-----------------------------------------------------------

Applied Mathematics Colloquium

Friday, February 6, 11:30 am
Cullimore Lecture Hall II
New Jersey Institute of Technology

-----------------------------------------------------------

Soap Films, Droplets, Electric Fields, Magnetic Fields, and Elasticity

John Pelesko

Department of Mathematical Sciences

University of Delaware

Newark, DE

Abstract

Soap bubbles have been described as the playthings of children and mathematicians alike. Studied by scientists such as Newton, da Vinci, and Plateau, “play” with soap bubbles and films has led to a surprising array of discoveries in both mathematics and physics. In this talk, we survey experimental and theoretical results obtained in our laboratory from studies of soap films and liquid drops interacting with electromagnetic fields and elastic bodies.

In the first part of the talk, we’ll look at soap films interacting with electric fields. In this case, we’ll treat the films as elastic membranes and attempt to understand the shapes these films assume in the presence of an elastic field. We’ll see how this study leads to a generalization of the well-known minimal surface equation (H=0) or the well-known constant mean curvature equation (H=1).

In the second part of the talk, we’ll look at soap films interacting with magnetic fields. Here, we focus on the flow of liquid within a soap film that has been impregnated with magnetic nanoparticles. In the modeling this system, we’ll encounter a typical thin film partial differential equation, but this time coupled to and driven by equations governing the magnetic field.

Finally, we’ll discuss some very recent experimental work on droplets interacting with both elastic bodies and electric and magnetic fields.

.