Transfer Dynamics of Hydrophilic and Lipophilic Surfactants in Turbulent Oil-Water Emulsions

We investigate the transfer dynamics of hydrophilic and lipophilic surfactants in turbulent oil-in-water emulsions, in which oil droplets are dispersed in a continuous water phase, with the surfactant hydrophilic-lipophilic balance (HLB) influencing its solubility in both phases. Using direct numerical simulations, we solve the turbulence dynamics in a closed channel, while the time evolution of the emulsion morphology and surfactant concentration field is obtained using a phase-field method (PFM) based on two Cahn-Hilliard-like equations obtained from a Ginzburg-Landau free energy functional. The effect of surfactant on interfacial tension is modeled via an equation of state. The PFM can account for varying solubility, distinguishing between water-soluble (high HLB), equally soluble (intermediate HLB), and oil-soluble (low HLB) surfactants. Our results show that while the overall topology of the dispersed phase remains relatively unaffected, significant differences arise in the surfactant distribution at the interface and in the bulk of the two phases. Oil-soluble surfactants exhibit higher concentrations at the interface compared to water-soluble ones. By analyzing surfactant concentration, transfer fluxes, and free energy, we identify the key mechanisms governing surfactant transport in turbulent emulsions.