Deep-subphase Marangoni flows of insoluble surfactants

Surfactant transport remains an important problem throughout various areas of science and engineering, with applications to the environment, biology, and other technological processes. While the spreading of insoluble surfactant fronts has been verified experimentally, few experiments consider the opposite process: the inward flow produced by a surfactant-free area in the midst of a contaminated surface (e.g., a hole). We report experimental results on the outward (spreading) and inward (filling) solutions of insoluble surfactant transport on a viscous substrate at low Reynolds number, in both axisymmetric and one-dimensional (planar) domains. We recover spreading power laws (where the front scales as r(t)∼ t^β) marginally higher than β = 1/3 and β = 1/2 for the axisymmetric and planar cases (Bickel & Detcheverry, 2022; Temprano-Coleto & Stone, 2024), respectively. Similarly, filling flows exhibit a behavior with a power law β = 1-2, though consistent with theoretical predictions from similarity of the second kind.