# NON-NEWTONIAN FLUIDS

# Newtonian Behavior

# The shear rate is directly proportional to the shear stress, and the plot begins at the origin.

# Typical Newtonian foods:

# -containing compounds of low molecular weight (e.g., sugars)

-do not contain large concentrations of either dissolved polymers (e.g., pectins, proteins, starches)

-containing insoluble solids.

Examples: water, sugar syrups, most honeys, most carbonated beverages, edible oils, filtered juices, and milk.

t(Shear stress)= -μ (dv/dr) ( shear rate)

μ constant ( independent of shear rate)

# All other types of fluid foods are non-Newtonian,

# – shear stress-shear rate plot is not linear

-and/or the plot does not begin at the origin

-or exhibits time-dependent rheological behavior

Flow behavior may depend only on shear rate and not on the duration of shear (time independent) or may depend also on the duration of shear (time dependent).

Foods that exhibit time-dependent shear-thinning behavior are said to exhibit thixotropic flow behavior.

Most of the foods that exhibit thixotropic behavior( reversible decrease in shear stress with time at constant shear rate)are heterogeneous systems containing a dispersed phase

( foods such as salad dressings and soft cheeses where the structural adjustments take place in the food due to shear until an equilibrium is reached. )

Time-dependent shear-thickening behavior is called antithixotropic( Formerly, it was called rheopectic) behavior. Reversible increase in shear stress with time at constant shear rate) ( ie gypsum suspension,bentonite suspension)

# Time-Independent Behavior

# Shear-Thinning Behavior ( pseudoplastic)

# n<1

t = K.(-dv/dr)n Power law eq.

t = K.(-dv/dr)n-1(-dv/dr)=μa(-dv/dr)

μa=apparent viscosity

K=consistency index ( N.sn/m2)

n=flow behavior index, dimensionless

may be due to breakdown of structural units in a food due to the hydrodynamic forces generated during shear.

Most non-Newtonian foods exhibit shear-thinning behavior, including biological fluids, xanthan gum soln, starch suspensions many salad dressings and some concentrated fruit juices.

# Shear-Thickening Behavior (Dilatant) n>1

# This type of flow has been encountered in partially gelatinized starch dispersions. Shear-thickening should be due to increase in the size of the structural units as a result of shear.

# Bingham plastic behavior

# The flow of some materials may not commence until a threshold value of stress,

the yield stress (ty), is exceeded

t= -μ.(dv/dr) +ty where ty is yield stress

Shear-thinning with yield stress behavior is exhibited by foods such as tomato concentrates, tomato ketchup, mustard, and mayonnaise.

If the shear rate-shear stress data follow a straight line with a yield stress, the food is said to follow the Bingham plastic model.

# Flow behavior of fluids under shear-stress

# 1-Flow: permenant deformation of fluid

Existance of flow mens: fluid does not recover its originl shape even we remove applied force

2- elastic behavior: all the applied force is stored as bond energy when force is removed it takes its original shape.

If some bonds are broken, so only some bonds are formed to store some of the applied force …. viscoelastic behavior

3-Yield stress(ty): elastic property changed at ty

(when you squeeze tooth paste,it comes out as a cylinder because t is max at wall so first wall side stars flowing)

4- n measures resistance to deformation

n=1 ( Newtonian)…deforms readily under force

As n 0 it becomes elastic( jells shows elastic behavior untill ty, after ty jell breaks down to deform fluid

# Complex rheological models

# ( containing more than 2 parameters)

Herschel-Bulkey Model

t= ty+K(-dv/dr)n (-dv/dr)=γ

μa= t/γ= ty / γ + K.γn-1

as γ increases μa decreases then μ becomes constant

When n =1 behaves like Bingham

When n 0 μa=(ty +K)/ γ so as γ increases μa decreaes

# Cassan Model

# If μ constant for very low and very high γ values and obeys Power law for intermediate γ values,

Then cassan is a sutable model

(μ)1/2 =(μ∞ )1/2 +(ty/γ)1/2

Where μ∞ is viscosity at very high γ

Example: chocolate, cocoa soln

Viscoelastic fluids: exhibits elastic recovery from the deformation that occur during flow. They show both viscous and elastic properties.

Part of deformation is recovered upon removal of the stress.

Example : flour dough, polymer melts

# LAMINAR FLOW OF TIME INDEPENEDENT NON-NEWTONIAN FLUIDS

# Commonly capillary tube viscometers are used to determine properties of the fluids.

ΔP for a given flowrate q is measured in a straigt tube length L and diameter D at different q values.

For a power law fluid:

tw=D.ΔP/4.L=K’(8V/D)n’

Plot of log (tw) vs log(8V/D) yields:

Slope n’ and intercept K’

For most fluids K’ and n’ are constant over wide range of D.ΔP/4.L or 8V/D For some fluids they will vary

In many cases rotational viscometers are used to determine fluid properties.

When the flow propertis are constant over a Range of shear stresses that ocurs for many fluids following equations hold;

n’=n K’=K((3n’+1)/4n’)n’

Generalised viscosity :γ=K’8n’-1

Table 3.5-1 gives n’, K’ and γ values for some foods.

# EQUATIONS FOR LAMINAR FLOW OF NON-NEWTONIAN FLUID IN TUBES

# To calculate pressure drop or mech energy loss due to friction in straight pipe

1- ΔP= (K’4L/D)/(8V/D)n’ ..Ff= ΔP/ρ

vave=(D/8)(ΔP.D/K’4L)1/n’

or

2- NRe,Gen for power law fluid

f=16/NRe,Gen…..

ΔP=4fρ(L/D)(v2/2)…. Ff= ΔP/ρ

Friction loss in contractons, expansions, fittings for non-newtonian fluid, laminar flow

1- kinetic energy correction factor:

# 2-Losses in contraction and fittings:Calculate α as in 1 and use.

# 3-losses in sudden expansion

Non-Newtonian turbulent flow

1- kinetic energy correction factor α=1

2-contractions for fittings α=1

3-expansion treat as newtonian

4-straight pipe:

For 0.36<n’<1 and upto NRe =3.5x104and smooth pipe use fig 3.5-3

For non-Newtonian, turbulent and rough tube use Moody with NRe,Gen as an approximation

Emprical testing instruments for foods

Measuring viscosity

Since viscosity is related with molecular momentum transportation, t, measurement of viscosity should be performed under laminar conditions( resistance is mainly due to viscosity)

There are three major group of viscometers

1- Capillary tube viscometer ( poiseuille flow)

Falling sphere (ball)viscometers

Rotational viscometers

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