## Non Newtonian Fluid

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# Non-Newtonian Fluid

• The fluid in which the shear stress is not directly proportional to the rate of shear strain or velocity gradient, is called as Non-Newtonian Fluid.

e.g. Slurries, tooth paste, gels, polymer solution paint, lubricant oils

• The non-linear relationship between shear stress and the rate fo deformation is called as Non-Newtonian fluid.

ζ ≠ μ du / dv

(a)

(b)

**Variation of shear stress with velocity gradient**

η = Apparent viscosity = [du / dy ]

^{n-1}• The viscosity which is defined as the slopes shown in called as apparent viscosity.

Where n = flow behaviour index

## Pseudo plastic or Fluid:

• Fluid in which the apparent viscosity decreases with increasing deformation rate (n<1) is called as Pseudo plastic fluid.• Examples are slurries, mud, polymer solution, gums, blood, milk, colloidal suspensions paper pulp in water.

ζ = μ (du / dy)

^{n}

## Dilatants or Fluid:

• Fluid in which the apparent viscosity increases with increasing deformation rate (n>1) is called as dilatants fluids.e.g. Suspension of sand, starch, butter, sugar solution.

ζ = μ (du / dy)

^{n}

## Bingham plastic Fluid or Ideal Plastic Fluid:

The fluid which possess a definite yield stress but then the relationship between shear stress and angular deformation is linear is called as Bingham plastic fluid.ζ = ζ

_{ y}+ μ (du / dy)

^{n}

e.g. Sewage sludge, tooth paste, oil paint, jellies, applesauce, drilling mud.

## Thyrotrophic Fluid or Plastic Fluid:

The fluid which possess a definite yield stress but then the relationship between shear and angular deformation is non-linear are called as Thixotrophic fluid. e.g. Printer ink, lipstick.ζ = ζ

_{ y}+ μ (du / dy)

^{n}

## Ideal Fluid:

The fluid which has zero viscosity or shear stress is always zero is called as ideal fluid, that’s why ideal fluid is represented by the horizontal axis.For more help in

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