Flow Behaviour Index and Consistency Index

Flow behavior index (n) and consistency index (k) are two important parameters used in the power law model which is commonly used to describe non-Newtonian fluids.

The power law model is given by:
τ = k(γ)^n
Where,
τ = shear stress
γ = shear rate

Consistency Index

The consistency index (k) is a measure of the fluid’s resistance to deformation or flow. It is also known as the flow coefficient or the apparent viscosity at low shear rates.

The consistency index has dimensions of Pa s^n or lb s^n/ft^2, where n is the flow behavior index.

Dimension Independence of Time

When the consistency index has dimensions that do not depend on time, it means that the fluid’s behavior is independent of the rate at which the shear stress is applied. This is also referred to as the fluid’s “pseudoplasticity” or “yield stress”. In other words, the fluid’s consistency is not affected by changes in the shear rate or the duration of the shear stress.

Flow Behaviour Index

The flow behavior index (n) is a measure of the degree of non-Newtonian behavior of the fluid. It indicates the extent to which the viscosity of the fluid changes with a change in the shear rate.

A fluid with a flow behavior index of 1 is said to exhibit “Newtonian behavior” because its viscosity remains constant regardless of the shear rate.

Answer

For what value of flow behavior index, does the consistency index have a dimension independent of time?
The correct answer is option 'C' - 2.

When the flow behavior index is equal to 2, the consistency index has dimensions of Pa s^2 or lb s^2/ft^2, which are independent of time.

This means that the fluid’s behavior is not affected by changes in the rate at which the shear stress is applied. Such fluids are referred to as “yield-stress” or “pseudoplastic” fluids.

In summary, when the flow behavior index is equal to 2, the fluid’s consistency is not affected by changes in the shear rate or the duration of the shear stress.