Rheology Part 1

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RheologyPart 1

• LMM

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Introduction to Rheology
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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.

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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.

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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.

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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.

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Ideal solids subjected to shear stresses react
with strain
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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.

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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.

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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.

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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.

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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.

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Shear induced flow in liquids can occur in 4
laminar flow model cases
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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.

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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.

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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.

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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.

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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.

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Aspects of Rheology
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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.

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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

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The parallel-plate model helps to define both
shear stress and shear rate
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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.

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Shear stress

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

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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.

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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.

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Shear rate
In case of the two parallel plates with a linear
speed drop across the gap the differential in the
equation reduces to
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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.

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Shear rate
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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.

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Dynamic viscosity

• Solving equation 2 for the dynamic viscosity ?
  gives

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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

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Typical viscosity values at 20C mPas
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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.

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Kinematic viscosity

• Kinematic viscosity ? and dynamic viscosity ? are
  linked.

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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 .

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Flow Curve
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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.

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Viscosity Curve
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Viscosity parameters

• Viscosity, which describes the physical property
  of a liquid to resist shear-induced flow, may
  depend on 6 independent parameters

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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.

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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.

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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.

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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.

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Substances
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Types of Fluids
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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 .

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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.
  

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Non-Newtonian Liquids

• All other liquids not exhibiting this ideal
  flow behavior are called Non-Newtonian Liquids.
  
• They outnumber the ideal liquids by far.

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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.

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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.

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Pseudo-plastic Liquids
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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.

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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.

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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.

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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.

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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.

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Pseudo-plastic Liquids
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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.

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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.

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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.

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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.

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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.

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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.

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Thixotropy
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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).

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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.

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Thixotropy
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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

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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.

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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.

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Types of Rheometers
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Controlled Stress
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When to Use
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Plate and Cone
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Plate and Cone
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Plate and Cone
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Plate and Cone
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Parallel Plate
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Parallel Plate
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Parallel Plate
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Capillary Rheometer
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Shear rate calculation for capillary rheometer
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Viscosity calculation for capillary rheometer