RheologyThe relationship between rheological

response and material structure

Márta BerkaUniversity 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.

PrincipleRheology (from the Greek, panta rhei = all things flows) is the science of the deformation and flow of matter. Different materials deform differentlyunder 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 thematerial 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 appliedwork 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 matterSolids: 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.

1relaxation timeobservation time

>> 1relaxation timeobservation time

<< ~ 1relaxationtimeobservation time

Viscous liquid Elastic solids 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.

Different way as the forces are applied

elon

gatio

n

Shear can be applied for any conditiongaseous, 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

εΔ=

0ll

ε relative deformation or strain

Linear relation: strain = constant×stress

E

stress τ= force/unit area, N/m2

ετ =

A

Hooke’s law

E=ετ 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

γ` (or D) shear rate s-1

dx/dt = v

v

dxdy

γ =

Shear deformation

y

x

stress τ= tangential force/unit area

strain

/ /` dx dy dx dt dvdt dy dy

γ = = =

Linear relation: shear stress = constant×shear rate

Shear deformation with constant speed on liquid flow

Force, deformation and time

γητ &= Newtonian viscosity

Dγ ≡& 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 resultsin a strain, or deformation, changing the squareinto a parallelogram.

Ideal viscous materialsDefinition of viscosity: Flow resistance to an external force applied

to a fluid sample

Dτ η=

Shear rate is proportional to the stress (force) – linear Newtonian liquid

Drateshearstressshearityvis τη === cos

Pas

γ` or D shear rateτ

D tg alfa: η

αβ

τ

tg alfa: η

α

β

D

η

τ , D

interchangeable plotting

flows-1 Pa resistance

Pa s-1

Ideal Plastic materials• Ideal plastic material almost does not exist. Ideal viscosity

with a yield value, τ0

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.

sliding of a block on a plane

0

Dτ τη −

=

0 Dτ τ η= +

τ0

Real 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 oscillatingsmall constant τsmall single deformation

Combination of viscous, elastic and plastic properties

Viscoelastic, real plastic materials

Non-Newtonian behaviour

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.

Where τ shear stress, η viscosity, γ` or D shear rate

Most dispersion (also blood)

Rheology and viscosity curves

Weissenberg hatás

Weissenberg effect

? olaj, méz, tészta ?

Newtonian fluidViscoelastic fluid

High viscosity Low viscosityShear thickening fluid

Influences on viscosity

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.

( )0*n

Dτ τ

η−

=

concentration

time

Shape, orientation, attraction between particles

Apparent viscosity

Shear thinning behaviors

Structural changes due to the forces – changes in viscosity: order

( )n

Dτ

η = n<1Effect of anisometry and time!

Shear thickening behaviours

Structural changes due to the forces – changes in viscosity, disorder

( )n

Dτ

η =

n>1

Wet sand or mixture of waterand cornstarch

http://video.google.com/videoplay?docid=-4684348427588167444&ei=4JfVStqgI86z-AbYhtGrCg&hl=hu#

Corn starch is a shear thickeningnon-Newtonian fluid meaning thatit becomes more viscous when it is disturbed

Yield stressWhere τ shear stress, η viscosity, γ` or D shear rate

τ, Pa

D, s-1

House of card

( )0*n

Dτ τ

η−

=

Below the yield value the sample keeps its shape behaves as a solid body abovethe yield value the structure breaks down and sample start to flow. The yield value shows how strong the structure is.

Thixotropy

Rheology curve

viscosity curve

Explanation of Yield value. Gel structure

V sec < 1~2 kT

Thixotropic

~ yield value

The height of the barrier indicates how stable the system is. Vmax>>kT kinetically stabil sol

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

sol

gel

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

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.

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.

Ketchup 15 Pa

Salad Dressing 30 Pa

Lithographic Ink 40 Pa

Mayonnaise 100 Pa

Skin Cream 110 Pa

Hair Gel 135 Pa

Yield stresses

Steady shear flow curves

The structure breaks down while shear rate increases, displaying reduced viscosity (2, 5 curve).

Newtonian: water, low molecular oilsShear thinning: Polymer melts, emulsions, ceramics

Shear thickening: wet sand, cornstarch and water mixture

1. Newtonian fluids 2. shear thinning or pseudoplastic,3. shear-thickening or dilatant, 4. Bingham type body,5. Thixotropic. t0 yield value.

D,s-1

Pa

s-1

Pas

Typical shear viscosity curves

τ0

Viscosity of dispersion of spherical particles

Rheology behavior depends on the structure of the system andthe external force as well , see starch suspension and silly putty

Very strong force, rigid solid

http://www.youtube.com/watch?v=f2XQ97XHjVw&feature=related

Hydrogel: 5% PVA + 5% sodium borate

Force~0 : viscous fluid

weak force : plastic

medium force, : elastic

More example

21 21 ...r k kη φ φ= + + +

Macromolecular solutions, non-ideal

1spec rη η= −

φ or concentration

[ ] 21 2 ...spec k c k c

cη

η= + +

0

50

100

150

200

250

0 0.02 0.04 0.06c, g/mL

ηspec/c

ln ηrel/c

[ ]01lim 2.5spec

ccc

ηη

ρ→ = =

ρc coil density

[ ] aK Mη =

K, a constants, M molar mass

Ideal (linear) behaviourif φ< 0.1

Linear polymer solution

folyásgörbe

0

200

400

600

800

1000

1200

1400

0 20 40 60 80 100 120 140

τ, Pa

D, s

-1

viszkozitás görbe

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0 20 40 60 80 100 120 140τ, Pa

, Pas

A thixotropic loop, the region between curves for the increasing and decreasing shear rate ramps

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 recovercompletely -- loop

Creams

0.0

0.1

0.2

0.3

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0τ, Pa

η, P

as

0ml5ml10ml15ml

0

20

40

60

80

100

120

140

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0

τ, PaD

, s- 1

0ml5ml10ml15ml

+water,ml

( )0n

Dτ τ

η−

=

Internal structure, concentration: the limits value of viscosity and the yield values of rheology curves decrease with the dilution of cream.

Added water

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=fvwpNon-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

Elastic recoil, reversible micro Brown motion (flexibility) and orientation (rod shape)

Irreversible macro Brown motion

Dynamic measurementsStress relaxation (recoil, loosen up, be tired out)

D

Small oscillation stress and strain

Elastic term in phase (δ=0),viscous term out of phase (δ=90°),viscoelastic (δ~45°)

shift