Non-Newtonian Fluids

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Types of Fluid

  1. Newtonian Fluid
  2. Non-Newtonian Fluid

Non- Newtonian Fluids and Types

These types of fluids do not obey Newton’s Law of viscosity. The relation between Shear Stress and Velocity gradient is given by the following formula-

τ = A (du/dy)n + B

Here A and B are constants that depend on the type of fluid and condition of flow.

The Non-Newtonian Fluids are further categorized as-

Time-Dependent
  • Dilatant Fluids
  • Bingham Plastic Fluids
  • Pseudoplastic Fluids
Time Independent
  • Thixotropic Fluids
  • Rheopectic Fluids

Non-Newtonian Fluids Conditions

For Dilatant Fluids

  • n > 1; and B = 0
  • Ex- Butter, Quicksand

For Bingham Plastic Fluids

  • n = 1; and B ≠ 0
  • These fluids always have certain minimum shear stress before yielding.
  • Ex- toothpaste, gel, sewage sludge, etc.

For Pseudoplastic Fluids 

  • n < 1 ; and B = 0
  • Ex- Paints, Blood, Paper pulp, Lipsticks, Rubber solution etc.

For Thixotropic Fluids

  • n < 1; and B ≠ 0
  • Viscosity increases with time.
  • Ex- Enamel, Printers Ink, etc.

For Rheopectic Fluids

  • Viscosity decreases with time.
  • Ex- Gypsum solution in water, etc.

Compressibility (β), Isothermal Bulk Modulus (kT) and Adiabatic Bulk Modulus

Compressibility (β)

  • It is the inverse of Bulk Modulus of Elasticity.

β = 1/k = -dv/(v × dp)

v = volume

Isothermal Bulk Modulus (kT)

kT = Pfinal = Ρrt

Adiabatic Bulk Modulus

ka = ϒ × Pfinal

ϒ = Cp/Cv