum shear stresses required to cause flow, is only
an approximation since this stress value is experimental time dependent.
Pseudoplastic or shear thinning fluids, The
yield stress is crucial in determining not
only their shelf life but also in application
for the end user.
Yield stresses
Ketchup
15 Pa
Salad Dressing
30 Pa
Lithographic Ink
40 Pa
Mayonnaise
100 Pa
Skin Cream
110 Pa
Hair Gel
135 Pa
Steady shear flow curves
Pa
The structure breaks down while
shear rate increases, displaying
reduced viscosity (2, 5 curve).
τ0
s-1
1. Newtonian fluids 2. shear thinning or pseudoplastic,
3. shear-thickening or dilatant, 4. Bingham type body,
5. Thixotropic. t0 yield value.
Pas
Newtonian: water, low molecular oils
Shear thinning: Polymer melts, emulsions, ceramics
D,s-1
Shear thickening: wet sand, cornstarch and water mixture
Typical shear viscosity curves
Viscosity of dispersion of spherical particles
Rheology behavior depends on the structure of the system and
the external force as well , see starch suspension and silly putty
Hydrogel: 5% PVA + 5% sodium borate
Force~0 : viscous fluid
weak force : plastic
medium force, : elastic
Very strong force, rigid solid
http://www.youtube.com/watch?v=f2XQ97XHjVw&feature=related
More example
Ideal (linear) behaviour
if φ< 0.1
Macromolecular solutions, non-ideal
ηr = 1 + k1φ + k2φ 2 + ...
φ or concentration
η spec
η spec = η r − 1
c
= [η ] + k1c + k2 c 2 ...
250
lim c →0
200
ηspec/c
η spec
c
= [η ] = 2.5
1
ρc
ρc coil density
150
100
[η ] = K M a
ln ηrel/c
50
0
0
0.02
0.04
c, g/mL
0.06
K, a constants,
M molar mass
Linear polymer solution
A thixotropic loop, the region between curves for the
increasing and decreasing shear rate ramps
folyásgörbe
0.9
0.8
1400
0.7
1200
viszkozitás görbe
0.6
D, s
, Pas
-1
1000
800
0.5
0.4
600
0.3
400
0.2
200
0.1
0.0
0
0
20
40
60
80
τ, Pa
100
120
140
0
20
40
60
80
100
120
τ, Pa
the orientation of the structure’s molecules or particles will change to align with the
flow direction. Its original orientation can be restored over a period of time after the
external force is removed. There is a delay in time for the structure to recover
completely -- loop
140
Creams
τ −τ 0 )
(
η=
Added water
n
D
0.3
140
0ml
5ml
10ml
15ml
120
+water,ml
100
0ml
5ml
10ml
15ml
80
-
D, s 1
η, Pas
0.2
0.1
60
40
20
0
0.0
0.0
1.0
2.0
3.0
4.0
τ, Pa
5.0
6.0
7.0
8.0
0.0
1.0
2.0
3.0
4.0
τ, Pa
Internal structure, concentration: the limits value of
viscosity and the yield values of rheology curves
decrease with the dilution of cream.
5.0
6.0
7.0
8.0
videos
•
http://www.youtube.com/watch?v=npZzlgKjs0I
(Weissenberg effect)
• http://www.youtube.com/watch?v=S5SGiwS5L6I
(cornstarch 1)
• http://www.youtube.com/watch?v=qfhw6I_uBQg&NR=1
(Liquid armor)
• http://www.youtube.com/watch?v=3zoTKXXNQIU&NR=1&feature=fvwp
Non-Newtonian Fluid on a Speaker Cone
• http://www.youtube.com/watch?v=f2XQ97XHjVw
A pool filled with non-newtonian fluid
• http://www.youtube.com/watch?v=UU7iuJ98fRQ
Cornstarch and vibrations
If a sample is sheared it may start to break down , therefore we use tiny
perturbation to measure the viscoelastic structure, so called dynamic
measurements:
Dynamic measurements show the elastic and permanent
deformation
Irreversible macro Brown
motion
Elastic recoil, reversible
micro Brown motion
(flexibility) and orientation
(rod shape)
Dynamic measurements
Stress relaxation (recoil, loosen up, be tired out)
Small oscillation stress and strain
shift
D
Elastic term in phase (δ=0),
viscous term out of phase (δ=90°),
viscoelastic (δ~45°)