Amphiphiles, such as alcohols, lipids and soaps can decrease the interfacial tension between water and other fluids, thus helping for the compartmentalization of matter in emulsions, foams, vesicles and cells. A difference in the concentration of amphiphiles along an interface between two media triggers an interfacial-tension-induced Marangoni flow whose occurrence is critical for transport phenomena in lipid nanotubes, the stability of emulsions and foams, pulmonary surfactant replacement therapy, insect locomotion and many industrial applications. Although most amphiphiles found in nature and used in the industry have a finite solubility in water, only few studies deal with Marangoni flows induced by water-soluble amphiphiles, while simultaneously considering the effect of the amphiphile finite solubility.
Here we provide a quantitative description of a model Marangoni flow, induced by the spreading and dilution of a local surfactant excess, both in terms of surfactant physicochemistry and hydrodynamics. We show experimentally that i) the spreading Marangoni flow induced by surfactants of finite solubility in water extends over a finite distance and ii) this distance varies monotonically with the critical micellar concentration (CMC). We provide evidence that the velocity field of this flow has universal features, and we identify the scaling laws that capture both the extent over which the Marangoni flow is observed and the magnitude of the maximum velocity.
These results are important for a better understanding of transport phenomena involving amphiphiles at liquid interfaces in out-of-equilibrium systems. In addition, our experimental approach could be adapted to design a new method to measure the critical micellar concentration of an amphiphile.
Figure 1 : Finite distance of the spreading Marangoni flow for surfactant of finite solubility: a surfactant solution is deposited on top of the liquid at constant rate, and oil droplets act as passive tracers to visualize the flow.
