Food physics
The study of structure-function relations from molecular to macroscopic scale using the colloidal
scale as an intermediate
Chapter 2: Bulk Rheology
Rheology: The science that studies the relation between forces applies on a material and its (rate of)
deformation
Fluids: Viscous liquids
Shear flows
- Velocity in the x-direction varies in the y-direction
- Shear flow found in flow of liquids between parallel plates of a heat exchanger or flow of
liquids in a pipe
- Liquid in the center flows faster than the outer liquid due to shearing
Equations
𝑆ℎ𝑒𝑎𝑟 𝑠𝑡𝑟𝑒𝑠𝑠: 𝜎𝑥𝑦 = 𝜂 ∗ 𝛾𝑥𝑦 η = shear viscosity
𝛿𝑉𝑥(𝑦)
𝑆ℎ𝑒𝑎𝑟 𝑟𝑎𝑡𝑒: 𝛾𝑥𝑦 = 𝛿𝑦
[unit = s-1]
When the shear viscosity (η) is constant, independent of time or shear rate (𝛾𝑥𝑦 ) we say the fluid
is a Newtonian fluid
When 𝛾𝑥𝑦 is the only non-zero shear rate, we generally speak of simple shear flow.
Extensional flows
When γxx, γyy or γzz are non-zero the flow is referred to as extensional flow
For simple molecular (Newtonian) fluids in extensional we again have;
𝑆ℎ𝑒𝑎𝑟 𝑠𝑡𝑟𝑒𝑠𝑠: 𝜎𝑥𝑥 = 𝜂 ∗ 𝛾𝑥𝑥
However, for complex fluids we generally find;
𝜎𝑥𝑥 = 𝜂𝐸 ∗ 𝛾𝑥𝑥 ; 𝜂𝐸 ≠ 𝜂
ηE is the extensional viscosity.
, Shear and extensional flow are related
Every shear flow can be decomposed into an extensional
and rotational contribution
For simple molecular fluids the rotational viscosity (viscosity
associated with rotational motion) is NEGLIGIBLE
Therefore; 𝜂𝐸 = 3𝜂
So, for a NEWTONIAN fluid the viscosity is equal for all 𝛾𝑖𝑗 (𝑖, 𝑗 = 𝑥, 𝑦, 𝑧)
Examples of Newtonian fluids = water, glycerol and maple syrup
In a complex system this is not the case because the rotational viscosity is not negligible due to large
structures present in the system that resist rotation
Short summary
- Newtonian fluids have a linear relation between stress and deformation rate
- The Shear viscosity and extensional viscosities are constant
Non-Newtonian Behavior
Most practical systems show linear behavior at low shear rates and non-linear behavior at higher
shear rates.
The total stress can be described by assuming that the viscosity 𝜂 is not constant.
In practical food systems we find several types of non-linear behavior.
Types of non-Newtonian behavior
1. Shear thinning
The most common behavior is shear-thinning behavior where the viscosity decreases with an
increasing shear rate.
The study of structure-function relations from molecular to macroscopic scale using the colloidal
scale as an intermediate
Chapter 2: Bulk Rheology
Rheology: The science that studies the relation between forces applies on a material and its (rate of)
deformation
Fluids: Viscous liquids
Shear flows
- Velocity in the x-direction varies in the y-direction
- Shear flow found in flow of liquids between parallel plates of a heat exchanger or flow of
liquids in a pipe
- Liquid in the center flows faster than the outer liquid due to shearing
Equations
𝑆ℎ𝑒𝑎𝑟 𝑠𝑡𝑟𝑒𝑠𝑠: 𝜎𝑥𝑦 = 𝜂 ∗ 𝛾𝑥𝑦 η = shear viscosity
𝛿𝑉𝑥(𝑦)
𝑆ℎ𝑒𝑎𝑟 𝑟𝑎𝑡𝑒: 𝛾𝑥𝑦 = 𝛿𝑦
[unit = s-1]
When the shear viscosity (η) is constant, independent of time or shear rate (𝛾𝑥𝑦 ) we say the fluid
is a Newtonian fluid
When 𝛾𝑥𝑦 is the only non-zero shear rate, we generally speak of simple shear flow.
Extensional flows
When γxx, γyy or γzz are non-zero the flow is referred to as extensional flow
For simple molecular (Newtonian) fluids in extensional we again have;
𝑆ℎ𝑒𝑎𝑟 𝑠𝑡𝑟𝑒𝑠𝑠: 𝜎𝑥𝑥 = 𝜂 ∗ 𝛾𝑥𝑥
However, for complex fluids we generally find;
𝜎𝑥𝑥 = 𝜂𝐸 ∗ 𝛾𝑥𝑥 ; 𝜂𝐸 ≠ 𝜂
ηE is the extensional viscosity.
, Shear and extensional flow are related
Every shear flow can be decomposed into an extensional
and rotational contribution
For simple molecular fluids the rotational viscosity (viscosity
associated with rotational motion) is NEGLIGIBLE
Therefore; 𝜂𝐸 = 3𝜂
So, for a NEWTONIAN fluid the viscosity is equal for all 𝛾𝑖𝑗 (𝑖, 𝑗 = 𝑥, 𝑦, 𝑧)
Examples of Newtonian fluids = water, glycerol and maple syrup
In a complex system this is not the case because the rotational viscosity is not negligible due to large
structures present in the system that resist rotation
Short summary
- Newtonian fluids have a linear relation between stress and deformation rate
- The Shear viscosity and extensional viscosities are constant
Non-Newtonian Behavior
Most practical systems show linear behavior at low shear rates and non-linear behavior at higher
shear rates.
The total stress can be described by assuming that the viscosity 𝜂 is not constant.
In practical food systems we find several types of non-linear behavior.
Types of non-Newtonian behavior
1. Shear thinning
The most common behavior is shear-thinning behavior where the viscosity decreases with an
increasing shear rate.
