# CBE 30355 - Lecture Notes - Oct. 26, 2023

## Announcements

## Class notes

Read through pages 204-217 of the notes and view the online narration below. Don't forget to complete the quiz in Canvas!

The main points of the lecture were
- The Streamfunction: Flow Past a Wiper

## Goals:

After this class you should be able to:
- Show how 2-D problems at low Re lead to the Biharmonic Equation.
- Apply this equation to calculate velocity distributions in 2-D flows.

## Reading

- The class notes.
- BS&L, chapter 4

## Additional Readings:

One subject which has always been of interest
to me is the wonderful shapes of snowflakes. If you've ever wondered why they grow
as they do, you should explore the link given
here - an entire website devoted to the detailed understanding of ice crystals.

## Regression Example

For homework you are asked to do a little linear regression. By request, a simple example of such an error analysis is given in the file regressionexample.m. This is in Matlab, but you can easily rewrite it in Python or other languages. This is also covered in your Numerical Analysis class notes.

## Demonstration:

In class today we demonstrated the phenomenon of Moffatt eddies. These eddies occur if you have low Re flows over pockets or grooves, and are an interesting result of the separable solution to the Biharmonic equation. The take-home message is that Moffatt eddies are the reason why it is so hard to clean stuff out of grooves: the flow separates and you just get recirculation in the pocket. This also has important implications in bioreactor systems where cells are in pits at the surface: nutrients and waste have to diffuse in and out which can lead to mass transport limitations. The original paper describing this phenomenon can be found here. A somewhat more simplified derivation of the phenomenon can be found here.

David.T.Leighton.1@nd.edu