Very viscous flows
Overview
Towards the end of Fluid Mechanics III, we saw that when a fluid is very viscous, very slow, or very small-scale, we can say that the nondimensional Reynolds number is small. In this limiting regime, we are led to the Stokes equations,
\[\mathbf{0} = -\boldsymbol{\nabla}p + \mu \nabla^2 \boldsymbol{u}.\]
In this project, we will take a look at flows in this regime. This may include:
- How microorganisms swim
- How particles move when they’re suspended in a viscous fluid
- Flow in thin films
- Lubrication theory
We will start by looking at the basic theory together, but the ultimate target will be directed by your interests. This field is nice and visual, with lots of applications in industry and biology, and we weren’t able to see any of them in Fluids III. Now is your chance!
Prerequisites
You need to have taken Fluid Mechanics III to do this project.
⚠️ This is an applied maths project and there will be significant computational work. You should be confident with Python (or a language of your choice).
How we might structure the the project
At the start, you could have something like:
- Mathematical derivation of Stokes flows
- Simple solutions of these flows
- Fluid–structure interactions
Reading list
- Acheson, Elementary Fluid Dynamics, chapter 7