Question

Describe Newton's Law of Viscosity and the constitutive behavior of non-Newtonian fluid

Answer 1

Answer:

- "Newton’s viscosity law’s states that, the shear stress between adjacent fluid layers is proportional to the velocity gradients between the two layers".

- A non-Newtonian fluid is a fluid which the relationship between the shear stress and the velocity gradient is not properly defined by the Newton's viscosity law, thus, the behavior is not lineal but potential.

Explanation:

Hello, here the answers:

- "Newton’s viscosity law’s states that, the shear stress between adjacent fluid layers is proportional to the velocity gradients between the two layers" (taken from Kundu, P. K., Cohen, I. M., & Dowling, D. R. (2012). Fluid mechanics.), thus, it means that when you have a fluid with an acting-on-it share stress (an external force which move the fluid), the related velocity gradient (variation or change in velocity) at which the layers are moving are related as:

$\pi =-v \frac{du}{dy}$

Whereas $\pi$ is the shear stress, $v$ is the viscosity and the differential accounts for the change in the velocity in the arbitrary $y$ coordinate.

- A non-Newtonian fluid is a fluid which the relationship between the shear stress and the velocity gradient is not properly defined by the Newton's viscosity law, thus, the behavior is not lineal but potential, based on:

$\pi =-v (\frac{du}{dy})^n$

Whereas $n$ accounts for a decreasing or increasing behavior of the shear stress.

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