2026 Eshima Surfactant Solubility Inertial Marangoni Flow

Surface active agents (surfactants) are prevalent contaminants at air-liquid interfaces, influencing fluid dynamics through surface tension gradients. This study aims to investigate the effects of surfactant solubility on inertial Marangoni flow, extending prior theoretical and numerical frameworks. We develop a systematic approach to analyze surfactant-induced flows, building on previous work that demonstrated the enhancement of these flows by surfactant solubility. Our methodology incorporates late-time similarity solutions to derive and characterize the flow behavior under varying surfactant solubilities. We quantitatively define relevant nondimensional parameters and explore a broad parameter space through theory and numerical simulations. The results indicate a transition from insoluble to infinitely soluble surfactants, where infinitely soluble limits act as intermediate solutions that gradually connect to the late-time behaviors emulating insoluble surfactants. Notably, we discover that smaller solubility correlates with accelerated thinning and enhanced front propagation, indicating significant implications for both natural and industrial processes where surfactant dynamics are critical. This research contributes a robust theoretical and computational framework to understand the complexities of surfactant behavior in fluid mechanics.