(398a) Quantifying the Rates of Viscous Spreading of Surfactant on a Deep Fluid Subphase

The spreading of an insoluble surfactant on a fluid-fluid interface through Marangoni forces is a fundamental fluid mechanics problem that has been investigated extensively due to its implications in colloid science, biology, and the environment. While many different regimes have been studied theoretically, analytical progress has proven especially challenging in the limit of a viscous, deep subphase at low Reynolds number. This is due to the non-local nature of the problem, with the interfacial velocity at any given point depending on the surfactant distribution everywhere on the interface. We study this problem from the perspective of self-similarity, which allows us to obtain power laws for the universal spreading behaviors that arise independently of the spatial details of the initial surfactant distribution. Using a phase-plane formalism and stability arguments, we identify six different similarity solutions with three distinct rates of spreading. In practice, each of these three rates manifests based on whether the initial state is a pulse of outward-spreading surfactant, or locally depleted dimples or holes of surfactant that flow inward. The discovered taxonomy of distinct spreading behaviors enhances our fundamental understanding of Marangoni flows, providing simple predictive laws to inform engineering applications.