l3 nonnewtonian fluids
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NON-IDEAL RHEOLOGICAL BEHAVIOR
FLUID (VISCOUS BEHAVIOR) SOLID (ELASTIC BEHAVIOR)
Newtonian Non-Newtonian Non-Hookean Hookean
FLUID-SOLID
Time-Dependent
Rheopectic Thixotropic
Structural Models
Time-Independent
Power Law Bingham Herschel-Bulkley Other Models
Non-Linear Elastic
Viscoelastic
Maxwell Burgers Kelvin
Dilatant Pseudoplastic
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shear stress
shear rate
According toNewton
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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?v=f2XQ97XHjVw
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Newtonian fluids, viscosity does not depend on
the shear rate. Fluid begins to flow when evera shear stress is applied
FLUID (mPa.s)
Water 1
Coffee cream 10
Vegetable oil 100
Honey 10,000
Asphalt 100,000
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Shear Rate (s-1).
Shear Stress (Pa)
Honey
Oil
Water
= slope ofthis line
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SHEAR-DEPENDENT FLUIDS
Plastic (Bingham Plastic): some finiteshear stress must be applied before the
material will flow. This minimum stressrequired is known as the yield stress.
Examples include margarine, whipped
toppings, mayonnaise, or catsup.
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Shear Rate (s-1).
Shear Stress (Pa)
True Bingham
Yield stress
Apparent viscosity
A=/given byslope of this line
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Shear Rate (s-1).
Apparent
Viscosity
A
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Pseudoplastic (shear thinning): Anincreasing 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 Rate (s-1).
Shear Stress (Pa)
A
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Shear Rate (s-1).
Apparent
Viscosity
A
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Dilatant (shear thickening): Increasing shearforce gives a less than proportional increase
in shear rate; the material seems to be moreviscous 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 Rate (s-1).
Shear Stress (Pa)
A
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Herschel-Bulkley: these fluids exhibitboth a yield stress and pseudoplastic
behavior
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Shear Rate (s-1).
Shear Stress (Pa)
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MODELS FOR SHEAR
DEPENDENT FLUIDS
Power Law model: shear stress variesas the shear rate to some power
where K is the consistencyindex, and n isthe flow behavior index.
K n
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Bingham model: model of Newtonianfluid, but includes a yield stress term,
and the plastic viscosity
o'
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Herschel-Bulkley model: power law butincludes a yield stress term to.
o K n
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Casson model: used to estimate yieldstress. Official method for interpreting
chocolate flow data. The Casson plasticviscosity is given by c=Kc
2, and theCasson yield stress by c=Koc
2.
o
a
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HERSCHEL-BULKLEY MODEL
One of the most used models
Viscous behavior of Newtonian fluids,
Bingham plastics, pseudoplastic, anddilatant materials can all be describedas special cases
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FLUID K n o EXAMPLESHerschel-Bulkley >0 00 1 0 Water, fruit juice, milkPseudoplastic >0 0
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TIME DEPENDENT VISCOUSBEHAVIOR
For some fluids, the shear stress maychange at a given shear rate as time
passes. This is another form of non-Newtonian behavior.
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Rheopectic: shear stress increases withtime at constant shear rate; the
apparent viscosity increases with time.The change is reversible. Rare in foodsystems.
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Shear Thickening: shear stressincreases with time at constant shear
rate; the apparent viscosity increaseswith time. The change is irreversible-the material stays thick once shear is
removed.
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At constant shear rate . . .
a
Time
Thixotropic
Shear thinning
Rheopectic
Shear thickening
Shear on Shear off
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MOLECULAR INTERPRETATIONSOF 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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Low shear-polymer entanglement
High shear-polymer entanglement
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Bingham plastic may be due to a highdegree of polymer entanglement
forming a pseudo-gel. The solventcannot flow through this structure until asufficient shear force is exerted tobreak up the structure. In systems with
aggregated particles, pseudoplasticbehavior may occur when increasedshear causes the particles to separate.
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Dilatancy: at low shear conditions, particlesare closely packed. The void spaces
between particles is minimal and are filledwith solvent (water). As shear stressincreases, the total volume increases,increasing the volume of void space.
However, the solvent doesnt fill all of the voidspace, creating a dryness which increases
the resistance to shearing stress.
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Time-Dependence
Similar arguments can be made for fluids thatbecome more or less viscous over time at
constant shear rate. For example, for athixotropic fluid, molecules become more andmore disentangled over time, thus leading toa decrease in viscosity. If the shear force is
removed, the molecules may reaggregate orbecome entangled again over time.