BE3002 Transport Phenomena in Biosystem Module 2_Segment 2

Summary

In this video, Yusuf from the Institute of Technology Bandung discusses the fundamental concepts of transport phenomena in biosystems. The focus is on conservation relations and momentum balances. He covers mass conservation in non-reacting systems, momentum accumulation, and the forces acting on fluids, including body and surface forces. Key concepts such as stress tensors, shear stress, and pressure are explained in relation to fluid dynamics. Boundary conditions for solid-fluid and fluid-fluid interfaces are also explored, emphasizing velocity and stress continuity. The video sets the stage for further discussions on fluid statics in the next segment.

Takeaways

• 😀 Conservation relations are essential in analyzing transport processes, and they can be expressed either in integrated or differential forms.
• 😀 Mass conservation involves tracking the total mass entering or leaving a control volume, with changes in concentration occurring due to chemical reactions (if any).
• 😀 Non-reacting systems are simplified by excluding the effects of chemical reactions, focusing on the mass balance at the control volume.
• 😀 Momentum balance is based on the relationship between mass, velocity, and forces acting on a system, including both body forces and surface forces.
• 😀 Body forces, like gravity, act on the entire fluid mass, while surface forces (stresses) act on control volume surfaces.
• 😀 Stresses are represented by stress tensors, where components like sigma_xx, sigma_xy, etc., describe normal and shear stresses on specific planes and directions.
• 😀 Stress tensors are symmetric and follow equilibrium principles in a fluid system, making them crucial in analyzing force distribution in fluids.
• 😀 A fluid at rest cannot support shear stress, and pressure is the only stress that can act in this condition. Pressure is compressive and acts normal to surfaces.
• 😀 For solid-fluid interfaces, boundary conditions require stress continuity across the interface, with the no-slip condition for velocity matching the solid surface velocity.
• 😀 Fluid-fluid interfaces also require stress continuity, and the velocities at the interface must be matched for the two fluids in contact.
• 😀 The next segment will focus on fluid statics, continuing the study of transport phenomena in biosystems.

Q & A

What is the importance of conservation relations in transport phenomena?

Conservation relations are critical for analyzing transport processes as they describe how mass, momentum, and energy behave within a system. These relations help in understanding the flow of materials and forces within a biosystem, providing a foundation for further analysis.

What is the difference between integrated and differential forms of conservation equations?

Integrated forms describe the average behavior of a fluid over a control volume, while differential forms describe the motion and forces at each point within the fluid, allowing for a more detailed, localized analysis.

What does the mass balance equation for a control volume represent?

The mass balance equation expresses the total mass entering and exiting a fixed control volume. It ensures that the mass is conserved over time, considering both fluid flows and any chemical reactions (though reactions are excluded in this context).

What are body forces and surface forces in fluid dynamics?

Body forces, such as gravity or electromagnetic fields, affect the entire fluid mass throughout the control volume. Surface forces, such as stresses, act on the fluid surfaces or interfaces between different phases.

How are stresses represented in a fluid system?

Stresses in a fluid are represented as tensors, denoted as sigma or sigma ij. The indices i and j specify the planes and directions of the stress, with normal stresses acting perpendicular to a surface and shear stresses acting tangentially.

What is the significance of the sign convention for stresses?

The sign convention for stresses determines whether they are considered positive or negative. Normal stresses are positive when they act in the direction of the outward normal vector, while compressive stresses are negative. Shear stresses are positive based on the direction of fluid motion on the surface.

Why can't a fluid at rest support shear stress?

A fluid at rest cannot support shear stress because there is no relative motion between the fluid layers to create a shear force. Only pressure, which acts uniformly in all directions, can exist in a static fluid.

What is the no-slip condition at a solid-fluid boundary?

The no-slip condition states that the fluid velocity at a solid surface is equal to the velocity of the solid surface itself. This means there is no relative motion between the fluid and the solid at the interface.

How do boundary conditions differ for solid-fluid and fluid-fluid interfaces?

At solid-fluid interfaces, the normal and tangential stresses must be continuous, and the no-slip condition applies. At fluid-fluid interfaces, the stress continuity also applies, and the velocities of the fluids must be the same at the interface.

What are the implications of stress tensors being symmetric in most fluids?

The symmetry of stress tensors implies that the forces acting on a fluid at a point are balanced and consistent in different directions. This property helps in simplifying the analysis of fluid flow and stresses within a system.