Direct numerical simulations of turbulent jets: vortex-interface-surfactant interactions

Many industrial applications involve the breakup of a jet into emulsions. A fundamental understanding of the physical mechanisms that control the droplet size distribution can aid the improvement of mixing/shearing devices. Additionally, those streams are usually contaminated with surface active agents triggering the formation of surfactant-induced Marangoni stresses. Here, we study the effect of surfactants on the spatio-temporal evolution of turbulent jets using three-dimensional numerical simulations that employ an interface-tracking/level-set method that accounts for surfactant-induced Marangoni stresses. The present study builds on our previous work (Constante et al., 2021, J. Fluid Mech., 922, A6) in which we examined in detail the vortex-surface interaction in the absence of surfactants. Numerical solutions are obtained for a wide range of Weber and elasticity numbers in which vorticity production is generated by surface deformation and surfactant-induced Marangoni stresses. The present work demonstrates, for the first time, the crucial role of Marangoni stresses, brought about by surfactant concentration gradients, in the formation of coherent, hairpin-like vortex structures. These structures have a profound influence on the development of the three-dimensional interfacial dynamics. We also present theoretical expressions for the mechanisms that influence the rate of production of circulation in the presence of surfactants for a general, three-dimensional, two-phase flow and highlight the dominant contribution surfactant-induced Marangoni stresses.