Breakup of surfactant-laden jets above the critical micelle concentration

Abstract

The breakup of viscous liquid jets that contain surfactant, that is potentially above the critical micelle concentration (CMC) is considered here within the long-wave approximation. The soluble surfactant is assumed to be present in three phases: as an interfacial species, bulk monomers and micelles. A model is developed for the interaction between these phases and the surface tension which obeys a nonlinear equation of state. The effects of the equation of state and the reservoir of surfactant created by micelles on breakup are investigated. The long-wave approximation naturally leads to a system of coupled one-dimensional equations that are solved numerically. It is demonstrated that jet breakup and satellite formation are critically affected by the presence of high surfactant concentrations above the CMC. This manifests itself by the formation of unusually large satellites. We present extensive numerical evidence that the mechanism for this phenomenon centres on the interplay between Marangoni stresses and the nonlinear surfactant equation of state; the latter exhibits a plateau at high interfacial concentrations.