BE3002 Transport Phenomena in Biosystem_Module 3 Segment 1

Summary

This module on transport phenomena in biosystems introduces Newton's Law of Viscosity, explaining how viscosity governs momentum transport between fluids and surfaces. The law is derived from the interaction between fluid layers of different velocities, with momentum transferring from high to low-velocity regions. Viscosity's dependence on pressure and temperature is discussed, noting that gases typically increase in viscosity with temperature, while liquids decrease. The concept of kinematic viscosity and its application in both gas and liquid systems is also explored, setting the stage for further discussions on momentum transport in biosystems.

Takeaways

• 😀 Newton's Law of Viscosity describes the relationship between shear force, velocity gradient, and viscosity in a fluid.
• 😀 In the given system, two parallel plates are separated by a fluid, and the lower plate moves at a constant velocity to establish a steady velocity profile in the fluid.
• 😀 The force required to maintain the motion of the lower plate is proportional to the area, velocity, and inversely proportional to the distance between the plates.
• 😀 The viscosity (μ) is a property of the fluid that determines the resistance to flow, and is the constant of proportionality in the equation for force.
• 😀 The shear stress per unit area (τ_yx) is proportional to the negative of the velocity gradient, forming the core of Newton's Law of Viscosity.
• 😀 Momentum is transferred in the fluid from regions of high velocity to low velocity, with the velocity gradient driving this transport.
• 😀 Kinematic viscosity is defined as the ratio of viscosity to fluid density, providing an important property of the fluid.
• 😀 The viscosity of fluids varies widely: air at 20°C has a viscosity of 1.8 × 10⁻⁵ Pa·s, while glycerol has a viscosity of about 1 Pa·s.
• 😀 Temperature affects viscosity differently for gases and liquids: gases' viscosity increases with temperature, while liquids' viscosity usually decreases.
• 😀 In gases, momentum transport happens through molecular collisions, while in liquids, it is mainly through intermolecular forces between molecules.
• 😀 The next segment of the course will explore the generalization of Newton's Law of Viscosity, extending the concepts discussed in this segment.

Q & A

What is the main focus of this module?

This module focuses on the transport phenomena in biosystems, specifically discussing Newton's Law of Viscosity, the generalization of this law, and the pressure and temperature dependence of viscosity.

What does Newton's Law of Viscosity describe?

Newton's Law of Viscosity describes the relationship between the shear force per unit area and the velocity gradient in a fluid, stating that the force is proportional to the negative of the velocity gradient.

How is the shear force in the x-direction defined in the context of the script?

The shear force in the x-direction is defined by the symbol tau yx, which represents the force exerted by the fluid of lesser y on the fluid of greater y, perpendicular to the y-direction.

What is the significance of the constant of proportionality 'mu'?

'Mu' represents the viscosity of the fluid, which is a property that characterizes the internal friction of the fluid and its resistance to flow.

What does the equation tau yx = - mu * (d vx / dy) describe?

This equation states that the shear force per unit area (tau yx) is proportional to the negative velocity gradient (d vx / dy) and is a fundamental expression of Newton's Law of Viscosity.

How does momentum transport occur in fluids?

Momentum transport occurs through the fluid by molecular interactions. In gases, it happens through free molecular motion between collisions, while in liquids, it primarily involves intermolecular forces between neighboring molecules.

What is kinematic viscosity and how is it calculated?

Kinematic viscosity is the ratio of a fluid's viscosity to its density, and it can be calculated using the formula nu = mu / rho, where mu is the viscosity and rho is the density of the fluid.

How does viscosity vary with temperature in gases and liquids?

In gases, viscosity increases with increasing temperature, while in liquids, viscosity generally decreases with increasing temperature.

What is the relationship between the velocity of fluid and the momentum transfer?

Momentum is transferred from regions of higher velocity to lower velocity within the fluid. The velocity gradient acts as a driving force for this momentum transport.

What is the behavior of fluid near a moving solid surface?

At the surface of a moving solid (y = 0), the fluid acquires momentum in the x-direction. This momentum is passed onto the adjacent fluid layers, causing the momentum to be transferred through the fluid.