non newtonian fluids_types of viscosity

http://server.fst.uga.edu/kerr/FDST%208080/PPT%20Slides/L3%20NonNewtonian%20Fluids.ppt

NON-IDEAL RHEOLOGICAL BEHAVIORNON-IDEAL RHEOLOGICAL BEHAVIOR

FLUID (VISCOUS BEHAVIOR) SOLID (ELASTIC BEHAVIOR)

Newtonian Non-Newtonian Non-Hookean Hookean

FLUID-SOLIDTime-Dependent

Rheopectic Thixotropic

Structural Models

Time-Independent

Power Law Bingham Herschel-Bulkley Other Models

Non-Linear Elastic

Viscoelastic

Maxwell Burgers Kelvin

Dilatant Pseudoplastic

Ý

shear stressshear rate

According to Newton

NON-NEWTONIANNON-NEWTONIAN FLUIDSFLUIDS

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

Newtonian fluids, viscosity does not depend on the

shear rate. Fluid begins to flow when ever a shear stress is applied

FLUID (mPa.s)Water 1Coffee cream 10Vegetable oil 100Honey 10,000Asphalt 100,000

Shear Rate Shear Rate (s (s-1-1))..

Shear StressShear Stress (Pa)(Pa)

HoneyHoney

OilOil

WaterWater

= slope of = slope of this linethis line

SHEAR-DEPENDENT FLUIDSSHEAR-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.

Shear Rate Shear Rate (s (s-1-1))..

Shear StressShear Stress (Pa)(Pa)

True BinghamTrue Bingham

Yield stressYield stress

Apparent viscosity Apparent viscosity AA== given by given by slope of this lineslope of this line

Shear Rate Shear Rate (s (s-1-1))..

Apparent Apparent ViscosityViscosity

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.

Shear Rate Shear Rate (s (s-1-1))..

Shear StressShear Stress (Pa)(Pa)

AA

Shear Rate Shear Rate (s (s-1-1))..

Apparent Apparent ViscosityViscosity

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.

Wet sandWet sand

Wet starch at Wet starch at 40-70% solids40-70% solids

Shear Rate Shear Rate (s (s-1-1))..

Shear StressShear Stress (Pa)(Pa)

AA

Shear Rate Shear Rate (s (s-1-1))..

Apparent Apparent ViscosityViscosity

Herschel-Bulkley: these fluids exhibit both a yield stress and pseudoplastic behavior

Shear Rate Shear Rate (s (s-1-1))..

Shear StressShear Stress (Pa)(Pa)

NewtonianBingham Plastic

Pseudoplastic

Herschel-Bulkley

Dilatant

MODELS FOR SHEAR MODELS FOR SHEAR DEPENDENT FLUIDSDEPENDENT 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.

KÝ n

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

o ' Ý

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

o KÝ n

Casson model: used to estimate yield stress. Official method for interpreting chocolate flow data. The Casson plastic viscosity is given by c=Kc

2, and the Casson yield stress by c=Koc

2.

o a Ý

Powell-Eyring model:

Ý o

sinh 1(Ý )

where where and and are constants, are constants, oo is the limiting viscosity is the limiting viscosity at zero shear rate, and at zero shear rate, and is the limiting viscosity at is the limiting viscosity at infinite shear rate. The Powell-Eyring models infinite shear rate. The Powell-Eyring models allow characterizing materials that show Newtonian allow characterizing materials that show Newtonian viscosities at very low or very high shear rates, but viscosities at very low or very high shear rates, but deviate at intermediate shear rates.deviate at intermediate shear rates.

HERSCHEL-BULKLEY MODELHERSCHEL-BULKLEY MODEL

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

FLUID K n o EXAMPLESHerschel-Bulkley >0 0<n< >0 Fish paste, raisin pasteNewtonian >0 1 0 Water, fruit juice, milkPseudoplastic >0 0<n<1 0 Applesauce, banana pureeDilatent >0 1<n< 0 40% raw corn starch, some honeyBingham Plastic >0 1 >0 Tomato paste, some yogurts

TIME DEPENDENT VISCOUS TIME DEPENDENT VISCOUS BEHAVIORBEHAVIOR

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

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.

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.

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

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.

At constant shear rate . . .At constant shear rate . . .

aa

TimeTime

ThixotropicThixotropic

Shear thinningShear thinning

RheopecticRheopectic

Shear thickeningShear thickening

Shear onShear on Shear offShear off

Time dependency also seen in experimentsTime dependency also seen in experimentsdesigned to test shear dependencydesigned to test shear dependency

Shear Rate Shear Rate (s (s-1-1))..

Shear StressShear Stress (Pa)(Pa)

upup

downdown

upup

downdown

MOLECULAR INTERPRETATIONS MOLECULAR INTERPRETATIONS OF VISCOSITY 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.

Stress (F/A) alongupper layer

Some molecules move alongupper layer. Some move to lowerlevels transferring momentum tomolecules there.. Some of thatenergy becomes directed in theflow direction. Some becomesrandomized into thermal motion

NON-IDEAL BEHAVIORNON-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.

Low shear-polymer entanglement

High shear-polymer entanglement

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.

Low Shear High Shear

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 doesn’t fill all of the void space, creating a “dryness” which increases the resistance to shearing stress.

No/Low ShearHigh Shear

Time-DependenceTime-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.