4.3.1. Molecular Levels and Viscosity

If I consider the same fluid flow through a parallel plate, okay. One of the plate 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 in a shear stress. Here what we consider that fluid element.

This chunk discusses the basic setup of fluid dynamics in a parallel plate scenario where one plate is stationary and the other is moving. In this context, viscosity is understood by examining how fluid elements behave due to the movement. The zero velocity of one plate demonstrates the no-slip condition, where fluid adheres to the surface. The top plate’s movement generates a velocity gradient within the fluid, which is crucial for analyzing shear stress, although the chunk does not delve into the molecular motions.

Consider moving your hand through water. While your hand moves through the water with some speed (analogous to the moving plate), the water directly in contact with your hand does not move (like the stationary plate). The water just below it starts to move slightly, creating a flow, similar to what is described with the fluid element between the plates.

As you know it that at the A point we will have the velocity V as the no-slip conditions. At the B point we will have velocity zero. So velocity assuming it, it will have a linear velocity variation from B to A. That linear velocity from zero to V as the y increases, the velocity will increase it and maximum velocity will be the V.

This chunk elaborates on the velocity gradient between the two plates. The no-slip condition means that at the surface of the stationary plate (point B), the fluid has zero velocity, while at the moving plate (point A), the fluid reaches its maximum velocity V. This creates a linear gradient across the gap between the plates, effectively demonstrating how velocity changes with distance. The key point here is that the change in velocity is not uniform but varies linearly according to the distance from the stationary plate.

Think of a slide at a playground. At the top (the no-slip condition), you’re not moving at all, but as you slide down, you accelerate. Similarly, in the fluid layer next to the stationary plate, the fluid does not move, but as you move away from it towards the moving plate, you gain speed until you reach maximum velocity.

After ∆t time these fluid element will be deformed as angular deformations will happen it that there will be angle θ will come it at the B and E, F and D.

This chunk introduces the concept of angular deformations that occur in the fluid element over time due to the velocity gradients. As the fluid moves, it experiences shear, causing it to change shape and form angles between different points of the fluid element. This deformation helps in understanding the relationship between stress and strain in fluid systems, showing that even without rigid boundaries, fluids can experience internal changes.

Imagine a soft sponge: when you press it down, it shifts and changes shape rather than just moving as a solid block. Similarly, as the fluid element between the plates flows, the layers can shift relative sideways, creating angular deformations as they respond to the differences in velocities.

Shear strain rate is equal to the velocity gradient, which indicates how much the fluid layers move relative to each other. The shear stress is proportional to this strain rate, which is aligned with Newton's laws of viscosity.

Here, the relationship between shear stress and shear strain rate is defined. As the fluid flows and experiences shear, there is a direct proportionality between the rate of deformation (shear strain rate) and the resulting shear stress. According to Newton’s laws of viscosity, this means the greater the velocity gradient, the greater the shear stress experienced by the fluid, affirming the concept of viscosity as a resistance to flow.

Think about squeezing honey from a bottle. The harder you squeeze (increasing the shear stress), the more honey flows out, which corresponds to an increase in shear strain rate. This is similar to how fluid elements respond under shear stress: they flow progressively more as shear stress increases.

Now let us commit that how how does the temperature effect on the coefficient of the viscosity. Now we have to look at the molecular levels okay. So if you look at this molecular levels, when you talk about the liquids, they will have a molecular bonding forces between two molecules okay. But that is much weaker when talk about the gases.

This chunk begins to discuss how temperature influences viscosity at a molecular level. In liquids, molecules are held together by stronger bonding forces compared to gases, where molecules are more loosely arranged and move in a more random motion. As temperature increases, these molecular bonds weaken in liquids, ultimately leading to a decrease in viscosity. This is significant as the ability of fluids to flow changes with temperature, impacting practical applications in various fields.

Think of melting butter. When it's solid, it doesn't flow (high viscosity), but as it heats up, it turns to liquid and flows easily (low viscosity). As temperature increases, similar changes occur in liquids regarding their viscosity, showcasing how temperature affects flow.

If you look at the temperatures, the temperatures related is that how much of collisions are happening. For liquids, let us look it that change of the pressures will not change that significantly through coefficients of viscosity which represent as a proportionality constant of mass exchange of the molecules or momentum exchange of molecules from one layer to other layers.

This segment highlights the fundamental differences in how liquids and gases respond to changes in temperature and pressure concerning their viscosity. It emphasizes that while an increase in pressure has minimal effect on the viscosity of a liquid, temperature plays a major role by increasing molecular collisions, resulting in significant changes in viscosity as temperature rises.

Imagine heating a pot of water versus a balloon filled with air. The water (liquid) becomes less viscous and flows better as heat is added, while the air (gas) becomes more energetic but its viscosity remains relatively constant. This illustrates how different states of matter react differently under the same conditions.

--