learnbin.net nav logo

Fluids can be divided into two categories based on the change in their viscosity when shear is applied.

Types of fluids
Figure 01: Types of fluids

Comparison of Newtonian and Non-Newtonian Fluids
Figure 02: Comparison of Newtonian and Non-Newtonian Fluids

Newtonian fluids

In Newtonian fluids, viscosity doesn’t change with the shear rate at a given temperature and pressure.

Newtonian and non newtonian fluids eq 01

Where,

  • τ = shear stress
  • γ̇ = shear rate
  • η = viscosity

Change of shear stress and viscosity vs shear rate of Newtonian fluids
Figure 03: Change of shear stress and viscosity vs shear rate of Newtonian fluids

Bingham fluids

Some materials exhibit an infinite viscosity until sufficient stress is applied. Afterward, it starts to flow. Initial intermolecular interactions prevent the dispersion of materials until the limiting stress. If the external force exceeds the intermolecular interactions, the material will start to flow.

Newtonian and non newtonian fluids eq 02

Where,

  • τ = shear stress
  • γ̇ = shear rate
  • ηB = viscosity for given shear rate
  • fB = yield point according to the Bingham model

The yield point is the maximum shear stress at the shear rate at zero.

Change of shear stress vs shear rate of Bingham fluids
Figure 04: Change of shear stress vs shear rate of Bingham fluids
  • τ0 = Limiting stress

There are several mathematical models to describe the flow behavior of such fluids. Bingham model describes the flow behavior of Newtonian fluids having limiting stress.

Non-Newtonian fluids

Those are Newtonian and Non- Newtonian fluids. Non-Newtonian fluids change their viscosity or flow behavior under applied stress. Viscosity is either increased or decreased when shear is applied.

Some non-Newtonian fluids increase their viscosity and get thicker under shear stress. This is called shear thickening.  Therefore, the fluid becomes less flowable and acts like a solid.

Some Non- Newtonian fluids decrease their viscosity under stress and become thinner fluids. This is known as shear thinning. Here the fluid becomes more flowable. These fluids come to their original viscosity when the stress is removed.

Pseudoplasticity

In many polymer materials (melts or liquids) viscosity of the medium decreases (shear thinning) with the increasing shear rates. So, these type of polymer melts requires less energy to flow during the processing step. In such a system, we can only define the apparent viscosity where viscosity is changing as a function of the applying shear rate

Newtonian and non newtonian fluids eq 03

Where,

  • k = viscosity for a given shear rate
  • n = n is the material index and it is always less than 1 in pseudoplastic materials.

Change of shear stress and viscosity vs shear rate of Pseudoplastics
Figure 05: Change of shear stress and viscosity vs shear rate of Pseudoplastics

Dilatancy

Dilatant materials increase their viscosity when applying shear stress (shear-thickening). This is a huge challenge in the polymer processing industry. Because dilatant materials need high energy to flow at a high shear rate. For dilatant materials, n is always higher than 1.

Newtonian and non newtonian fluids eq 03

Change of shear stress and viscosity vs shear rate of Dilatant
Figure 06: Change of shear stress and viscosity vs shear rate of Dilatant

Mathematical models that describe the flow behavior of fluids

Herschel and Bulkley model

According to Herschel and Bulkley model (Herschel-Bulkley model), both Newtonian and non-Newtonian fluids can be described. This describes the relationship between shear stress and the shear rate of fluids.

Newtonian and non newtonian fluids eq 05

FluidLimiting stressn
Pure Newtonian fluid01
Bingham fluids>01
Pseudoplastic0<1
Dilatant0>1
Table 01: Limiting stress and material indexes for different types of fluids

Ellis model

This describes materials with power-law behavior at high shear rates. But it describes Newtonian behavior at low shear stresses.

Newtonian and non newtonian fluids eq 06

Where,

  • K1 and k2 are materials constants and n is the material index.

Casson model

This model is used for materials that tend to Newtonian flow only at stresses much higher than the material yield stress.

Newtonian and non newtonian fluids eq 07

Temperature-dependent flow behavior

The viscosity of Newtonian fluids decreases with the increase in temperature, approximately in line with the Arrhenius relationship.

Newtonian and non newtonian fluids eq 08

Except in some cases, viscosity decreases with the increase in temperature.

Temperature-dependent flow behavior
Figure 07: Temperature-dependent flow behavior
  • A - Materials that increase viscosity with temperature
  • B - Materials that increase viscosity with temperature

Time-dependent flow behavior

Polymer materials show time-dependent flow behavior where the time taken to stress accumulation and the time taken to stress release are different. There are two types of flow behaviors depending on the time.

Thixotropic

Thixotropic fluids take a longer time to stress relaxation. Therefore, restoring the viscosity to its original level takes a longer time. Thixotropic behavior is coupled with shear thinning behavior.

Viscosity vs time of Thixotropic materials
Figure 08: Viscosity vs time of Thixotropic materials
  • t1 < t2
  • t1 - Loading time
  • t2 - Relaxation time

Flow and viscosity curves for a pseudoplastic and thixotropic system
Figure 09: Flow and viscosity curves for a pseudoplastic and thixotropic system

Rheopexy

Rheopexy material shows the opposite time behavior compared to thixotropic polymer melts. Rheopexy is coupled with shear thickening behavior.

Viscosity vs time of Rheopexy materials
Figure 10: Viscosity vs time of Rheopexy materials
  • t1 < t2
  • t1 - Loading time
  • t2 - Relaxation time

Flow and viscosity curves for a rheopectic system
Figure 11: Flow and viscosity curves for a rheopectic system

Weissenberg effect

Weissenberg effect is used to identify Newtonian and non-Newtonian fluids. During this test, a propeller (impeller) is dipped inside the liquid or the melt. Newtonian liquids will be thrown outward from the propeller. The fluid body will arise along the propeller body in Newtonian fluids. This phenomenon is known as the Weissenberg effect.

Weissenberg effect
Figure 12: Weissenberg effect

Buy me a coffee

References and Attributes

Figures:

The cover image was created using an image by PublicDomainPictures from Pixabay


Express your thoughts below!

Leave a Reply

Your email address will not be published. Required fields are marked *

0 Comments

© 2023 learnbin.net. All rights reserved.
linkedin facebook pinterest youtube rss twitter instagram facebook-blank rss-blank linkedin-blank pinterest youtube twitter instagram