This document discusses rheological properties of food materials. It defines rheology as the science studying deformation and flow of materials. Rheological data is needed for product quality evaluation, engineering calculations, and process design. The document classifies and describes different types of stresses, strains, moduli, and behaviors exhibited by materials under stress including elastic, plastic, viscous, and viscoelastic. It provides examples of evaluating the modulus of elasticity and Poisson's ratio for dry pasta fibers under tensile stress.

1. Food Processing
Engineering-I
FMP-302
Rheological properties of food materials
Lecture# 3-4

2. Introduction
 Rheology is the science that studies the deformation of materials
including flow.
 Rheological properties are defined as mechanical properties that
result in deformation and the flow of material in the presence of a
stress.
 Rheological data are required in product quality evaluation,
engineering calculations, and process design.
 An understanding of flow behavior is necessary to determine the
size of the pump and pipe and the energy requirements.
 Effects of processing on rheological properties must be known for
process control.
 Rheological properties also effect filling operations and most of
handling procedures.

3. Classification of Rheology

4. Deformation of materials
 Stress: This internal force per unit area at any section of the body
is known as unit stress or simply a stress.
Stress, σ = P/A
where P = Force or load acting on a body, and A = Cross-sectional
area of the body.
In S.I. units, the stress is usually expressed in Pascal (Pa).
 Strain: The deformation per unit length is known as unit strain
or simply a strain.
Strain, ε = δl / l or δl = ε.l
where δl = Change in length of the body, and l = Original length of
the body.
It is dimension less quantity.

5. Cont’d…
Tensile Stress and Strain
 When a body is subjected to two equal and opposite axial pulls as
shown in Fig. a, the stress induced at any section of the body is
known as tensile stress as shown in Fig. b, then there will be a
decrease in cross-sectional area and an increase in length of the
body. The ratio of the increase in length to the original length is
known as tensile strain.
 Tensile stress, σt = P/A
 Tensile strain, ε t = δl / l

6. Cont’d…
Compressive Stress and Strain
 When a body is subjected to two equal and opposite axial pushes
as shown in Fig. a, the stress induced at any section of the body is
known as compressive stress as shown in Fig. b, then there will
be a decrease in cross-sectional area and an increase in length of
the body. The ratio of the increase in length to the original length
is known as compressive strain.
 Compressive stress, σc = P/A
 Compressive strain, εc = δl /l

7. Cont’d…
Young's Modulus or Modulus of Elasticity
 Hooke's law states that when a material is loaded within elastic
limit, the stress is directly proportional to strain.
σ ∝ ε or σ = E.ε
∴ E = σ/ ε = P×l/A× δl
Where E is a constant of proportionality known as Young's modulus
or modulus of elasticity.
 In S.I. units, it is usually expressed in Pa

8. Cont’d…
Shear Stress and Strain
 When a body is subjected to two equal and opposite forces acting
tangentially across the resisting section, as a result of which the
body tends to shear off the section, then the stress induced is
called shear stress.
 The corresponding strain is known as shear strain and it is
measured by the angular deformation accompanying the shear
stress.
 Shear stress, τ = Tangential force/Resisting area

9. Cont’d…
Shear Modulus or Modulus of Rigidity
 It has been found experimentally that within the elastic limit, the
shear stress is directly proportional to shear strain.
Mathematically
 τ ∝ φ or τ = C . φ or τ / φ = C
where τ = Shear stress,
 φ = Shear strain, and
 C = Constant of proportionality, known as shear modulus or
modulus of rigidity.

10. Cont’d…
 Linear and Lateral Strain: every direct stress is accompanied
by a strain in its own direction which is known as linear strain
and an opposite kind of strain in every direction, at right angles to
it, is known as lateral strain.
 Poisson's Ratio: It has been found experimentally that when a
body is stressed within elastic limit, the lateral strain bears a
constant ratio to the linear strain, Mathematically,
Lateral strain/Linear strain = Constant
 This constant is known as Poisson's ratio and is denoted by μ.

11. Cont’d…
 *Volumetric Strain: The ratio of the change in volume to the
original volume is known as volumetric strain. Mathematically,
volumetric strain,
*Volumetric Stresses and strains can also be described as either
dilatational or deviatoric.
εv = δV / V
Where δV = Change in volume, and V = Original volume.
 Bulk Modulus: When a body is subjected to three mutually
perpendicular stresses, of equal intensity, then the ratio of the
direct stress to the corresponding volumetric strain is known as
bulk modulus. It is usually denoted by K. Mathematically, bulk
modulus,
K = Direct stress/Volumetric strain = σ/(δV/V)

12. Cont’d…
 Impact Stress: The stress produced in the member due to the
falling load is known as impact stress.
 Resilience: When a body is loaded within elastic limit, so long as
it remains loaded, it has stored energy in itself. This energy,
which is absorbed in a body when strained within elastic limit, is
known as strain energy. The strain energy stored in a body due to
external loading, within elastic limit, is known as resilience and
the maximum energy which can be stored in a body up to the
elastic limit is called proof resilience. The proof resilience per
unit volume of a material is known as modulus of resilience.
 It is an important property of a material and gives capacity of the
material to bear impact or shocks.

13. Cont’d…
 Strength: Ability to bear a load before fracture.
 Elasticity: Ability to restore to original shape and size after
removal of external deforming loads
 Plasticity - the deformation of a material undergoing non-
reversible changes of shape in response to applied forces
 Stiffness: Resistance to ELASTIC (or RECOVERABLE)
Deformation .
 Hardness: Resistance to PLASTIC (or PERMANENT)
Deformation which Includes Indentation, Scratching or Marking.
 Fracture: Splitting of a component into at least two halves
 Creep: Permanent Deformation and/or Failure of a component
when subjected to high stresses at high temperature.
 Bioyield point is defined as the point at which an increase in
deformation is observed with a decrease or no change of force.

14. Cont’d…
 When a stress is applied to a purely elastic solid, it will deform
finitely but then it will return to its original position after the
stress is removed. Material showing elastic behavior is known as
a Hookean solid.
 Foods that follow Hookean’s law are dry pasta, egg shells, and
hard candies when subjected to small strains (e.g., < 0.01)
 The ratio of stress to strain is known as modulus while the ratio
of strain to stress is known as compliance.
 Different types of moduli are defined for a Hookean solid.

15. Example
 Dry commercial semolina fibers with a diameter of 1.65
mm are used to examine the rheological properties of
dry spaghetti. A tensile stress of 15MPa is applied on
fibers of 150 mm length.
1. Determine the value of the modulus of elasticity. When
length of fiber exceeded by 0.3% of original length
2. What is the Poisson ratio if the fibers exhibit a diameter
change of 2.43×10−3 mm under the stress of 15 MPa?

16. Solution
 Given: σt = 15MPa, L = 150 mm, D = 1.65 mm, ∆D =
2.43×10−3
 ∆L =
0.3
100
× 150 = 0.45 mm
 εl =
∆L
L
=
0.45
150
= 0.003
 Modulus of elasticity is defined as: E =
σ
ε
=
15
0.003
= 5000 MPa
 εd =
∆D
D
=
2.43×10−3
1.65
= 0.0015
 Poisson ratio is μ =
∆D/D
∆L/L
=
0.0015
0.003
= 0.49

17. Viscoelastic Behavior
 When a force is applied to a viscous fluid, it will start to deform
and this deformation is proportional with the magnitude of force
applied. It deforms continuously until the force is removed so that
it cannot return to its original position.
 Viscous fluids generally exhibit viscosity while solids exhibit
elasticity.
 Some foods show both viscous and elastic properties which are
known as viscoelastic materials.
 The typical food example for viscoelastic fluids is wheat flour
dough. Dairy cream, ice cream mix, marshmallow cream, cheese,
and most gelled products are also viscoelastic foods.

18. Cont’d…
 When a viscous fluid is agitated, the circular motion causes a
vortex. If a viscoelastic fluid is stirred by a rotating rod it tends to
climb the rod, which is known as the Weissenberg effect.
 When the flow of viscoelastic material is stopped, tensile forces
in the fluid cause particles to move back. However, viscous fluids
stay where they are when their motion is stopped. This is called
the recoil phenomenon.

19. Cont’d…