Food Rheology An overvie

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Food Rheology

• An overview
• http//sst.tees.ac.uk/external/U0000504/Notes/mscn
  otes/

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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

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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

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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

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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

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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

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The Newtonian fluid (2)

• In symbols

g-dot is the shear rate
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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
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Non-Newtonian models

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

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Apparent viscosity

• By rearranging the power law we can define a
  property called apparent viscosity, happ

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Time dependant viscosity

• There are two time dependant types of fluid
• Thixotropic, where viscosity decreases with time
• Dilatent where viscosity increases with time

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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

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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
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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

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Dashpot and spring models

• Maxwell element

• Kelvin or Voigt element

This element models stress relaxation
This element models creep
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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.

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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

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Complex stress and strain (2)

• The response to an applied oscillatory shear is
  illustrated below

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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
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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.

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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/mscn
  otes/