Understanding Newtonian Material

 In the realm of materials science, understanding how substances flow and deform under various conditions is crucial. To make sense of this complexity, scientists have categorized materials into two fundamental groups: Newtonian systems and non-Newtonian systems. The classification hinges on whether the flow properties of the material adhere to Newton's Law of Flow, a cornerstone concept in fluid dynamics.

Newton's Law of Flow:

Imagine a block of liquid comprised of parallel plates of molecules, akin to a deck of cards stacked neatly. If the bottom layer remains fixed while the top plane of the liquid is set in motion at a constant velocity, each subsequent layer will move with a velocity directly proportional to its distance from the stationary bottom layer.

The disparity in velocity, represented as dv, between two planes of liquid separated by an infinitesimal distance, dr, constitutes the velocity gradient or rate of shear, dv/dr. The force per unit area, denoted as F′/A, required to induce this flow is termed shearing stress, symbolized by F.

Sir Isaac Newton was the pioneering figure who delved into the quantitative study of liquid flow properties. He discerned that the viscosity of a liquid dictates the magnitude of force per unit area (shearing stress) needed to generate a specific rate of shear. This rate of shear, denoted as G, is directly proportional to the shearing stress, as expressed by the equation:

F = η * G

Here, η (eta) denotes the coefficient of viscosity, commonly referred to simply as viscosity.

This relationship, encapsulated in Equation , is often represented as:

F = η * (dv/dr)

A graphical representation of this principle, known as a flow curve or rheogram, is depicted in Figure  As per Equation, a straight line passing through the origin is characteristic of a Newtonian system.

where F = F′/A and G = dv/dr.

Units of Viscosity:

The poise serves as the unit of viscosity, defined in terms of shearing force required to induce a velocity of 1 cm/sec between two parallel planes of liquid, each 1 cm² in area, and separated by a distance of 1 cm. In the cgs system, the poise is expressed as dyne sec cm⁻² or g cm⁻¹ sec⁻¹.

For practical purposes, the centipoise (cp) emerges as a more convenient unit, with 1 cp being equivalent to 0.01 poise.

Fluidity:

Fluidity, denoted by φ, is occasionally utilized as a term in this context. It is defined as the reciprocal of viscosity.

In summary, the classification of materials into Newtonian and non-Newtonian systems hinges on their adherence to Newton's Law of Flow. Understanding the relationship between shearing stress, rate of shear, and viscosity is pivotal in comprehending the behavior of fluids under various conditions, offering invaluable insights into their practical applications across diverse industries.