Chapter 2
- Rheology: the science that studies the relation between forces applied on a material and its
rate of deformation.
Applied force, F (N) / stress σ (F/area).
Deformation γ / deformation rate (d γ /dt): de change in strain (spanning/rek) over time.
This relation between stress and deformation
is often very complex, due to the complex structures of food. However, a limiting case is a
purely viscous liquid. 2 type of deformations can be studied:
1. Shear flow.
2. Extensional flow.
- Shear flow: Adjacent layers of fluid move parallel to each other, with
different speeds. The velocity in the x-direction differs in the y-direction.
o Shear flow is encountered in the flow of liquids between parallel plates of
a heat exchanger, or the flow of liquids in pipes or channels.
- Shear rate: velocity gradient in the y-direction ( γ˙xy).
∂ ν x ( y ) -1
γ˙xy = (s ) σ xy =η y˙xy (accounts for Newtonian fluids)
∂y
η: shear viscosity.
∂ : derivative.
- Extensional flow: as the fluid is moving forward, it is accelerating in the x-direction.
- Extensional rate: velocity gradient in the x-direction.
∂ ν x (x )
γ ˙x x = σ xx =ηE y˙xx (accounts for Newtonian fluids)
∂x
η E: extensional viscosity.
Every shear flow can be decomposed into an extensional contribution and a
rotational contribution.
o Shear rate = extensional rate + rotational rate.
o For simple (Newtonian) molecular fluids, the rotational viscosity
is negligible η R=0.
- Newtonian fluid: η E=3 η.
Both shear viscosity and extensional viscosity are constant and independent of time or
deformation rate.
Newtonian fluids are ideal fluids. Examples are water, glycerol and maple syrup.
For Newtonian fluids there is a linear relation between stress and the deformation rate (see
equations in green).
Most liquid foods are non-Newtonian viscous fluids. This means: η E ≠3 η .
o Also, rotational resistance plays a role now, so η R ≠0 .
, For Newtonian fluids, both shear and extensional viscosity
were constant. This is not the case for non-Newtonian fluids.
Viscosity will depend on deformation rate and time:
η=η ¿ η E=ηE ¿
There are 4 types of non-Newtonian (non-linear) behavior:
1. Shear thinning
Shear thinning means that the viscosity decreases for an increasing shear
rate.
When viscosity is plotted against the shear rate (log/log), it drops
significantly. A Newtonian fluid would simply give a horizontal line (constant
viscosity).
Also, stress can be plotted against the shear rate. For a Newtonian fluid, a
straight, linear line will appear. For a non-Newtonian fluid, the curve will
level off significantly.
This type of behavior generally occurs in solutions of macromolecules,
(concentrated) dispersions and/or (concentrated) emulsions.
o Milk, custard, yoghurt.
2. Shear thickening
Shear thickening is basically the reversed process of
shear thinning; viscosity increases upon increasing
shear rate.
It occurs mainly in concentrated dispersions.
o Peanut butter.
3. Bingham and plastic flow
An example of a product with this type of behavior, is ketchup. When you turn the bottle
upside down, nothing comes out, but when you start to shake the suspension, it becomes
liquid.
- Yield stress (σ 0): minimum stress that should be applied to a system like that of ketchup,
before it starts to flow.
o Below this stress, the material behaves solid-like.
- Bingham material: the material shows linear behavior after the
system has yielded.
σ xy =σ 0 +η0∗γ ˙xy
- Plastic material: the material shows shifted behavior after the
system has yielded.
σ xy=σ 0 +η( γ̇ )∗γ̇
For both Bingham and plastic flow, there is a decrease in viscosity.
Dough, margarine, tomato ketchup, whipped cream.
4. Thixotropic behavior
Dependent on time, instead of flow rate.
The structural changes, that are the cause for shear
thinning behavior, take time to occur. So, if you
- Rheology: the science that studies the relation between forces applied on a material and its
rate of deformation.
Applied force, F (N) / stress σ (F/area).
Deformation γ / deformation rate (d γ /dt): de change in strain (spanning/rek) over time.
This relation between stress and deformation
is often very complex, due to the complex structures of food. However, a limiting case is a
purely viscous liquid. 2 type of deformations can be studied:
1. Shear flow.
2. Extensional flow.
- Shear flow: Adjacent layers of fluid move parallel to each other, with
different speeds. The velocity in the x-direction differs in the y-direction.
o Shear flow is encountered in the flow of liquids between parallel plates of
a heat exchanger, or the flow of liquids in pipes or channels.
- Shear rate: velocity gradient in the y-direction ( γ˙xy).
∂ ν x ( y ) -1
γ˙xy = (s ) σ xy =η y˙xy (accounts for Newtonian fluids)
∂y
η: shear viscosity.
∂ : derivative.
- Extensional flow: as the fluid is moving forward, it is accelerating in the x-direction.
- Extensional rate: velocity gradient in the x-direction.
∂ ν x (x )
γ ˙x x = σ xx =ηE y˙xx (accounts for Newtonian fluids)
∂x
η E: extensional viscosity.
Every shear flow can be decomposed into an extensional contribution and a
rotational contribution.
o Shear rate = extensional rate + rotational rate.
o For simple (Newtonian) molecular fluids, the rotational viscosity
is negligible η R=0.
- Newtonian fluid: η E=3 η.
Both shear viscosity and extensional viscosity are constant and independent of time or
deformation rate.
Newtonian fluids are ideal fluids. Examples are water, glycerol and maple syrup.
For Newtonian fluids there is a linear relation between stress and the deformation rate (see
equations in green).
Most liquid foods are non-Newtonian viscous fluids. This means: η E ≠3 η .
o Also, rotational resistance plays a role now, so η R ≠0 .
, For Newtonian fluids, both shear and extensional viscosity
were constant. This is not the case for non-Newtonian fluids.
Viscosity will depend on deformation rate and time:
η=η ¿ η E=ηE ¿
There are 4 types of non-Newtonian (non-linear) behavior:
1. Shear thinning
Shear thinning means that the viscosity decreases for an increasing shear
rate.
When viscosity is plotted against the shear rate (log/log), it drops
significantly. A Newtonian fluid would simply give a horizontal line (constant
viscosity).
Also, stress can be plotted against the shear rate. For a Newtonian fluid, a
straight, linear line will appear. For a non-Newtonian fluid, the curve will
level off significantly.
This type of behavior generally occurs in solutions of macromolecules,
(concentrated) dispersions and/or (concentrated) emulsions.
o Milk, custard, yoghurt.
2. Shear thickening
Shear thickening is basically the reversed process of
shear thinning; viscosity increases upon increasing
shear rate.
It occurs mainly in concentrated dispersions.
o Peanut butter.
3. Bingham and plastic flow
An example of a product with this type of behavior, is ketchup. When you turn the bottle
upside down, nothing comes out, but when you start to shake the suspension, it becomes
liquid.
- Yield stress (σ 0): minimum stress that should be applied to a system like that of ketchup,
before it starts to flow.
o Below this stress, the material behaves solid-like.
- Bingham material: the material shows linear behavior after the
system has yielded.
σ xy =σ 0 +η0∗γ ˙xy
- Plastic material: the material shows shifted behavior after the
system has yielded.
σ xy=σ 0 +η( γ̇ )∗γ̇
For both Bingham and plastic flow, there is a decrease in viscosity.
Dough, margarine, tomato ketchup, whipped cream.
4. Thixotropic behavior
Dependent on time, instead of flow rate.
The structural changes, that are the cause for shear
thinning behavior, take time to occur. So, if you
