Surfactant Dynamics from the Arnold Perspective
Published in SIURO, 2021
In 1966, V. Arnold established an important connection between the incompressible Euler equations and a particular set of geodesic flows, using variational techniques to characterize the latter as solutions to the former. Motivated by his results, we investigate a series of similar PDEs characterizing constrained critical points of action functionals, paying particular interest to those associated with surfactant dynamics. Starting with the Arnold functional, we introduce various complications, adding terms associated to potential energies, surface tension, and surfactant momentum to derive different PDEs.