BE3002 Transport Phenomena in Biosystem Module 2_Segment 4

Summary

In this video, Yusuf from the Institute of Technology Bandung delves into the topic of constitutive relations in fluid mechanics, focusing on Newton's Law of Viscosity. He explains how shear stress relates to shear rate and introduces different types of fluids, including Newtonian and non-Newtonian. Non-Newtonian fluids are further categorized into Bingham plastics, power-law fluids, and viscoelastic fluids. The video also touches on rheology, the study of fluid deformation, and sets the stage for the next segment, which will explore laminar and turbulent flow.

Takeaways

• 😀 Constitutive relations are mathematical models that describe the behavior of fluids under stress, providing necessary relations between shear stress and fluid velocity.
• 😀 Newton's law of viscosity is a fundamental example of a constitutive relationship, where shear stress is proportional to the shear rate for Newtonian fluids.
• 😀 Unlike conservation relations that are universally applicable, constitutive relationships are specific to a particular class of fluids and require experimental data to derive.
• 😀 Shear stress applied to a control volume leads to deformation, with the rate of deformation directly proportional to the shear stress.
• 😀 The rate of deformation is quantified as the shear rate, which can be expressed as the velocity gradient.
• 😀 Constitutive relations can be generalized into a linear relationship between shear stress and shear rate for many fluids, described by Newton's law of viscosity.
• 😀 Newtonian fluids obey a simple linear relationship where the apparent viscosity remains constant for all shear rates.
• 😀 Non-Newtonian fluids show varying apparent viscosity depending on the shear rate, and their behavior is influenced by factors like temperature and pressure.
• 😀 Non-Newtonian fluids are categorized into types like Bingham plastics, power-law fluids, and viscoelastic fluids based on how their shear stress relates to their shear rate.
• 😀 Bingham plastics exhibit no flow until the yield stress is exceeded, at which point they flow like Newtonian fluids.
• 😀 Power-law fluids have an apparent viscosity that changes with the shear rate raised to a power, while viscoelastic fluids exhibit both elastic and viscous properties depending on time and force application.

Q & A

What is the role of constitutive relations in fluid mechanics?

Constitutive relations describe the relationship between stress and strain (or the rate of deformation) in materials, specifically fluids. Unlike conservation laws, which are universal, constitutive relations apply to specific classes of materials and require experimental measurements to determine.

How do conservation relationships differ from constitutive relationships?

Conservation relationships are universal and apply to all materials, while constitutive relationships are material-specific and only valid for certain fluids. Constitutive equations describe how fluids behave under stress, while conservation equations apply to quantities like mass, momentum, and energy.

What does Newton's law of viscosity state?

Newton's law of viscosity states that for Newtonian fluids, the shear stress is linearly proportional to the shear rate, with viscosity (μ) being the constant of proportionality. This relationship holds for all shear rates in Newtonian fluids.

What is the significance of the velocity gradient in constitutive relations?

The velocity gradient is crucial because it represents the rate of deformation in a fluid under shear stress. It is used in constitutive relations to describe how shear stress and shear rate are related in a fluid.

What defines a Newtonian fluid?

A Newtonian fluid is a fluid that obeys a linear relationship between shear stress and shear rate, where the viscosity remains constant regardless of the shear rate. This is described by Newton's law of viscosity.

How does the apparent viscosity behave in non-Newtonian fluids?

In non-Newtonian fluids, the apparent viscosity is not constant and varies depending on the shear rate. Factors like temperature and pressure also influence the viscosity of non-Newtonian fluids.

What is a Bingham plastic fluid?

A Bingham plastic is a type of non-Newtonian fluid that behaves as a solid until the applied shear stress exceeds a critical value known as the yield stress. After this point, it flows like a fluid.

What characterizes a power-law fluid?

A power-law fluid is a non-Newtonian fluid where the apparent viscosity depends on the shear rate raised to a specific power. This relationship allows the viscosity to change based on the shear rate.

What is rheology and why is it important?

Rheology is the branch of mechanics that studies the deformation and flow of fluids. It is important because it helps distinguish between different fluid behaviors, such as Newtonian and non-Newtonian, based on how they respond to applied forces.

What are viscoelastic fluids and how do they behave?

Viscoelastic fluids exhibit both elastic and viscous behaviors. They experience instantaneous deformation due to their elastic properties and time-dependent deformation due to their viscous nature when subjected to forces.