Food RheologyFood Rheology

An overviewAn overviewhttp://sst.tees.ac.uk/external/U0000504/Notes/http://sst.tees.ac.uk/external/U0000504/Notes/mscnotes/mscnotes/

The Scope of RheologyThe Scope of Rheology

The study of the deformation and flow of The study of the deformation and flow of mattermatter

Concerned with Concerned with the effect of shear stresses on materials having the effect of shear stresses on materials having

properties of fluidsproperties of fluids The properties of materials lying between two The properties of materials lying between two

ideal states:ideal states: the elastic solidthe elastic solid the Newtonian liquidthe Newtonian liquid

Stress and strainStress and strain

When a material is subject When a material is subject to static forces, the to static forces, the material is deformedmaterial is deformed

The degree of deformation The degree of deformation depends ondepends on the material propertiesthe material properties the dimensions of the objectthe dimensions of the object

In order to standardise the In order to standardise the latter we define two latter we define two quantities, stress and quantities, stress and strainstrain

Length Original

nDeformatioStrain

Area

ForceStress

Shear Shear

Shear is the result of two Shear is the result of two forces acting out of line.forces acting out of line.

It is illustrated in the It is illustrated in the diagram oppositediagram opposite

Shear stress, Shear stress, and and shear strain, shear strain, are are defined fromdefined from

y

xA

F

The elastic solidThe elastic solid

An elastic solid is one which returns to its original An elastic solid is one which returns to its original state after being deformed.state after being deformed.

The relationship between shear stress and shear The relationship between shear stress and shear strain is a linear onestrain is a linear one

For shear, the slope of the line is called the For shear, the slope of the line is called the shear shear modulus, modulus, G and is defined as G and is defined as

The Newtonian FluidThe Newtonian Fluid

If a force is applied to a fluid, it shearsIf a force is applied to a fluid, it shears As a result a velocity gradient is set up in the fluid As a result a velocity gradient is set up in the fluid

which is proportional to the shear stresswhich is proportional to the shear stress This constant of proportionality is called the This constant of proportionality is called the

viscosityviscosity

The Newtonian fluid (2)The Newtonian fluid (2)

In symbolsIn symbols

or dy

dv

-dot is the shear rate -dot is the shear rate

Non-Newtonian flowNon-Newtonian flow

For a Newtonian fluid, For a Newtonian fluid, viscosity is a constant and viscosity is a constant and a graph of shear stress vs. a graph of shear stress vs. shear rate is a straight lineshear rate is a straight line

Fluids whose viscosity is Fluids whose viscosity is not constant are called not constant are called Non-newtonian. There Non-newtonian. There are three main categoriesare three main categories Shear thinningShear thinning Shear thickeningShear thickening Time dependantTime dependant

Properties of time independent Properties of time independent fluidsfluids

Non-Newtonian modelsNon-Newtonian models

Time independent Time independent non-Newtonian fluids non-Newtonian fluids conform to one of the conform to one of the following modelsfollowing models Bingham plasticBingham plastic Power lawPower law Herschel BulkleyHerschel Bulkley

n0

n

0

K

Bulkley-Herschel

K

lawPower

Bingham

p

Apparent viscosityApparent viscosity

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

app

napp

nn

K

KK

hence

1

1

Time dependant Time dependant viscosityviscosity

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

Visco-elasticityVisco-elasticity

Some solids display liquid-like properties. Some solids display liquid-like properties. Such solids are described as Such solids are described as visco-elasticvisco-elastic.. Two particular properties characterise Two particular properties characterise

visco-elastic solids. These arevisco-elastic solids. These are CreepCreep Stress relaxationStress relaxation

Visco-elasticity (2)Visco-elasticity (2)

Creep is the Creep is the continuing extension continuing extension of a solid when a of a solid when a constant load is constant load is appliedapplied

Stress relaxation is Stress relaxation is the reduction in stress the reduction in stress needed to maintain needed to maintain constant strainconstant strain

Creep curveCreep curve

Models of visco-elastic Models of visco-elastic behaviourbehaviour

Visco elastic behaviour can be modelled by spring Visco elastic behaviour can be modelled by spring and dashpot models. and dashpot models.

The spring represents the elastic propertiesThe spring represents the elastic properties The dashpot represents the viscous propertiesThe dashpot represents the viscous properties The two simplest are the Maxwell and Kelvin The two simplest are the Maxwell and Kelvin

elements elements These are shown on the next two slidesThese are shown on the next two slides

Dashpot and spring Dashpot and spring modelsmodels

Maxwell elementMaxwell element Kelvin or Voigt elementKelvin or Voigt element

This element models stress This element models stress relaxationrelaxation

This element models This element models creepcreep

Dashpot and spring Dashpot and spring models (2)models (2)

Neither the Maxwell nor Neither the Maxwell nor the Kelvin model on their the Kelvin model on their own fully explain visco-own fully explain visco-elastic behaviour and elastic behaviour and more complex models are more complex models are requiredrequired

The example on the right The example on the right quite effectively models quite effectively models the behaviour of cheese.the behaviour of cheese.

Complex stress & strainComplex stress & strain

Another method of Another method of characterising visco-elastic characterising visco-elastic materials is to apply varying materials is to apply varying strainstrain

This is usually achieved by This is usually achieved by applying an oscillatory shear applying an oscillatory shear strain to a samplestrain to a sample

The equations describing the The equations describing the response to such a strain response to such a strain involve complex numbers, involve complex numbers, hence the term “complex stress hence the term “complex stress and strain”and strain”

Complex stress and Complex stress and strain (2)strain (2)

The response to an applied oscillatory shear is The response to an applied oscillatory shear is illustrated belowillustrated below

Complex moduliComplex moduli

The rheological properties in The rheological properties in oscillatory shear are oscillatory shear are characterised by the complex characterised by the complex moduli.moduli. The storage modulus, G’The storage modulus, G’ The loss modulus, G”The loss modulus, G”

These are related by the phase These are related by the phase angle, angle,

These are defined on the rightThese are defined on the right

tan

sin

cos

G

G

G

G

m

m

m

m

mm and and mm are the maximum values of shear stress and are the maximum values of shear stress and

shear strain respectivelyshear strain respectively

Complex moduliComplex moduli

The storage modulus relates to the bulk properties The storage modulus relates to the bulk properties of the solidof the solid

The loss modulus relates to the vibrational state of The loss modulus relates to the vibrational state of the molecules.the molecules.

They can be combined to give an overall complex They can be combined to give an overall complex modulus, G*, though this property is not as useful modulus, G*, though this property is not as useful as the separate moduli.as the separate moduli.

22* GGG

For more informationFor more information

This lecture has only been an overview.This lecture has only been an overview. More information is available via the More information is available via the

Module website. Module website. Or go directly toOr go directly to

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