Droplet behavior in the presence of insoluble surfactants

Abstract

The time-dependent behavior of droplets in the presence of insoluble surfactants, i.e., droplet elongation in supercritical flow (capillary number Ca=0.1) and droplet breakup in a quiescent matrix, is studied using a finite element method. The interfacial tension coefficient σ as a function of the surfactant concentration Γ is described using the Langmuir equation of state, σ=σ0 + RTΓ∞ln(1-Γ/Γ∞). For droplets in an equal viscosity system, the influence of parameters and the Péclet number (ratio between surfactant convection and diffusion rate) on the elongation behavior has been investigated, whereas droplet breakup is considered for various values of the Péclet number for trace concentrations of an insoluble surfactant. Depending on the surfactant used, a surfactant covered droplet in supercritical flow may deform more than or less than a clean droplet, as is the case in subcritical flow. Two processes compete: surfactant accumulation near the tips due to convection and overall surfactant dilution due to an increase of interfacial area. Nevertheless, the main effect of surfactants on dispersive mixing is due to the fact that upon breakup, the daughter droplets have a different interfacial tension coefficient. Especially in time-dependent processes, this may have a huge impact on the final droplet distribution. © 2004 American Institute of Physics.