Teaching & Experiential Learning
I teach MATH121 (Calculus) and PHYS106 (General physics) courses at Bader College. When teaching, I always focus on aiding students to understand the real-world applications of the tools and methods we are studying. I strive to have an interactive classroom where students can discuss concepts and exercises in a friendly environment where mistakes are seen as a method of improvement.
In PHYS 106, we have problem-based, exploratory lab sessions. Outside of these times, we also have one experiential learning activity each semester. This semester the students will engage in a workplace simulation investigating the elastic properties of rubber during temperature changes.
The MATH 121 ELOs focus on furthering the students' understanding of the role mathematics can play in modern society.Research
My research has two main topics:
- Determining stability criteria of capillary structures.
- Understanding the evolution of evaporating droplets on slippery liquid-infused porous surfaces
A capillary structure is a small liquid volume held in place by its surface tension dominating the gravitational forces. For example, you may think of the liquid that attaches to your finger as you slowly withdraw it from a glass of water. I analyse these structures analytically and numerically. I also work with experimental groups to validate my results.
Slippery liquid-infused porous surfaces (or SLIPS) are a relatively new type of surface that has the interesting property that liquid droplets cannot rest on them if there is even the slightest imbalance. From this easy of motion, droplets can be seen to jump (or snap) as they evaporate. It is this process that interests me.
Beyond these points, I also regularly partake in industrial mathematics workshops. These allow industrial partners to present problems that they are facing for a group of mathematicians to analyse and describe practical solutions.
Supervision
Students can freely contact me if they are interested in projects concerning the mathematical modelling of a physical phenomenon.
Recent Publications
- Haynes, M., O'Brien, S.B.G. and Benilov, E. (2016) ‘Asymptotics of a horizontal liquid bridge’
- Haynes, M., Vega, E.J., Herrada, M.A, Benilov, E.S., Montanero, J.M. (2018) 'Stabilization of axisymmetric liquid bridges through vibration-induced pressure fields'
- Haynes, M. (2019) 'Static capillary structures and their stability'
- Haynes, M., Pradas, M. (2022) 'On the lifetimes of two-dimensional droplets on smooth wetting patterns'