Mathematical Capillarity

Department: 
Math
Course Number: 
4803-MCC
Hours - Lecture: 
3
Hours - Lab: 
0
Hours - Recitation: 
0
Hours - Total Credit: 
3
Typical Scheduling: 
Not regularly scheduled

Special topics course on Mathematical Capillarity, offered in Spring 2021 by John McCuan.

Prerequisites: 

No formal prerequisites are required beyond calculus and ODE’s

Course Text: 

Equilibrium Capillary Surfaces by Robert Finn (Springer 1986)

Topic Outline: 

The subject will be presented with a unifying framework from the calculus of variations. Within this framework, students will learn aspects of differential geometry, elementary molecular physics, partial differential equations, ordinary differential equations, geometric measure theory, and asymptotic analysis.

An outline of topics is as follows:

1. surface tension, adhesion, and mean curvature

2. equations of Young and Laplace

3. variational framework of Gauss

4. axially symmetric capillary tube

5. maximum principles and the comparison theorem

6. rise height: Laplace’s asymptotic formula

7. capillary surfaces in corners; zero gravity

8. parametric surfaces

9. sessile drops

10. parametric comparison

11. pendant drops and stability

12. Laplace’s parallel plates and floating bodies