Simon Cox: The mathematics of soap bubbles

Abstract: A soap film spanning a wire frame is a minimal surface, i.e. it is a surface of zero mean curvature. A soap film enclosing a certain volume of gas, i.e. a bubble, is a surface of constant mean curvature. Hence an aqueous foam at equilibrium is a collection of cmc surfaces subject to volume constraints. The way in which soap films meet, known as Plateau's laws, are a consequence of the fact that soap films minimize their surface area. I will introduce the basics of foam structure and describe the Kelvin problem, which is the search for the least area partition of space into bubbles of equal volume, and some of the, often surprising, consequences of area-minimization in driving foam dynamics in different applications.

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Mar 23, 2017
from 11:00 AM to 12:00 PM



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