CBE 30355 - Lecture Notes - Oct. 27, 2026

Announcements

Class notes

• The Reynolds Lubrication Equation

Goals:

• Use the Reynolds Lubrication Equation to calculate the forces in 2-D lubrication flows.

Reading

• The class notes.
• BS&L, chapter 4

Additional Readings:

One of the most interesting examples of lubrication flows is that found in ice- skating. In that winter sport, the friction between the blade and the ice melts a small quantity of water, forming a thin lubricating layer. The old story that it's the pressure of the blade which melts the ice isn't true - and the later theory that it's the frictional heating that does the trick isn't quite right either. Instead, the current theory is that there is a very thin layer of water at the surface of ice even well below freezing due to thermodynamic effects. A good discussion of the effects of a thin layer of water on ice (taken from a Physics Today article) is given here.

Demonstration:

Last class we demonstrated the squeeze flow of a Newtonian liquid (glycerin) between two plates, demonstrating that the radius grows such that R^8 is linear in time. Very different (and rich) behavior occurs for a non-Newtonian fluid! In today's demonstration we see what happens if a suspension of glass spheres is squeezed instead. Because of the parabolic flow in the gap between the plates, the spheres will migrate to the centerline of the gap and accumulate at the radially advancing meniscus. This (now packed) layer is much more viscous than the displacing fluid, and thus is unstable to the classic miscible viscous fingering instability - the same effect that makes tertiary oil recover so hard - resulting in trapped islands of sediment and a wavy interface. A paper describing this fascinating phenomenon is given here, and the radial location of where the packed layer first forms can be estimated via dimensional analysis.