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Rheology Part 1


Rheology Part 1 LMM Thixotropy It is typical for many dispersions that they not only show this potential for orientation but additionally for a time-related particle ... – PowerPoint PPT presentation

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Title: Rheology Part 1

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
  • Solids can be subjected to both tensile and shear
    stresses while liquids such as water can only be

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

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

Introduction to Rheology
  • While solids and fluids react very differently
    when deformed by stresses, there is no basic
    difference rheologically between liquids and
  • Gases are fluids with a much lower viscosity than
  • 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
  • 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
  • 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
  • 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

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
  • 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
  • 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 ?

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

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
  • 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
  • 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

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
  • 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.

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 ?
  • 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.
  • 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

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
  • 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

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
  • 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

  • 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.

  • 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

  • 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.

  • 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
  • This orientation is again lost just as fast as
    orientation came about in the first place.

  • 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.

  • It is typical for many dispersions that they not
    only show this potential for orientation but
    additionally for a time-related
  • 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).

  • 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.

  • 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

  • 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
  • When these liquids are allowed to rest they will
    recover the original -- i.e. the low -- viscosity
  • 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
  • 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
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