Definition::

Rheology is the science of flow and deformation of matter.

There are basically two types of fluids, defined by the relationship

between shear stress and shear rate.

These are:

Newtonian

Non-Newtonian

Newtonian and Non-Newtonian Fluid

If the gradient m is constant, the fluid is termed as Newtonian fluid. Otherwise, it is known as non-

Newtonian fluid. Fig. 1.5 shows several Newtonian and non-Newtonian fluids.

Newtonian and Non-Newtonian Fluids (habib)

A Newtonian fluid is a fluid whose viscosity remains constant when the shear rate changes. The

viscosity will still change with a change in temperature or pressure, but a pushing it faster, the viscosity

stays constant.

Example:

Water and simple liquids such as ethyl alcohol; air and simple … are Newtonian fluids.

A non-Newtonian fluid is a fluid whose viscosity changes (drops) when the shear rate changes i.e.

increase.

Exmple :

Fluids in food industry, gels, polymers, slurries, drilling muds, blood

… are Non-Newtonian fluid.

Figure: Classification of fluids with shear stress as a function of shear rate.

Examples of Viscoelastic Fluid

Paint

Crude oil

Asphalt

Cosmetics

Biological fluids

Blood

Protein solutions

Pulp and coal slurries

Toothpaste

Grease

Foodstuffs

Ketchup

Dough

Salad dressing

Plastics

Polymer melts

Rubbers &Polymer solutions

Classification of fluids

Time Independent Fluids (the relation between shearing stress and rate is unique but

non-linear)

Bingham plastics

Pseudoplastic fluids

Dilatant plastics

Time Dependent Fluids (the shear rate depends on the shearing time or on the previous

shear rate history)

Thixotropic fluids

Reopectic fluids

Viscoelastic fluids (the shear stress is determined by the shear strain and the rate of

shear strain)

Time-Independent Fluids

Bingham plastics : depends on a critical/yield shear stress ( ) and then becomes constant.

Ex. sludge

paint

blood

Time-Independent Fluids

Bingham plastics :

Time-Independent Fluids Power law fluids Pseudoplastic fluids : decreases as the shear rate increases (shear rate thinning)

Ex. polymer melts

paper pulp in water

clay solutions

molasses

whipped cream

Definition of Newtonian Fluid: Newtonian fluid is any fluid that exhibits a viscosity that remains constant regardless of any external

stress that is placed upon it, such as mixing or a sudden application of force.

Rheological Properties Stress

Shear stress

Normal stress

Normal Stress differences

Viscosity

Steady-state (i.e. shear) ( Most commonly sought rheological quantity).

Extensional

Complex

Viscoelastic Modulus

G’ – storage modulus

G” – loss modulus

Creep, Compliance, Decay

Relaxation times

Tensile or Compressive Stress - Normal Stress

Three kinds of differential stress occur::

Tensional stress (or extensional stress), which stretches rock.

Compressional stress, which squeezes rock; and

Shear stress, which result in slippage and translation.

Robert Hooke

Robert Hooke (28 July 1635-3 March 1703) was an English natural philosopher. Robert

Hooke was born in 1635 in Freshwater on the Isle of Wight to John Hooke and Cecily Gyles.

Dashpot

Dashpot: A model for Newtonian fluids consisting of a piston and

cylinder containing a viscous liquid.

Normal and Shear Stress ::

traction’s on the planes that intersect at the origin of figure can be subdivided into perpendicular and

parallel components to each plane. The component perpendicular to each plane is termed normal stress

( ) and the component parallel to each plane is termed shear stress ( ). Figure illustrates the

relationship between the traction (s) and the normal ( ) and shear stress ( ) components acting on a

single plane whose trace in two dimensions the line segment AB.

Shear Stress::

Stress parallel to the plane is usually denoted ‘shear stress’ and can be expressed as

τ = Fp /A, where

τ = shear stress ((Pa) N/m2, psi)

Fp = parallel component force (N, lbf)

A = area (m2, in2)

Ideal (elastic) Solid

Hooks Law

Response is independent of time and

the deformation is dependent on the spring constant.

Maxwell Model

James Clerk Maxwell (1831–1879) Edinburgh, Scotland

Died 5 November 1879

(1879-11-05) (aged 48)

In series connection of Hook’s Spring and Dash pot

Maxwell Model

Figure: Stress- time plot for stress relaxation in the Maxwell model

Maxwell model

In series

Viscous strain remains after load removal.

The rate of strain d/dt is equal to zero under

conditions of constant stress (s)

Then

Thus , according to above equation for the Maxwell model or

element, under conditions of constant strain, the stress will decrease

exponentially with time and at the relaxation time t=, s will be equal to

1/e=1/2.7 or 0.37 of its original values (so)

Lord Kelvin

26 June 1824

17 December 1907

William Thomson is popularly known as 1st Baron Kelvin

He was the first British scientist to be elevated to the House of Lords. The title refers to the

River Kelvin, which flows close by his laboratory at the University of Glassgow. His home was

the imposing red sandstone mansion Netherhall, in Largs.

The Kelvin-Voigt model, also called the Voigt model, can be represented by a purely viscous

damper and purely elastic spring connected in parallel as shown in the picture.

A Kelvin–Voigt material, also called a Voigt material, is a viscoelastic material having the

properties both of elasticity and viscosity. It is named after the British physicist and engineer

Lord Kelvin and after German physicist Woldemar Voigt

The spring and dash pot are parallel in the Voigt-Kelvin

model

If G is much larger than , the retardation time (/G) or is small, and is large if

is much larger than G

While polymers melts and elastomers flow readily when stress is applied,

structural plastics must resist irreversible deformation and behave as elastic solids

when relatively small stresses are applied. These plastics are called ideal or

Bingham plastics as described

Kelvin or Voigt model

In parallel

Nonlinear increase in strain with time

Strain decreases with time after load removal because of the action

of the spring (and dashpot).

Descriptive term for a liquid having both viscous and elastic properties.

A viscoelastic liquid will deform and flow under the influence of an applied shear

stress, but when the stress is removed the liquid will slowly recover from some of

the deformation.

Viscoelastic fluids have molecules in which the load-deformation relationship is

time dependant.

The Newtonian model has no value in predicting the behaviour of a drilling fluid,

as the majority of drilling fluids do not conform to the govering Newtonian fluids.

The Bingham Plastic model establishes a distinct relationship between

shear stress, yield point, plastic viscosity and shear rate.

Shear stress:

The force required to overcome a fluid’s resistance to flow, divided by the area

that force is acting upon.

Shear rate:

The relative velocity of the fluid layers divided by their normal separation

distance.

Viscosity is the resistance a material has to change in form. This property

can be thought of as an internal friction.