Summary Chapter 2 - Food Physics (20306)

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