Food Reology

8/2/2019 Food Reology

1/13

3/4/2011

1

One may classify fluids in two different ways:

Classification of fluid behaviour

either according to their response to the externallyapplied pressure or

according to the effects produced under the action of ashear stress.

Newtonian

Fluids

Non-Newtonian


2/13

3/4/2011

2

Newtonian fluids

Consider a thin layer of a fluid contained between two

parallel planes a distance dy apart

Newtonian fluids

At any shear plane there are two equal

and opposite shear stress

a positive one on the slower moving fluid

and

a negative on the faster moving fluid layer

The Negative sign on the right hand side

of equation indicates that shear stress

is a measure of the resistance to

motion.


3/13

3/4/2011

3

Newtonian fluids

For an incompressible fluid of density

x x

d( V )

y

The quantity Vx is the linear momentum in the

x direction per unit volume (momentum

concentration).

yx represent the momentum flux in y directionThe negative sign indicates that the momentum

transfer occurs in the direction of decreasing

velocity

Newtonian fluids

The constant of proportionality, , is called

Newtonian viscosity

Independent of shear rate or shear stress

Depends only on the material and its T and PThe plot of shear stress against shear rate for a

,

straight line of slope, , and passing through

the origin


4/13

3/4/2011

4

Newtonian fluids

Gases, simple organic liquids, solution of low

molecular wei ht inor anic salts molten metal

and salts are Newtonian fluids.

Newtonian fluids

Typicalshearstresscookingoilandacornsyrup


5/13

3/4/2011

5

Newtonian fluids

For the more complex case of three-dimensional flow, it is necessary to

set up the appropriate partial differential equations.

For instance, the more general case of an incompressible Newtonian

u may e expresse or e x -p ane area or en e norma o e x

-direction) as follows ( Bird et al ., 1987, 2002 ):

Stress components in three-dimensionalflow

By considering the equilibrium of a fluid element, it can be shown that:

yx xy xz zx yz zy


6/13

3/4/2011

6

Stress components in three-dimensional

flowThenormalstressescanbevisualizedasbeingmadeupoftwocomponents:

isotropicpressure acontributionduetoflow

xx xxP p

yy yyP p

zz zz

xx yy zz

1p (P P P )

3

ForanincompressibleNewtonianfluid,theisotropicpressureisgivenby:

1P P P xx yy zz

3


7/13

3/4/2011

7

Non-Newtonian fluids

Time independent fluids (purely viscous,

inelastic, or generalized Newtonian

fluids (GNF))

Time dependent fluids

sco-e ast c u s

Time-independent fluid behaviour

In simple shear, the flow behaviour of this class

of materials may be described by a constitutive

relation of the form,

This equation implies that the value of the

shear rate at any point within the sheared fluid

is determined only by the current value of shear

stress at that point or vice versa.


8/13

3/4/2011

8

Time-independent fluid behaviour

these fluids may be further subdivided into

three types:

(a)Shear-thinning or pseudoplastic

(b)Viscoplastic

(c)Shear-thickening or dilatant.

Types of time-independent flow behaviour


9/13

3/4/2011

9

Shear-thinning or pseudoplastic fluids



10/13

3/4/2011

10


Mathematical models for shear-thinningfluid behaviour

More widely used viscosity models:

i. The power-law or Ostwald de Waele

model

ii. The Carreau viscosity equation

iii. The Cross viscosit e uation

iv. The Ellis fluid model


11/13

3/4/2011

11

The power-law or Ostwald de Waele model

An expression of the following form is applicable:n

yx yxm( )

Thus the apparent viscosity is given by:

n 1

app yx yx yxm( )

m: fluid consistenc coefficient

For n1, the fluid shows shear thickening behavior

n: flow behavior index


12/13

3/4/2011

12

The Carreau viscosity equation

When there are significant deviations from the

power-law model at very high and very low

s ear ra es , s necessary o use a mo e

which takes account of the limiting values of

viscosities 0 and

(n 1) / 2app 2

yx

0

1 ( )

The Carreau viscosity equation

Another four parameter model (Cross 1965),

which in simple shear, is written as:

app

n0 yx

1

1 k( )

n (


13/13

3/4/2011

13

The Ellis fluid model

When the deviations from the power-law modelare significant only at low shear rates, it is

perhaps more appropriate to use the Ellis model.

0app 1

yx 1/ 21 ( )

When the deviations from the power-law model

are significant only at low shear rates, it isperhaps more appropriate to use the Ellis model.

Food Reology

Documents

Transcript of Food Reology