L3 NonNewtonian Fluids

8/13/2019 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.

L3 NonNewtonian Fluids

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