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RheologyPart 1

- LMM

Introduction to Rheology

Introduction to Rheology

- Rheology describes the deformation of a body

under the influence of stresses. - Bodies in this context can be either solids,

liquids, or gases. - Ideal solids deform elastically.
- The energy required for the deformation is fully

recovered when the stresses are removed.

Introduction to Rheology

- Ideal fluids such as liquids and gases deform

irreversibly -- they flow. - The energy required for the deformation is

dissipated within the fluid in the form of heat - and cannot be recovered simply by removing

the stresses.

Introduction to Rheology

- The real bodies we encounter are neither ideal

solids nor ideal fluids. - Real solids can also deform irreversibly under

the influence of forces of sufficient magnitude - They creep, they flow.
- Example Steel -- a typical solid -- can be

forced to flow as in the case of sheet steel when

it is pressed into a form, for example for

automobile body parts.

Introduction to Rheology

- Only a few liquids of practical importance come

close to ideal liquids in their behavior. - The vast majority of liquids show a rheological

behavior that classifies them to a region

somewhere between the liquids and the solids. - They are in varying extents both elastic and

viscous and may therefore be named

visco-elastic. - Solids can be subjected to both tensile and shear

stresses while liquids such as water can only be

sheared.

Ideal solids subjected to shear stresses react

with strain

Introduction to Rheology

- t G dL/dy G tan ? G ?
- t shear stress force/area, N/m 2 Pa
- G Youngs modulus which relates to the

stiffness of the solid, N/m 2 Pa - ? dL/y strain (dimensionless)
- y height of the solid body m
- ?L deformation of the body as a result of shear

stress m.

Introduction to Rheology

- The Youngs modulus G in this equation is a

correlating factor indicating stiffness linked

mainly to the chemical-physical nature of the

solid involved. - It defines the resistance of the solid against

deformation.

Introduction to Rheology

- The resistance of a fluid against any

irreversible positional change of its volume

elements is called viscosity. - To maintain flow in a fluid, energy must be added

continuously.

Introduction to Rheology

- While solids and fluids react very differently

when deformed by stresses, there is no basic

difference rheologically between liquids and

gases. - Gases are fluids with a much lower viscosity than

liquids. - For example hydrogen gas at 20C has a viscosity

a hundredth of the viscosity of water.

Introduction to Rheology

- Instruments which measure the visco-elastic

properties of solids, semi-solids and fluids are

named rheometers. - Instruments which are limited in their use for

the measurement of the viscous flow behavior of

fluids are described as viscometers.

Shear induced flow in liquids can occur in 4

laminar flow model cases

Flow between two parallel flat plates

- When one plate moves and the other is stationary.

- This creates a laminar flow of layers which

resembles the displacement of individual cards in

a deck of cards.

Flow in the annular gap between two concentric

cylinders.

- One of the two cylinders is assumed to be

stationary while the other can rotate. - This flow can be understood as the displacement

of concentric layers situated inside of each

other. - A flow of this type is realized for example in

rotational rheometers with coaxial cylinder

sensor systems.

Flow through pipes, tubes, or capillaries.

- A pressure difference between the inlet and the

outlet of a capillary forces a Newtonian liquid

to flow with a parabolic speed distribution

across the diameter. - This resembles a telescopic displacement of

nesting, tube-like liquid layers sliding over

each other.

Flow through pipes, tubes, or capillaries.

- A variation of capillary flow is the flow in

channels with a rectangular cross-section such as

slit capillaries. - If those are used for capillary rheometry the

channel width should be wide in comparison to the

channel depth to minimize the side wall effects.

Flow between two parallel-plates or between a

cone-and-plate sensor

- Where one of the two is stationary and the other

rotates. - This model resembles twisting a roll of coins

causing coins to be displaced by a small angle

with respect to adjacent coins. - This type of flow is caused in rotational

rheometers with the samples placed within the gap

of parallel-plate or cone-and-plate sensor

systems.

Aspects of Rheology

The basic law

- The measurement of the viscosity of liquids first

requires the definition of the parameters which

are involved in flow. - Then one has to find suitable test conditions

which allow the measurement of flow properties

objectively and reproducibly.

The basic law

- Isaac Newton was the first to express the basic

law of viscometry describing the flow behavior of

an ideal liquid - shear stress viscosity shear rate

The parallel-plate model helps to define both

shear stress and shear rate

Shear stress

- A force F applied tangentially to an area A being

the interface between the upper plate and the

liquid underneath, leads to a flow in the liquid

layer. - The velocity of flow that can be maintained for a

given force is controlled by the internal

resistance of the liquid, i.e. by its viscosity.

Shear stress

- t F (force)/A (area)
- N (Newton)/m 2 Pa Pascal

Shear rate

- The shear stress t causes the liquid to flow in a

special pattern. - A maximum flow speed Vmax is found at the upper

boundary. - The speed drops across the gap size y down to

Vmin 0 at the lower boundary contacting the

stationary plate.

Shear rate

- Laminar flow means that infinitesimally thin

liquid layers slide on top of each other, similar

to the cards in a deck of cards. - One laminar layer is then displaced with respect

to the adjacent ones by a fraction of the total

displacement encountered in the liquid between

both plates. - The speed drop across the gap size is named

shear rate and in its general form it is

mathematically defined by a differential.

Shear rate

In case of the two parallel plates with a linear

speed drop across the gap the differential in the

equation reduces to

Shear rate

- In the scientific literature shear rate is

denoted as - The dot above the ? indicates that shear rate is

the time-derivative of the strain caused by the

shear stress acting on the liquid lamina.

Shear rate

Solids vs Liquids

- Comparing equations 1 and 7 indicates another

basic difference between solids and liquids - Shear stress causes strain in solids but in

liquids it causes the rate of strain. - This simply means that solids are elastically

deformed while liquids flow. - The parameters G and ? serve the same purpose of

introducing a resistance factor linked mainly to

the nature of the body stressed.

Dynamic viscosity

- Solving equation 2 for the dynamic viscosity ?

gives

Dynamic viscosity

- The unit of dynamic viscosity ? is the Pascal

second Pas. - The unit milli-Pascal second mPas is also

often used. - 1 Pa s 1000 mPa s
- It is worthwhile noting that the previously used

units of centiPoise cP for the dynamic

viscosity ? are interchangeable with mPas. - 1 mPas 1 cP

Typical viscosity values at 20C mPas

Kinematic viscosity

- When Newtonian liquids are tested by means of

some capillary viscometers, viscosity is

determined in units of kinematic viscosity ?. - The force of gravity acts as the force driving

the liquid sample through the capillary. - The density of the sample is one other

additional parameter.

Kinematic viscosity

- Kinematic viscosity ? and dynamic viscosity ? are

linked.

Flow and viscosity curves

- The correlation between shear stress and shear

rate defining the flow behavior of a liquid is

graphically displayed in a diagram of t on the

ordinate and on the abscissa. - This diagram is called the Flow Curve.
- The most simple type of a flow curve is shown In

Figure 4. - The viscosity in equation(2) is assumed to be

constant and independent of .

Flow Curve

Viscosity Curve

- Another diagram is very common ? is plotted

versus - This diagram is called the Viscosity Curve.
- The viscosity curve shown in Fig. 5 corresponds

to the flow curve of Fig. 4. - Viscosity measurements always first result in the

flow curve. - Its results can then be rearranged

mathematically to allow the plotting of the

corresponding viscosity curve. - The different types of flow curves have their

counterparts in types of viscosity curves.

Viscosity Curve

Viscosity parameters

- Viscosity, which describes the physical property

of a liquid to resist shear-induced flow, may

depend on 6 independent parameters

Viscosity Parameters

- S - This parameter denotes the

physical-chemical nature of a substance being the

primary influence on viscosity, i.e. whether the

liquid is water, oil, honey, or a polymer melt

etc. - T - This parameter is linked to the temperature

of the substance. Experience shows that viscosity

is heavily influenced by changes of temperature.

As an example The viscosity of some mineral oils

drops by 10 for a temperature increase of only

1C.

Viscosity Parameters

- p - This parameter pressure is not

experienced as often as the previous ones. - Pressure compresses fluids and thus increases

intermolecular resistance. - Liquids are compressible under the influence of

very high pressure-- similar to gases but to a

lesser extent. - Increases of pressure tend to increase the

viscosity. - As an example Raising the pressure for drilling

mud from ambient to 1000 bar increases its

viscosity by some 30.

Viscosity Parameters

- -Parameter shear rate is a decisive factor

influencing the viscosity of very many liquids. - Increasing shear rates may decrease or increase

the viscosity. - t Parameter time denotes the phenomenon that

the viscosity of some substances, usually

dispersions, depends on the previous shear

history, i.e. on the length of time the substance

was subjected to continuous shear or was allowed

to rest before being tested.

Viscosity Parameters

- E - Parameter electrical field is related to

a family of suspensions characterized by the

phenomenon that their flow behavior is strongly

influenced by the magnitude of electrical fields

acting upon them. - These suspensions are called either

electro-viscous fluids (EVF) or

electro-rheological fluids (ERF). - They contain finely dispersed dielectric

particles such as aluminum silicates in

electro-conductive liquids such as water which

may be polarized in an electrical field. - They may have their viscosity changed

instantaneously and reversibly from a low to a

high viscosity level, to a dough-like material or

even to a solid state as a function of electrical

field changes, caused by voltage changes.

Substances

Types of Fluids

Newtonian Liquids

- Newton assumed that the graphical equivalent of

his equation 2 for an ideal liquid would be a

straight line starting at the origin of the flow

curve and would climb with a slope of an angle a. - Any point on this line defines pairs of values

for t and . - Dividing one by the other gives a value of ?

(8). - This value can also be defined as the tangent of

the slope angle a of the flow curve ? tan a .

Newtonian Liquids

- Because the flow curve for an ideal liquid is

straight, the ratio of all pairs of t and

-values belonging to this line are constant. - This means that ? is not affected by changes in

shear rate. - All liquids for which this statement is true are

called Newtonian liquids (both curves 1 in Fig.

6). - Examples water, mineral oils, bitumen, molasses.

Non-Newtonian Liquids

- All other liquids not exhibiting this ideal

flow behavior are called Non-Newtonian Liquids.

- They outnumber the ideal liquids by far.

Pseudo-plastic Liquids

- Liquids which show pseudo-plastic flow behavior

under certain conditions of stress and shear

rates are often just called pseudo-plastic

liquids (both curves 2 in Fig. 6) - These liquids show drastic viscosity decreases

when the shear rate is increased from low to high

levels.

Pseudo-plastic Liquids

- Technically this can mean that for a given force

or pressure more mass can be made to flow or the

energy can be reduced to sustain a given flow

rate. - Fluids which become thinner as the shear rate

increases are called pseudo-plastic. - Very many substances such as emulsions,

suspensions, or dispersions of technical and

commercial importance belong to this group.

Pseudo-plastic Liquids

Pseudo-plastic Liquids

- Many liquid products that seem homogeneous are in

fact composed of several ingredients particles

of irregular shape or droplets of one liquid are

dispersed in another liquid. - On the other hand there are polymer solutions

with long entangled and looping molecular chains. - At rest, all of these materials will maintain an

irregular internal order and correspondingly they

are characterized by a sizable internal

resistance against flow, i.e. a high viscosity.

Pseudo-plastic Liquids

- With increasing shear rates, matchstick-like

particles suspended in the liquid will be turned

lengthwise in the direction of the flow. - Chain-type molecules in a melt or in a solution

can disentangle, stretch and orient themselves

parallel to the driving force. - Particle or molecular alignments allow particles

and molecules to slip past each other more

easily.

Pseudo-plastic Liquids

- Shear can also induce irregular lumps of

aggregated primary filler particles to break up

and this can help a material with broken-up

filler aggregates to flow faster at a given shear

stress. - For most liquid materials the shear-thinning

effect is reversible -- often with some time lag

-- i.e. the liquids regain their original high

viscosity when the shearing is slowed down or

terminated the chain-type molecules return to

their natural state of non-orientation.

Pseudo-plastic Liquids

- At very low shear rates pseudo-plastic liquids

behave similarly to Newtonian liquids having a

defined viscosity ?0 independent of shear rate --

often called the zero shear viscosity. - A new phenomenon takes place when the shear rate

increases to such an extent that the shear

induced molecular or particle orientation by far

exceeds the randomizing effect of the Brownian

motion the viscosity drops drastically.

Pseudo-plastic Liquids

- Reaching extremely high shear rates the viscosity

will approach asymptotically a finite constant

level ?1. - Going to even higher shear rates cannot cause

further shear-thinning The optimum of perfect

orientation has been reached.

Pseudo-plastic Liquids

Dilatant Liquids

- There is one other type of material characterized

by a shear rate dependent viscosity dilatant

substances -- or liquids which under certain

conditions of stress or shear rate show

increasing viscosity whenever shear rates

increase. (Curves 3 in Fig. 6) - Dilatancy in liquids is rare.
- This flow behavior most likely complicates

production conditions, it is often wise to

reformulate the recipe in order to reduce

dilatancy.

Plasticity

- It describes pseudo-plastic liquids which

additionally feature a yield point. (both curves

4 in Fig. 6) - They are mostly dispersions which at rest can

build up an intermolecular/interparticle network

of binding forces (polar forces, van der Waals

forces, etc.). - These forces restrict positional change of volume

elements and give the substance a solid character

with an infinitely high viscosity.

Plasticity

- Forces acting from outside, if smaller than those

forming the network, will deform the shape of

this solid substance elastically. - Only when the outside forces are strong enough to

overcome the network forces -- surpass the

threshold shear stress called the yield point

-- does the network collapse. - Volume elements can now change position

irreversibly the solid turns into a flowing

liquid.

Plasticity

- Typical substances showing yield points include

oil well drilling muds, greases, lipstick masses,

toothpastes and natural rubber polymers. - Plastic liquids have flow curves which intercept

the ordinate not at the origin, but at the yield

point level of t0.

Thixotropy

- For pseudo-plastic liquids, thinning under the

influence of increasing shear depends mainly on

the particle/molecular orientation or alignment

in the direction of flow surpassing the

randomizing effect of the Brownian movement of

molecules. - This orientation is again lost just as fast as

orientation came about in the first place.

Thixotropy

- Plotting a flow curve of a non-Newtonian liquid

not possessing a yield value with a uniformly

increasing shear rate -- the up-curve --, one

will find that the down-curve plotted with

uniformly decreasing shear rates will just be

superimposed on the up-curve they are just on

top of each other or one sees one curve only.

Thixotropy

Thixotropy

- It is typical for many dispersions that they not

only show this potential for orientation but

additionally for a time-related

particle/molecule-interaction. - This will lead to bonds creating a

three-dimensional network structure which is

often called a gel. - In comparison to the forces within particles or

molecules, these bonds -- they are often hydrogen

or ionic bonds -- are relatively weak they

rupture easily, when the dispersion is subjected

to shear over an extended period of time (Fig. 9).

Thixotropy

- When the network is disrupted the viscosity drops

with shear time until it asymptotically reaches

the lowest possible level for a given constant

shear rate. - This minimum viscosity level describes the

sol-status of the dispersion. - A thixotropic liquid is defined by its potential

to have its gel structure reformed, whenever the

substance is allowed to rest for an extended

period of time. - The change of a gel to a sol and of a sol to a

gel is reproducible any number of times.

Thixotropy

Thixotropy

- Fig. 10 describes thixotropy in graphical form.
- In the flow curve the up-curve is no longer

directly underneath the down-curve. - The hysteresis now encountered between these two

curves surrounds an area A that defines the

magnitude of this property called thixotropy. - This area has the dimension of energy related

to the volume of the sample sheared which

indicates that energy is required to break down

the thixotropic structure

Thixotropy

- For the same shear rate there are now two

different points I and II. - These two viscosity values are caused by a shear

history at I being much shorter than at II. - If it took 3minutes to get to point I and 6

minutes to the maximum shear rate, it will be 9

minutes until point II is reached.

Rheopectic Flow Behavior

- Rheopective liquids are characterized by a

viscosity increase related to the duration of

shear. - When these liquids are allowed to rest they will

recover the original -- i.e. the low -- viscosity

level. - Rheopective liquids can cycle infinitely between

the shear-time related viscosity increase and the

rest-time related decrease of viscosity. - Rheopexy and thixotropy are opposite flow

properties. - Rheopexy is very rare.

Types of Rheometers

Controlled Stress

(No Transcript)

When to Use

Plate and Cone

Plate and Cone

Plate and Cone

Plate and Cone

Parallel Plate

Parallel Plate

Parallel Plate

Capillary Rheometer

Shear rate calculation for capillary rheometer

Viscosity calculation for capillary rheometer