Food Rheology Introduction

1. Part I
Dr. Kshitiz Kumar
Dr. Kshitiz Kumar

2.  The first use of the word "rheology" is
credited to Eugene C. Bingham (1928)
 The motto of the subject as "panta rhei,“
meaning "everything flows“
 Rheology is the science that studies the flow
and deformations of solids and fluids under
the influence of mechanical forces.
Dr. Kshitiz Kumar

3.  Process engineering calculations involving a wide range of
equipment such as pipelines, pumps, extruders, mixers,
coaters, heat exchangers, homogenizers.
 Determining ingredient functionality in product
development
 Intermediate or final product quality control
 Shelf life testing
 Evaluation of food texture by correlation to sensory data
 Analysis of rheological equations of state or constitutive
equations.
Dr. Kshitiz Kumar

4. Dr. Kshitiz Kumar

5. Dr. Kshitiz Kumar

6.  Consider a fluid between two large parallel plates of area A, separated by a
very small distance Y .
 The system is initially at rest but at time t = 0, the lower plate is set in
motion in the z-direction at a constant velocity V by applying a force F in
the z-direction while the upper plate is kept stationary.
 At t = 0, the velocity is zero everywhere except at the lower plate, which
has a velocity V .
 Then, the velocity distribution starts to develop as a function of time.
 Finally, steady state is achieved and a linear velocity distribution is
obtained.
 The velocity of the fluid is experimentally found to vary linearly from zero
at the upper plate to velocity V at the lower plate, corresponding to no-slip
conditions at each plate.
Dr. Kshitiz Kumar

7.  Experimental results show that the force required to maintain the
motion of the lower plate per unit area is proportional to the velocity
gradient, and the proportionality constant, μ, is the viscosity of the fluid:
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8.  Subscripts: z represents the direction of force and y
represents the direction of normal to the surface on which
the force is acting.
 A negative sign is introduced into the equation because the
velocity gradient is negative, that is, velocity decreases in
the direction of transfer of momentum.
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9.  Viscosity is defined as the resistance of a fluid to flow.
 The unit of dynamic viscosity is (Pa · s) in the SI system.
 The temperature effect on viscosity can be described by an
Arrhenius type equation:
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10.  Viscosities of liquids decrease as temperature
increases.
 In most liquids, viscosity is constant up to a
pressure of 10.134MPa, but at higher
pressures viscosity increases as pressure
increases.
 In most gases, viscosity increases with
increasing temperature.
 Reasons ??
 ASSIGNMENT 1
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11.  It is the ratio of dynamic viscosity to density
of fluid.
 Its unit is m2/s in SI and stoke (cm2/s) in CGS.
 It has the same units as thermal diffusivity [α =
k/(ρ cp)] in heat transfer and mass diffusivity (DAB)
in mass transfer.
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12.  Ideal Viscous Fluid: Fluids tend to deform and
flow as soon as shear stress is applied is called
ideal viscous fluid.
 They dissipate energy hence cannot return to original
state when stress is removed.
 Ideal Plastic fluid: When a stress is applied, then
there will be no physical change unless and until
the applied stress reaches the yield stress of the
material.
 They are always non-Newtonian fluids
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13. Dr. Kshitiz Kumar

14.  Fluids that follow Newton’s law of viscosity are
called Newtonian fluids.
 The slope of the shear stress versus shear rate
graph, which is viscosity, is constant and
independent of shear rate in Newtonian fluids.
 Example: Gases, oils, water, and most liquids that
contain more than 90% water such as tea, coffee,
beer, carbonated beverages, fruit juices, and milk
show Newtonian behavior.
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15. The slope of the line increases with increasing viscosity.
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16.  Fluids that do not follow Newton’s law of viscosity
are known as non-Newtonian fluids.
 It may be both viscous as well as plastic fluids.
 Shear thinning or shear thickening fluids obey the
power law model and hence also called power law
fluid.
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17.  Newtonian fluids can be considered as a
special case of this model in which n = 1 and k
= μ.
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18.  The slope of shear stress versus shear rate graph is not constant for non-
Newtonian fluids
 For different shear rates, different viscosities are observed.
 The ratio of shear stress to the corresponding shear rate is therefore called
apparent viscosity at that shear rate.
 For Newtonian fluid,
 Hence
 For non-Newtonian fluid,
 Hence
 Apparent viscosity can be found out through the secant modulus at given
shear rate.
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20.  They are power law fluid where n < 1
 The fluid flow curve begin at the
origin of shear stress-shear rate plot
and is convex towards shear stress
axis.
 An increasing shear rate gives less than
proportional increase in stress.
 The apparent viscosity decreases
with increase in shear rate and the
change is irreversible.
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21.  In these types of fluids, as shear rate
increases friction between layers decreases.
 Shearing causes entangled, long-chain
molecules to straighten out and become
aligned with the flow, reducing viscosity.
 Example: paint, ink, banana puree,
concentrated fruit juices
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22.  They are power law fluid where n >1
 The fluid flow curve begin at the
origin of shear stress-shear rate plot
and is concave towards shear stress
axis.
 An increasing shear rate gives more
than proportional increase in stress.
 The apparent viscosity increases
with increase in shear rate and the
change is irreversible.
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23.  In these types of fluids, as shear
rate increases, the internal
friction increase.
 Shear thickening is due to
increase in size of the structural
units as a result of shear.
 Example: corn starch
suspension, sausage slurry,
homogenized peanut butter,
whipped cream, whipped egg
white, pulp in water.
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24.  If the increase in viscosity is accompanied by
volume expansion, shear thickening fluids
are called dilatant fluids.
 Example: Liquid chocolate, 60% suspension
of corn starch.
 All the dilatant fluids are shear thickening but
not all shear thickening fluids are dilatant.
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25.  In these types of fluids, fluid
remains rigid when the magnitude
of shear stress is smaller than the
yield stress (τ0) but flows like a
Newtonian fluid when the shear
stress exceeds τ0.
 Example: toothpaste,
mayonnaise, tomato paste, and
ketchup
 Equation for the behavior of
Bingham plastic fluids can be
written as:
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26.  The apparent viscosities for Bingham plastic
fluids can be determined by taking the ratio
of shear stress to the corresponding shear
rate:
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27.  These fluids do not behave as Newtonian
fluid beyond the yield stress.
 In these types of fluids, a minimum shear
stress known as yield stress must be
exceeded before flow begins, as in the case of
Bingham plastic fluids.
 However, the graph of shear stress versus
shear rate is not linear.
 Fluids of this type are either shear thinning or
shear thickening with yield stress.
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28.  If the fluid has a yield stress and
shear stress versus shear rate
curve is convex towards the
shear stress axis then the fluid is
called H-B fluid i.e. it is a
pseudoplastic fluid with yield
point.
 The governing equation is:
 where n < 1
 Example: Minced fish paste, rice
flour based batter, raisin paste
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29. 1) Casson Model::
▪ Molten milk chocolate obeys Casson Model.
2) Ellis Model: Suitable to predict Newtonian viscosity at small
value of shear rate.
3) Sisko Model: For semi solid material at high shear rate.
4) Reiner-Philippoff Model: Predict lower and higher viscosities at
low and high value of shear rate.
5) Carreau Model
6) Cross Model
7) Van-Wazer Model
8) Powell-Erying Model
9) Brodkey Model
10) Mizrahi and Berk Model
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30. Time-dependent behavior of fluids
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31.  When some fluids are subjected to a constant shear rate, they
become thinner (or thicker) with time.
 Thixotropic fluids (shear thinning with time): Fluids that
exhibit decreasing shear stress and apparent viscosity with
respect to time at a fixed shear rate .
 This phenomenon is probably due to the breakdown in the structure of
the material as shearing continues.
 Example:Gelatin, egg white, shortening.
 Thixotropic behavior may be reversible, partially reversible,
or irreversible when the applied shear is removed (fluid is
allowed to be at rest).
 Irreversible thixotropy is called rheomalaxis or
rheodestruction
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32.  If the shear stress is
measured as a function
of shear rate, as the
shear rate is first
increased and then
decreased, a hysteresis
loop will be observed
in the shear stress
versus shear rate curve
Shear stress versus shear rate
curve showing hysteresis
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33.  Rheopectic fluids (shear thickening with
time): Shear stress and apparent viscosity
increase with time, that is, the structure
builds up as shearing continues.
 Bentonite–clay suspensions show this type of
flow behavior.
 It is rarely observed in food systems.
 One example reported is fenugreek paste
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