CBE 30356 - Lecture Notes - April 11, 2023
Announcements
Class notes
Read through pages 307-325 of the notes and view the online narration below. Don't forget to complete the quiz in Canvas!
The narration is divided into two parts. The first looks at unsteady diffusion from an initial point distribution, and the second looks at solute spread due to convective diffusion in flow through a channel.
The main points of the lecture were
- Diffusion an initial point distribution in the absence of convection
- The relationship between the variance of the concentration distribution and the diffusion coefficient
- The Method of Moments calculation of the Taylor Dispersivity for channel flow
Goals:
After this class you should be able to:
- Know the relationship between variance and diffusion.
- Understand how shear combines with the -inverse- of diffusivity to lead to dispersion.
- Calculate the spread of a solute slug in laminar channel or tube flow.
Reading
- The class notes.
- BS&L, 20.5
Problem of the Day:
In this problem we will show how you can use the concept of random walk motion (e.g., Brownian motion) to easily simulate Taylor dispersion in a complex domain: all you need is the velocity distribution, a random number generator, and a whole lot of CPUs. The notes for this material are found here and the code is pod22.m.
Demonstration:
David.T.Leighton.1@nd.edu