4.6.1. Definition and Effects

If I consider the same fluid flow through a parallel plate, okay. One of the plate the velocity is zero which is at the rest conditions and other the top plate is moving with a velocity V. So as a microscopic point of view I am not talking about the molecular motions or exchange of the molecular motions or the momentum flux that what is resulting a shear stress.

This chunk introduces the concept of fluid flow between two parallel plates—one at rest and the top one moving with velocity V. In this scenario, we are going to analyze how the motion of the top plate affects fluid flow, particularly focusing on shear stress without concerning ourselves with molecular details of the fluid.

Imagine you have a sandwich with peanut butter spread between it. The bottom slice of bread is stationary while you spread the top slice across the peanut butter. The way the peanut butter spreads and changes shape illustrates how fluid flows and deforms under shear stress due to the movement of the top plate.

Here what we consider that fluid element. That means, I consider some space of A, B, C, D, this is what the fluid element. As you know, at the A point we will have velocity V as the no-slip conditions. At the B point we will have velocity zero. So velocity assuming it will have a linear velocity variation from B to A.

In this chunk, we define what a fluid element is and how to visualize the velocity distribution across this fluid. Point A, closer to the moving plate, has a velocity V, while point B, resting against the stationary plate, has a velocity of 0. This results in a linear change in velocity from B to A, describing a smooth gradient.

Think of a slide that is smooth at the top (high velocity) and gradually becomes rough at the bottom (low or no velocity). As you slide down, you would speed up initially, but if you were to encounter a rough patch, your speed would drop, just like how fluid velocity changes between the plates.

If as a linear velocity distribution as you assume it as we got it some of the parallel flow conditions after ∆t time these fluid element will be deformed as angular deformations will happen.

This part discusses how, after a small time interval (∆t), the fluid element (A, B, C, D) will undergo angular deformations due to the shear stress caused by the velocity difference between the two plates. This deformation can be quantitatively analyzed to understand how the fluid behaves under shear conditions.

Consider stretching a rubber band. If you pull on it, it undergoes deformation and changes shape. In analogy, the fluid element deforms in response to varying forces around it, just as the rubber band changes shape under tension.

We remember this is what is indicating us is that the velocity gradient. If I consider this is the y directions how the velocity varies along the y directions that is the constant which is equal to the shear strain rate.

Here we focus on the concept of the velocity gradient, which is the rate of change of velocity over distance (in this case, the y-direction). The velocity gradient within the fluid corresponds to the shear strain rate, which is a valuable concept in fluid mechanics for understanding how fluids deform under stress.

Imagine you are mixing a thick paint with a stick. The faster you stir, the more the paint changes its shape and flows. The change in the paint’s resistance to flow and its velocity with respect to your stirring speed is similar to how velocity gradients work in fluids.

But here, we are talking about the stress is proportional to the strain rate. That means the change of the shear strain rate with respect to time, not the absolute value of the shear strain.

This section introduces Newton's laws of viscosity, which highlight the relationship between shear stress and shear strain rate. For fluids, it is key to distinguish that shear stress is proportional to the rate of deformation (strain rate) over time, unlike in solid mechanics where it is proportional to shear strain itself.

Think of how honey flows slowly when poured, compared to water which flows quickly. Honey exhibits a higher viscosity; thus, it has a greater resistance to flow and deformation compared to water due to how quickly their shear rates change under force.

Now let us commit that how does the temperature effect on the coefficient of the viscosity. Now we have to look at the molecular levels okay.

In this chunk, we analyze how temperature impacts viscosity. The concept is that, as temperature increases, the kinetic energy of the molecules in a fluid increases, which affects intermolecular bonding and results in variations in viscosity.

Imagine how syrup becomes runnier when heated. At high temperatures, molecular movements increase, causing less resistance to flow. This transformative effect is what happens to all fluids, including water or oil, as temperatures rise.

If you increase the temperature which manifests to the molecular motions to sustain that temperatures. In that conditions what it will happen it, it will reduce the binding force, the intermolecular binding force between two molecules.

The chunk compares the behavior of liquids and gases under temperature changes. In liquids, increased temperatures generally decrease viscosity due to the reduction in intermolecular forces, while gases exhibit an opposite trend and require less force to flow as temperature increases. Understanding how viscosity varies systematically across states of matter enhances grasp on fluid dynamics.

Consider blowing up a balloon. In warm air, the balloon expands easily, demonstrating how gas viscosity decreases as temperature increases. In contrast, liquids like oil become easier to pour when heated, showing a similar reduction in viscosity.

Those fluid flow problems we call the Newtonian fluids, okay. That group of the fluid flow problems we call Newtonian fluids, where you have the shear stress causing by any shear forces is directly proportional to the velocity gradient or the shear strain rate.

This last chunk distinguishes between Newtonian fluids, which obey the simple rule of viscosity (shear stress is proportional to shear rate), and non-Newtonian fluids, where this relationship can vary. Evaluating different fluid types based on their viscosity behavior is crucial in multiple engineering applications.

Think of classic Newtonian fluids as water flowing easily and predictably down a drain. In contrast, a non-Newtonian fluid like cornstarch mixed with water (oobleck) behaves differently; it can act rigid under fast movement and liquid when moving slowly, showcasing the nature of non-Newtonian behavior.

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