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**An overview http://sst.tees.ac.uk/external/U0000504/Notes/mscnotes/**

Food Rheology An overview

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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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**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

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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

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