Food Rheology

1. Mechanical Models for
Viscoelastic Food
Munna Iype
Joy
315009
M.Tech. -
FSQM

2. VISCOELASTICITY
• Materials with time dependent
deformation.
• The deformation dependent on the
rate at which deformation is made or
deformation causing loads are applied.
• The term visco-elasticity is a
combination of Viscosity and Elasticity

3. • Relation between stress and strain for
a viscoelastic material
Where:
VISCOELASTICITY
σ = σ(ε,έ)
σ = stress
ε = strain
έ = Strain
rate

4. Spring and Dashpot
Analogies
Spring
SpringElastic material
σ = E
ε
σ = stress
E = Modulus of
elasticity
ε = strain
F = k
x
F = Force
k = spring’s
constant
x =
Displacement

5. Analogy between linear
spring and an elastic solid

6. The Dashpot
Dashpot is a simple piston–cylinder
or a syringe type of arrangement.
A force applied on the piston will
advance the piston in the direction of
the applied force.
Spring and Dashpot
Analogies

7. F = Force
μ = Coeff. of friction
ẋ = Velocity
The Dashpot Analogy
F = μ ẋ
Force–displacement rate
diagram of dashpot

8. For viscous material
σ = η έ
σ = shear stress
η = coeff. of
viscosity
έ = strain rate

9. σ = η έ
σ = shear stress
η = Coeff. of
viscosity
έ = strain rate
F = Force
μ = Coeff. of
friction
ẋ = Velocity
F = μ ẋ
The Dashpot Analogy

10. Empirical Models of
Viscoelasticity

11. 1. Kelvin – Voight Model
 Spring and dashpot connected in
parallel
 A stress σ applied is shared by the
spring and dashpot elements.
σ = σ + σ

12. 1. Kelvin – Voight Model
 Since the spring and dashpot are
connected in parallel, the strain
developed will be equal.
 stress strain relation for spring
 stress strain relation for Dashpot
ε = εs =
εd
σs = E
εs
σd = η
έd

13. 1. Kelvin – Voight Model
σ = E ε + η έ
• έ can be written as dε/dt
 This is Kelvin – Voight model
σ = E ε + η
dε/dt

14. Application of Kelvin – Voight Model
• Research on Mechanical Behaviour of French Roll in the
Mode of Compressed Chewing

15. 2. The Maxwell Model
• Connecting a spring and dashpot in
series.
• Stress are equally applied σ = σs =
σd
• Strain will be ε = εs + εd

16. 2. The Maxwell Model
Stress strain relation for spring
 Stress strain relation for Dashpot
εs= σs/E έd = σd/η
 Differentiating ε = εs + εd & εs= σs/E
 έ = έd + έ s & έ s = σs´/E
σs = E
εs
σd = η
έd

17. 2. The Maxwell Model
έ = έd + έ s becomes έ = σ/η + σ´/E
Cross multiplying and rearranging,
 This is Maxwell Model

18. Applications
 Maxwell model is used to study stress relaxation/
step strain of viscoelastic materials
Free spring accounts for equilibrium stress

19. Stress relaxation behaviour of moth bean flour
dough
 Low strain data modelled by 4 - element Maxwell model
Suitability of Maxwell model for the relaxation of raw moth bean dough
having (A) 30% and moisture content subjected to low strain (0.05).

20. Stress relaxation behaviour of moth bean flour
dough
Suitability of Maxwell model for the relaxation of raw moth bean dough
having (B) 32% and moisture content subjected to low strain (0.05).

21. Stress relaxation behaviour of moth bean flour
dough
Suitability of three-parameter non-linear model for the relaxation
characteristics of raw moth bean dough having 32% moisture content
subjected to high strain (0.50).

22. 3. The Burgers Model
 Burgers model is used to study creep
compliance
 In creep test instantaneous strain is
applied to the sample and the change in
strain is observed over time
ε= f(t) = σ0/E 0 + σ0/E 1 [ 1- EXP (t/λ ret)]
+ σ0 t / η 0Application

23. 3. The Burgers Model

24.  Viscoelastic materials cannot be
represented by Maxwell / Kelvin models /
Burgers model solely.
 Hence we use Generalized Maxwell or
Kelvin models for the accurate
representation.
 The generalized Maxwell model consists
of N different Maxwell units in parallel.
Generalized Viscoelastic
Models

25. Generalized Viscoelastic
Models

26. Generalized Viscoelastic
Models
 Generalized Kelvin chain consists of a
chain of Kelvin units

27. Generalized Viscoelastic
Models
General form of viscoelastic models :
Above equation is written in short as follows:
 More the elements used higher the degree of d.e

28. Applications
1. Stress relaxation characteristics of low-fat chicken
sausages made in Argentina

29. Applications
2. Use of the generalized Maxwell model for describing the
stress relaxation behaviour of solid-like foods

30. Applications
2. Use of the generalized Maxwell model for describing the
stress relaxation behaviour of solid-like foods

31. Thank You….