Direct numerical simulations of the dispersion dynamics of liquid-liquid surfactant-laden flows in static mixers*

This study focuses on the effect of adding surfactants to enhance dispersion performance for manufacturing applications. We implement three-dimensional direct numerical simulations with a hybrid front-tracking/level-set interface capturing algorithm to provide a deep insight into the relevant physical mechanisms that govern fundamental processes during the dispersion (i.e., droplet deformation, breakage and coalescence). In this work, a 2-element SMX static mixer is set-up operating in a laminar regime under three main scenarios: 1) insoluble surfactant trapped at the interface between phases; 2) insoluble and Marangoni-free surfactant, where tangential stresses arising from surfactant concentration gradients are removed; and 3) fully-soluble surfactant, where there is mass exchange between the interface and the dispersed phase. For Cases 1 and 2, the surfactant’s influence on the surface tension is analysed through the elasticity parameter and the Marangoni effects are isolated. For Case 3, the surfactant’s adsorption and desorption capabilities are investigated via parameters reflecing the  ratio of desorption to inertia,  ratio of adsorption to desorption and ratio of bulk vs. interfacial surfactant concentration and contrasted against the clean and insoluble cases. A larger number of droplets are generated in the presence of surfactants but the dispersion process follows a different mechanism compared to the clean case, where a delay in the formation of droplets is seen. This is attributed to the concentration gradients acting on the initial ligaments, which set back early interfacial instabilities but prompt a larger number of daughter droplets once breakage occurs via Rayleigh-Plateau instability. The initial interfacial concentration of surfactant was observed to heavily influence the early droplet deformation and thus its subsequent breakage mechanism and daughter drop count.