Types of Viscosity

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NON-IDEAL RHEOLOGICAL BEHAVIOR

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According to Newton
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NON-NEWTONIAN FLUIDS

• Fluid systems may be non-ideal in two ways
• 1. The viscosity may depend on shear rate
• 2. The viscosity may depend on time
• Some (many) may have both

http//youtube.com/watch?vf2XQ97XHjVw
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• Newtonian fluids, viscosity does not depend on
  the shear rate. Fluid begins to flow when ever a
  shear stress is applied
• FLUID h (mPa.s)
• Water 1
• Coffee cream 10
• Vegetable oil 100
• Honey 10,000
• Asphalt 100,000

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Honey
Shear Stress t (Pa)
? slope of this line
Oil
Water
.
Shear Rate g (s-1)
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SHEAR-DEPENDENT FLUIDS

• Plastic (Bingham Plastic) some finite shear
  stress must be applied before the material will
  flow. This minimum stress required is known as
  the yield stress.
• Examples include margarine, whipped toppings,
  mayonnaise, or catsup.

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True Bingham
Shear Stress t (Pa)
Apparent viscosity hAt/g given by slope of this
line
Yield stress
.
Shear Rate g (s-1)
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Apparent Viscosity hA
.
Shear Rate g (s-1)
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• Pseudoplastic (shear thinning) An increasing
  shear force gives a more than proportional
  increase in shear rate.
• The material seems less viscous at higher shear
  rates.
• Examples include some salad dressings,
  concentrated fruit juices, and French mustard.

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Shear Stress t (Pa)
hA
.
Shear Rate g (s-1)
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Apparent Viscosity hA
.
Shear Rate g (s-1)
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• Dilatant (shear thickening) Increasing shear
  force gives a less than proportional increase in
  shear rate the material seems to be more
  viscous at higher shear rates.
• Dilatant food systems are not common.
• Examples are some cooked starch suspensions.

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Wet sand
Wet starch at 40-70 solids
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Shear Stress t (Pa)
hA
.
Shear Rate g (s-1)
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Apparent Viscosity hA
.
Shear Rate g (s-1)
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• Herschel-Bulkley these fluids exhibit both a
  yield stress and pseudoplastic behavior

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Herschel-Bulkley
Shear Stress t (Pa)
Bingham Plastic
Pseudoplastic
Newtonian
Dilatant
.
Shear Rate g (s-1)
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MODELS FOR SHEAR DEPENDENT FLUIDS

• Power Law model shear stress varies as the shear
  rate to some power
• where K is the consistency index, and n is the
  flow behavior index.

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• Bingham model model of Newtonian fluid, but
  includes a yield stress term, and the plastic
  viscosity h

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• Herschel-Bulkley model power law but includes a
  yield stress term to.

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• Casson model used to estimate yield stress.
  Official method for interpreting chocolate flow
  data. The Casson plastic viscosity is given by
  hcKc2, and the Casson yield stress by tcKoc2.

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• Powell-Eyring model

where a and b are constants, ?o is the limiting
viscosity at zero shear rate, and h is the
limiting viscosity at infinite shear rate. The
Powell-Eyring models allow characterizing
materials that show Newtonian viscosities at
very low or very high shear rates, but deviate
at intermediate shear rates.
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HERSCHEL-BULKLEY MODEL

• One of the most used models
• Viscous behavior of Newtonian fluids, Bingham
  plastics, pseudoplastic, and dilatant materials
  can all be described as special cases

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• FLUID K n to EXAMPLES
• Herschel-Bulkley gt0 0ltnlt gt0
  Fish paste, raisin paste
• Newtonian gt0 1 0 Water, fruit
  juice, milk
• Pseudoplastic gt0 0ltnlt1 0
  Applesauce, banana puree
• Dilatent gt0 1ltnlt 0 40 raw
  corn starch, some honey
• Bingham Plastic gt0 1 gt0 Tomato
  paste, some yogurts

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TIME DEPENDENT VISCOUS BEHAVIOR

• For some fluids, the shear stress may change at a
  given shear rate as time passes. This is another
  form of non-Newtonian behavior.

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• Thixotropic shear stress decreases with time at
  constant shear rate alternately, the apparent
  viscosity decreases with time. The change is
  reversible the fluid rebuilds itself once
  shearing is removed. Includes some starch paste
  gels.

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• Shear Thinning apparent viscosity decreases with
  time however, the change is irreversible-the
  material is less viscous once the shearing is
  removed. Foods more often behave as shear
  thinning materials than as true thixotropic
  materials.

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• Rheopectic shear stress increases with time at
  constant shear rate the apparent viscosity
  increases with time. The change is reversible.
  Rare in food systems.

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• Shear Thickening shear stress increases with
  time at constant shear rate the apparent
  viscosity increases with time. The change is
  irreversible-the material stays thick once shear
  is removed.

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At constant shear rate . . .
Shear thickening
Rheopectic
ha
Thixotropic
Shear thinning
Shear on
Shear off
Time
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Time dependency also seen in experiments designed
to test shear dependency
up
Shear Stress t (Pa)
down
up
down
.
Shear Rate g (s-1)
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MOLECULAR INTERPRETATIONS OF VISCOSITY

• Viscosity and Energy Dissipation
• viscosity represents the resistance to flow
  introduced by frictional forces in the fluid.
  Some of the energy is dissipated as heat.
  Increased heat does in fact represent increased
  motion at the molecular level, but this motion is
  random, not directed.

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NON-IDEAL BEHAVIOR

• Shear Dependency. Shear dependency usually arises
  in high molecular weight polymers (xanthan gum,
  starches). One explanation is that at low shear
  rates, interchain entanglements greatly increase
  the viscosity. As shear rate increases , the
  individual chains become more oriented along the
  lines of flow.

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• Bingham plastic may be due to a high degree of
  polymer entanglement forming a pseudo-gel. The
  solvent cannot flow through this structure until
  a sufficient shear force is exerted to break up
  the structure. In systems with aggregated
  particles, pseudoplastic behavior may occur when
  increased shear causes the particles to separate.

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• Dilatancy at low shear conditions, particles are
  closely packed. The void spaces between
  particles is minimal and are filled with solvent
  (water). As shear stress increases, the total
  volume increases, increasing the volume of void
  space. However, the solvent doesnt fill all of
  the void space, creating a dryness which
  increases the resistance to shearing stress.

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Time-Dependence

• Similar arguments can be made for fluids that
  become more or less viscous over time at constant
  shear rate. For example, for a thixotropic
  fluid, molecules become more and more
  disentangled over time, thus leading to a
  decrease in viscosity. If the shear force is
  removed, the molecules may reaggregate or become
  entangled again over time.