Applied Rheology in Polymer

Processing

Rheological systems

Purely Elastic Behaviour

• Purely elastic response of materials is characterized by their stress

strain curves

• Different materials give different stress-strain curves, for example

brittle materials and metals and alloys are characterized by high

stress and low strain but brittle plastic suffer the brittle failure

whereas the metals undergo yield i.e. the ductile failure.

•The rubber and rubber like materials show low stress and very

high elongation and their stress strain curves pass through a number

of stages.

•The cross linking or vulcanization increase the stress valves but

reduces the elongation where as the fillers give the similar effect but

to the lesser extent.

Rheological systems...

Purely Viscous Behaviour

• Purely viscous behavior is characterized

by the dependence of shear stress on the

rate of shear (also sometimes written as

the rate of deformation or the shear rate).

• The liquids are capable of sustaining

infinite deformation and the linear

relationship between shear stress, τ and

the rate of shear γ◦ is the well known

Newton’s law of viscosity representing the

Newtonian flow behaviour.

•The behavior of such fluids can

be best demonstrated by shearing

a fluid between two parallel plates

Viscous deformation

Purely Viscous Behaviour...

If the distance between the plates is y and a force F is

applied to the top of surface area A so that it moves

with a velocity of Vx with the lower plate being

fixed, the shear stress and the rate of shear can be

calculated and the relationship between them can be

written

• Most of the low molecular weight liquids organic

solvents and dilute solution of polymers follow this

equation. The viscosity for these liquids is constant

over the entire range of rate of shear at a particular

temperature.

• A plot of shear stress and rate of shear gives a

straight line passing through the origin and the slope

of the line is the viscosity of the fluid.

Time independent non-Newtonian fluids

A large no of liquids like polymer and rubber

melts, concentrated polymer solutions, solid

suspensions and slurries invariably do not follow

the Newtons law but show the viscosity to be a

function of rate of shear, γ◦ only. Such fluids are

known as the time independent non Newtonian

fluids.

• For these fluids the viscosity is either found to decrease

with rate of shear as in the case of pseudoplastic fluids or to

increase in the case of dilatent fluids.

•The Bingham plastic fluids on the other hand demonstrate

the existence of yield stress , i.e. to say that these fluids

require a definite amount of energy before they start flowing

and then flow as Newtonian fluids.

• Some polymer melts may flow as pseudoplastic liquids after

yielding, these are known as plastoviscous or viscoplastic

fluid.

Pseudoplastic fluids

The viscosity of these fluids reduces with the shear

rate and the curve of shear stress versus rate of

shear is concave downwards.

A log log plot of shear stress and rate of shear

clearing show three different regions. These are

•A low shear region of a small range with the

slope of the line =1, known as the first

Newtonian region

•An intermediate shear region with line of slope

<1 known as pseudoplastic or shear thinning

region and

•A high shear region with slope of the line again

=1 known as second Newtonian region

Plot of ln Ʈ versus ln γ◦ for

Pseudoplastic fluids

Pseudoplastic fluids...

• Depending on the type of polymer the slope of

the line in the intermediate region many vary

form just <1 to very close to zero.

•The extent of pseudoplasticing or the shear

thinning behavior increases with the decrease in

the value of slope below 1.

•The viscosity and shear stress or rate of shear

plot for such fluids shows a general nature with

the viscosity being constant at low shear region,

continuously falling in the intermediate region

and the again constant in the high shear region

particularly for the polymer solutions and low

molecular weight polymer melts.Variation of viscosity with rate of

shear

Pseudoplastic fluids...• Such a behavior can be explained by

assuming that in the polymer melts and

solutions, which show shear thinning

nature the macromolecules or the

particles are completely random in the

spatial orientation when at rest Fig a) and

are bound by weak intermolecular forces.

•When the applied stress is relatively low

the molecules maintain their randomness

and the molecular forces do not allow

them to be oriented in the direction of

force resulting in constant viscosity in this

region.

Pseudoplastic fluids under shear

deformation

•As the shear rate increases the polymer molecules

start orienting in the direction of flow. As the

polymer system contains a molecular weight

distribution the small molecules, which require less

energy to change the direction start orienting,

initiating the reduction in the viscosity. The high

molecular weight molecules have very long coiled

chains, which are entangled with each other. these

molecules require higher energy for

disentanglement, uncoiling and then orientation.

Pseudoplastic fluids...• As the shear stress and shear rate

increases further the system is subjected to

increasingly higher energy for deformation

resulting in more and more molecules

being oriented.

•The resistance to the flow of the oriented

molecules is reduced due to the fact that

the oriented molecules can slip past each

other with relative ease. This gives a

continuous decrease in the viscosity till all

the molecules are oriented at some higher

value of rate of shear.

•Beyond this value of rate of shear there is no

further increase in the extent of orientation of

molecules and the systems show a constant

viscosity or the second Newtonian region.

The greatest man of our times.

- Einstein called Gandhiji

The real hero of Mine.

- Obama called Gandhiji

Mohandas Karamchand Gandhi was the

preeminent leader of Indian independence

movement in British-ruled India.

Born:October 2, 1869, Porbandar

Assassinated: January 30, 1948, New Delhi

Spouse:Kasturba Gandhi (m. 1883–1944)

Parents:Karamchand Gandhi, Putlibai Gandhi