Transcript Food Rheology - Teesside University

Food Rheology
An overview
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notes/
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
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
Force
Area
Deformatio n
Strain 
Original Length
Stress 
Shear


Shear is the result of two
forces acting out of line.
It is illustrated in the
diagram opposite
stress, t and
shear strain, g are
defined from
Shear
F
t
A
x
g
y
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

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
The Newtonian fluid (2)
 In
symbols
dv
t
or
dy
t    g
g-dot is the shear rate
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
Non-Newtonian models

Time independent
non-Newtonian fluids
conform to one of the
following models



Bingham plastic
Power law
Herschel Bulkley
Bingham
t  t0   p g
Power law
t  Kg n
Herschel - Bulkley
t  t0  Kg n
Apparent viscosity

By rearranging the power
law we can define a
property called apparent
viscosity, app


t  Kg n  Kg n 1 g

app  Kg n 1
hence
t  app g

Time dependant viscosity

There are two time dependant types of fluid:


Thixotropic, where viscosity decreases with time
Dilatent where viscosity increases with time
Visco-elasticity
 Some
solids display liquid-like properties.
 Such solids are described as visco-elastic.
 Two particular properties characterise viscoelastic solids. These are
Creep
 Stress relaxation

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
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

Dashpot and spring models
Maxwell element
Kelvin or Voigt element
This element models stress
relaxation
This element models
creep
Dashpot and spring models (2)


Neither the Maxwell nor
the Kelvin model on their
own fully explain viscoelastic behaviour and
more complex models are
required
The example on the right
quite effectively models
the behaviour of cheese.
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”
Complex stress and strain (2)

The response to an applied oscillatory shear is
illustrated below
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, 
These are defined on the right
t m cos 
G 
gm
t m sin 
G  
gm
G 
 tan 
G
tm and gm are the maximum values of shear stress and
shear strain respectively
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.

G* 
G
2
 G2

For more information
 This
lecture has only been an overview.
 More information is available via the
Module website.
 Or go directly to

http://sst.tees.ac.uk/external/U0000504/Notes/
mscnotes/