Newtonian and non-newtonian

behavior of fluidsGroup Members

Waheed Ahmed (2k11-ChE-09)

Adnan Rafi (2k11-ChE-16)

Ahmed Haroon (2k11-ChE-23)

Shahzad Ali Zahid (2k11-ChE-49)

Fluids which obey the Newton's law of viscosity are called as Newtonian fluids

Newton's law of viscosity is given by

= shear stress

= viscosity of fluid

dv/dy = shear rate, rate of strain or velocity gradient

Newtonian fluids

dy

dv

Examples of Newtonian fluids

All gases and most liquids which have simpler molecular formula and low molecular weight such as

Water

Benzene

ethyl alcohol

CCl4

Hexane

and most solutions of simple molecules are Newtonian fluids

Non-Newtonian fluids

Fluids which do not obey the Newton's law of

viscosity are called as non-Newtonian fluids

η is the apparent viscosity and is not constant

for non-Newtonian fluids

dy

dv

Apparent Viscosity

If the viscosity is influenced by the shear rate,

it is important to specify that the values are

different from the constant ones of an ideally

viscous fluid. The values obtained are

'apparent viscosity' or 'apparent shear viscosity'

values

Examples of Non-Newtonian fluids

Generally non-Newtonian fluids are complex

mixtures such as

slurries

Pastes

Gels

polymer solutions etc

Various non-Newtonian Behaviors

Time-independent:

Time-dependent

Viscoelastic

Time-Independent Fluid Behavior

• Fluids for which the rate of shear at any point

is determined only by the value of the shear

stress at that point at that instant; these fluids

are variously known as “time independent”,

“purely viscous. these fluids may be further

subdivided into three different types:

• Shear-thinning or pseudoplastics

• Visco-plastics

• Shear-thickening or dilatant

Time-Independent Fluid Behavior

A shear-thinning or pseudoplastic substance is

characterized by an apparent viscosity that

decreases with increasing shear rate the rate of

decrease of the apparent viscosity is not the

same for each fluid

1. Shear thinning or pseudoplastic fluids

The Power-Law or Ostwald-De

Waele Model

The relationship between shear stress and shear rate for pseudoplastic fluids can often be approximated by a straight line over a limited range of shear rate, and hence this part of the flow curve can be described by the power-law expression

τyx =m(˙γyx)n

Where n and m, known as the power-law index and the fluid consistency coefficient,for a Newtonian fluid=1 and for a pseudoplasticsubstance n<1

flow curves for different types of non-

Newtonian fluids

Pseudoplastics

Flow of pseudoplastics is consistent

with the random coil model of polymer

solutions and melts. At low stress, flow

occurs by random coils moving past

each other w/o coil deformation. At

moderate stress, the coils are deformed

and slip past each other more easily. At

high stress, the coils are distorted as

much as possible and offer low

resistance to flow.

Pseudoplastic (Shear thinning) Foods

Shear stress

Shear rate

Examples:

•Banana puree

• Orange juice concentrate

• Oyster sauce

Shear Thinning Behavior

Shear thinning behavior is often a result of:

Orientation of non-spherical particles in the direction of

flow. An example of this phenomenon is the pumping of

fiber slurries

Orientation of polymer chains in the direction of flow and

breaking of polymer chains during flow. An example is

polymer melt extrusion

Deformation of spherical droplets to elliptical droplets in

an emulsion. An industrial application where this

phenomenon can occur is in the production of low fat

margarine

Breaking of particle aggregates in suspensions. An

example would be stirring paint

yxBB

yx 0 forB

yx 0

0yx forB

yx 0

Often the two model parameters t0B and mB are treated as curve fitting

constants, even when there is no true yield stress

2. Viscoplastic Fluid BehaviorViscoplastic fluids behave as if they have a yield stress (t0). Until t0is exceeded they do not appear to flow. A Bingham plastic fluid has

a constant plastic viscosity

3. Shear-thickening or Dilatant Fluid BehaviorEq. (*) is applicable with n>1.

Viscosity increases with shear stress. Dilatant: shear thickening

fluids that contain suspended solids. Solids can become close

packed under shear

Dilatant (Shear thickening) Foods

Shear stress

Shear rate

Examples:

• Liquid Chocolate

• 40% Corn starch solution

The apparent viscosity of a fluid changes with

time as the fluid is continuously sheared

Thixotropic

Rheopectic

Time-dependent Fluid Behavior

Thixotropic

If the apparent viscosity decreases with time

e.g. paints, cream, aqueous iron oxide gels,

some drilling mud's

Result of a break down in the microstructure of

the material as shearing continues

This happens when the sheer is exceeded of a

limit

It leads to non-linear stress-strain behavior

Thixotropy in a Cement Paste

Typical experimental data showing

thixotropic behavior in red mud

suspension

Rheopectic

Is the rare property of some non-newtonian

fluids if the apparent viscosity increases with

time

The longer the fluid undergoes shearing force,

the higher its viscosity

Examples are gypsum pastes and printer inks

Also termed as negative thixotropy

Rheopectic behavior in a saturated

polyester

Qualitative shear stress–shear rate

behavior for thixotropic and rheopectic

materials

Time dependent behaviors

Non - newtonian

Time independent Time dependent

A EC D F GB

_ _

Rheological curves of Time - Independent and Time – Dependent Liquids

++

Visco-elastic Fluid Behavior

A visco-elastic fluid displays both elastic and

viscous properties. A true visco-elastic fluid

gives time dependent behavior

Examples

steel or aluminum

Quartz

Some phenomena in viscoelastic

materials are

If the stress is held constant, the strain

increases with time

If the strain is held constant, the stress

decreases with time

During rolling, frictional resistance occurs

Types of viscoelasticity

Linear viscoelasticity

o It usually happens when the deformations are

Small

Nonlinear viscoelasticity

o Usually happens when the deformations are

Large

Measuring viscoelasticity

broadband viscoelastic spectroscopy (BVS)

resonant ultrasound spectroscopy (RUS)

Thanks