Summary of Fluid Mechanics | Module 1 | Rheological Behaviour of Fluid (Lecture 5)

Summary of "Fluid Mechanics | Module 1 | Rheological Behaviour of Fluid (Lecture 5)"

This lecture focuses on the rheological behavior of fluids, an important topic in Fluid Mechanics, especially relevant for GATE and SSC exams. The main concepts revolve around understanding different types of fluids based on how they deform and flow under applied forces.

Main Ideas and Concepts

1. Rheology and Rheological Behavior
   • Rheology is the branch of science that studies the deformation and flow behavior of fluids.
   • It helps classify fluids based on their response to applied stresses and strain rates.
2. Ideal Fluid
   • An ideal fluid is incompressible and has no viscosity (zero viscosity).
   • It does not resist shear stress (no shear stress).
   • Normal stress (pressure) remains constant throughout.
   • Ideal fluids do not exist in reality but serve as a theoretical model.
   • Newton’s law of viscosity does not apply to ideal fluids because viscosity is zero.
3. Newtonian Fluids
   • Fluids that follow Newton’s law of viscosity: shear stress (τ) is directly proportional to the rate of shear strain (du/dy).
   • The proportionality constant is the dynamic viscosity (μ).
   • Graph of shear stress vs. shear rate is a straight line passing through the origin.
   • Examples include water, air, and many common liquids.
4. Non-Newtonian Fluids
   • Fluids that do not follow Newton’s law of viscosity.
   • Their shear stress and shear rate relationship is nonlinear.
   • Described by the power law model:
     τ = K (du/dy)n
   • where:
     • K = consistency index (thickness or consistency measure)
     • n = flow behavior index (flow index)
   • Categories based on n:
     • Dilatant (shear-thickening) fluids: n > 1 Viscosity increases with shear rate (e.g., starch suspensions).
     • Pseudo-plastic (shear-thinning) fluids: n < 1 Viscosity decreases with shear rate (e.g., blood).
5. Bingham Plastic and Herschel-Bulkley Fluids
   • These fluids require an initial yield stress (τ₀) to start flowing.
   • Bingham Plastic fluids behave like a solid until the yield stress is exceeded, then flow like Newtonian Fluids:
     τ = τ₀ + μ (du/dy)
   • Herschel-Bulkley Fluids generalize Bingham plastics with a power law after yield stress:
     τ = τ₀ + K (du/dy)n
   • Examples: toothpaste, ketchup, some sludges.
   • Important property: these fluids behave like solids below the yield stress.
6. Time-Dependent Viscosity
   • Some fluids exhibit viscosity that changes over time under constant shear.
   • Two types:
     • Thixotropic fluids: viscosity decreases with time (e.g., paint).
     • Rheopectic fluids: viscosity increases with time.
   • Practical examples include printer ink drying and some suspensions.

Methodology / Key Points to Remember

• Classify fluids based on shear stress vs. shear rate behavior:
  • Ideal fluid: zero viscosity, no shear stress.
  • Newtonian fluid: linear relation, constant viscosity.
  • Non-Newtonian fluid: nonlinear relation, described by power law.
  • Bingham Plastic: requires yield stress to flow.
  • Herschel-Bulkley: yield stress + power law behavior.
• Equations to remember:
  • Newton’s law of viscosity:
    τ = μ (du/dy)
  • Power law model (non-Newtonian):
    τ = K (du/dy)n
  • Bingham Plastic model:
    τ = τ₀ + μ (du/dy)
  • Herschel-Bulkley model:
    τ = τ₀ + K (du/dy)n
• Identify fluid type based on flow index n:
  • n = 1 → Newtonian
  • n > 1 → Dilatant (shear-thickening)
  • n < 1 → Pseudo-plastic (shear-thinning)

Category

Educational

Video