1. An overview http://sst.tees.ac.uk/external/U0000504/Notes/mscnotes/
Food Rheology
An overview

2. The Scope of Rheology The study of the deformation and flow of matter
Concerned with
the effect of shear stresses on materials having properties of fluids
The properties of materials lying between two ideal states:
the elastic solid
the Newtonian liquid

3. Stress and strain
When a material is subject to static forces, the material is deformed
The degree of deformation depends on
the material properties
the dimensions of the object
In order to standardise the latter we define two quantities, stress and strain

4. Shear Shear is the result of two forces acting out of line.
It is illustrated in the diagram opposite
Shear stress, t and shear strain, g are defined from

5. The elastic solid
An elastic solid is one which returns to its original state after being deformed.
The relationship between shear stress and shear strain is a linear one
For shear, the slope of the line is called the shear modulus, G and is defined as

6. The Newtonian Fluid If a force is applied to a fluid, it shears
As a result a velocity gradient is set up in the fluid which is proportional to the shear stress
This constant of proportionality is called the viscosity

7. The Newtonian fluid (2)
In symbols
g-dot is the shear rate

8. Properties of time independent fluids
Non-Newtonian flow
For a Newtonian fluid, viscosity is a constant and a graph of shear stress vs. shear rate is a straight line
Fluids whose viscosity is not constant are called Non-newtonian. There are three main categories
Shear thinning
Shear thickening
Time dependant
Properties of time independent fluids

9. Non-Newtonian models
Time independent non-Newtonian fluids conform to one of the following models
Bingham plastic
Power law
Herschel Bulkley

10. Apparent viscosity
By rearranging the power law we can define a property called apparent viscosity, happ

11. Time dependant viscosity
There are two time dependant types of fluid:
Thixotropic, where viscosity decreases with time
Dilatent where viscosity increases with time

12. Visco-elasticity Some solids display liquid-like properties.
Such solids are described as visco-elastic.
Two particular properties characterise visco-elastic solids. These are
Creep
Stress relaxation

13. Visco-elasticity (2)
Creep is the continuing extension of a solid when a constant load is applied
Stress relaxation is the reduction in stress needed to maintain constant strain
Creep curve

14. Models of visco-elastic behaviour
Visco elastic behaviour can be modelled by spring and dashpot models.
The spring represents the elastic properties
The dashpot represents the viscous properties
The two simplest are the Maxwell and Kelvin elements
These are shown on the next two slides

15. Dashpot and spring models
Maxwell element
Kelvin or Voigt element
This element models stress relaxation
This element models creep

16. Dashpot and spring models (2)
Neither the Maxwell nor the Kelvin model on their own fully explain visco-elastic behaviour and more complex models are required
The example on the right quite effectively models the behaviour of cheese.

17. Complex stress & strain
Another method of characterising visco-elastic materials is to apply varying strain
This is usually achieved by applying an oscillatory shear strain to a sample
The equations describing the response to such a strain involve complex numbers, hence the term “complex stress and strain”

18. Complex stress and strain (2)
The response to an applied oscillatory shear is illustrated below

19. Complex moduli
The rheological properties in oscillatory shear are characterised by the complex moduli.
The storage modulus, G’
The loss modulus, G”
These are related by the phase angle, d
These are defined on the right
tm and gm are the maximum values of shear stress and shear strain respectively

20. Complex moduli
The storage modulus relates to the bulk properties of the solid
The loss modulus relates to the vibrational state of the molecules.
They can be combined to give an overall complex modulus, G*, though this property is not as useful as the separate moduli.

21. For more information This lecture has only been an overview.
More information is available via the Module website.
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