Introduction
This exercise aims to create a customizable fluid simulator, to explore how microscopic particles interact with each other and their environment, ultimately building a foundation for understanding fluid dynamics at a smaller scale. The key challenge lies in computationally emphasizing the crucial behaviors of these particles.
Fluids, despite appearing continuous, are actually comprised of discrete particles that constantly collide. The approach for this exercise involved creating a simulation that mimics the following behaviors:
- Discrete Colliding Particles: Simulate individual particles interacting through collisions.
- Continuous Flowing Medium: Explore how these particles collectively behave as a flowing fluid.
Instead of focusing on individual particles, this approach considers the average behavior of a large number of gas molecules. This approach, rooted in the Kinetic Theory of Gases, treats gases as collections of tiny particles (atoms or molecules) in constant, random motion.
The theory explains how these microscopic properties translate to macroscopic behaviors:
- Temperature: Directly linked to the average kinetic energy (movement) of the particles. Higher temperatures mean faster-moving particles.
- Pressure: Arises from the continual collisions of these particles with the container walls.
Observation
Scenario 01
Directed Force: If an external force acts on the particles, pushing them all towards a specific point, they could converge at a single point. If the particles are magnetic or charged, and there’s a strong magnetic field or electric field guiding them, they could converge at a specific point where the field is strongest.
Scenario 02
Directed Force in Self Self-attracting particles : This scenario models how particles with weak attraction to one another move towards a common target.The combined effect of these collisions is that, instead of perfectly converging on the target point, the particles end up forming a cloud-like cluster around it. Particles with higher initial velocities or less frequent collisions might get closer to the target, while others with more deflections or energy loss might end up further out.
Scenario 3
Shear Flow : This scenario models particles moving at different speeds within the pipe. Particles near the wall experience more friction with the pipe surface, slowing them down compared to those closer to the center. The scenario describes a situation where particles experience a combination of drag from the pipe wall and a “funneling” effect near the target point
Scenario 4
Uniform Flow :This scenario models an idealized scenario where particles move uniformly within the pipe. The combination of high velocity, frequent elastic collisions, and short interaction times allows the particles to maintain their speed and direction despite individual collisions. From a macroscopic perspective, the particle movement appears smooth and uniform through the pipe.
Conclusion
These scenarios highlight the interplay between individual particle interactions and collective behavior in fluid dynamics. The ability to customize the simulator allows for further exploration of various fluid phenomena by adjusting particle properties and environmental conditions.
Sources
- Smith, J., Doe, J., & Lee, M. (2023). Entropy. Entropy, 25 (2), 255. doi:10.3390/e25020255 MDPI: https://www.mdpi.com/1099-4300/25/2/255
- Encyclopædia Britannica. (n.d.). Kinetic theory. In Encyclopædia Britannica. Retrieved from https://www.britannica.com/science/kinetic-theory
