Surfactant dynamics in confined geometries

Speaker's Name: Richard McNair
Speaker's Affiliation: University of Nottingham
Speaker's Research Theme(s): Applied Mathematics,
Abstract:
Surfactants reduce interfacial tension and, through the Marangoni effect, can drive fluid flows along liquid–gas interfaces. Because trace surfactants are ubiquitous in industrial and biological settings, they often act as hidden variables that generate unexpected transport and stresses. We will consider three model problems to show how endogenous surfactant fields, which are pre-existing surfactant on an interface, produce non-local dynamics when disturbed by added exogenous surfactant. First, we will consider surfactant-driven cavity flow and recast the governing equations as an eigenvalue problem, revealing the dominant global modes selected by confinement and aspect ratio. Second, we will look at Marangoni-driven transport in networks (motivated by lung airway-like geometries and experiments in mazes) using a graph-based discrete calculus to connect topology to dynamics of a sharp exogenous-endogenous surfactant boundary. Finally, we will look at a Lagrangian, point-tracking formulation of surfactant motion and relate it to optimal transport theory, characterizing redistribution in terms of the Wasserstein distance. Together, these problems show how ubiquitous endogenous surfactants induce global, non-local flow responses in confined geometries, where dynamics at a point depend on global geometry and boundary conditions.

Venue: Maths A17