The effects of surfactant solubility on inertial Marangoni flow: theory and numerics

Surface active agents (surfactants) significantly influence the dynamics at air-liquid interfaces by creating concentration gradients that lead to varying surface tension and resultant flow patterns. This study aims to expand on previous research by developing a comprehensive theoretical and numerical framework to explore how surfactant solubility enhances inertial Marangoni flows. We employ a systematic approach to define relevant nondimensional parameters and span the accessible physical parameter space, linking the behavior of finitely soluble surfactants to the asymptotic limits of both insoluble and infinitely soluble surfactants. Our findings indicate that the solution corresponding to infinitely soluble surfactants acts as a transient intermediate state that increasingly resembles the late-time solution as surfactant solubility increases, ultimately mapping onto solutions for insoluble surfactants. This research offers a deeper understanding of surfactant-induced flows and their critical role in various contexts, from environmental processes to industrial applications.