Highly concentrated surfactant solutions influence cross-stream migration of a drop in a Poiseuille flow

Surfactants are usually added in droplet-based systems to stabilise them. When their concentration exceeds the critical micelle concentration (CMC), they self-assemble into micelles, which act as reservoirs regulating the availability of monomers in the continuous phase, thereby promoting interfacial remobilisation. The monomers get adsorbed onto a drop’s interface to alter its surface tension, and thus, governs how the drop moves within the suspending phase. Indeed, fine tuning droplet trajectories remain crucial in many classical as well as modern applications. Yet, the role of soluble surfactants in modulating droplet movement, especially at high concentrations, hitherto remains poorly understood. To address this, here we investigate the motion and cross-stream migration of a non-deforming drop in an unbounded Poiseuille flow, in the presence of bulk-soluble surfactants at concentrations above the CMC. We build a mixed semi-analytical-cum-numerical framework using spherical harmonics to determine the ensuing velocity and concentration fields. Our results suggest that the drop migrates towards the flow centreline, the extent of which depends on the interplay between the bulk concentration and the sensitivity of the interfacial tension to the surfactant molecules. This propensity for migration plateaus in the presence of micelles, although changing their specific properties seems to have relatively little impact. We further establish that adsorption–desorption between the interface and the bulk tends to suppress migration, while a relatively stronger coupling between bulk and interfacial transport facilitates the same. These findings highlight the crucial role of micelles in droplet motion, with implications in microfluidic control strategies and surfactant-driven flow manipulation.