CBE 30355 - Lecture Notes - Oct. 15, 2024
Announcements
Class notes
Read through pages 182-190 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
Goals:
After this class you should be able to:
- Scale the transport equations to get the Reynolds Lubrication Equation.
- Apply this equation to calculate the forces in simple lubrication flows.
Reading
- The class notes.
- BS&L, chapter 4
Additional Readings:
Lubrication flows are just one example of flows at low Reynolds numbers where
inertia may be neglected. One active area of research in low Re system is the field of
microfluidics, in which chemical laboratories are reduced to a microscale and reactants
are pumped around through microchannels etched on a chip. Wikipedia does a decent
job of describing some of the uses of this technology. That article can
be found
here.
Demonstration:
In the lecture we talk about the detachment of a disk from a plane. The reverse of this (and a very similar problem mathematically) is the velocity profile produced by squeezing a fluid between two disks. Here we show via calculation and demonstration that the radius of a Newtonian liquid with constant squeezing force grows such that R^8 is linear in time. As a bonus we also demonstrate what happens when the fluid is a non-Newtonian suspension, yielding fascinating particle migration mechanics and flow instabilities. A paper describing this latter phenomenon is given here.
David.T.Leighton.1@nd.edu