Lachlan is currently a second year student, studying a Bachelor of Mathematics, majoring in Applied and Computational Mathematics. He is interested in applied mathematics, particularly calculus and differential equation models. He is also interested in physics and modeling physical systems mathematically.
Evolving Bubbles In A Hele-Shaw Cell
There is a well-studied problem in applied mathematics of determining the shape of a bubble as it moves through a device called a Hele-Shaw cell. The problem is two-dimensional, and involves solving Laplaces equation in an unknown domain. Thus, complex variable techniques can be applied. In particular, the goal is to determine a conformal mapping from a canonical domain (like the unit disc) to the fluid area. One of the relevant boundary conditions includes the effects of surface tension on the bubble boundary. In this project, we shall revisit the so-called “selection problem” of determining the shape and speed of bubbles.