Can surfactant fluxes induce interfacial instability?

Understanding the non-equilibrium dynamics of microscopic droplets is central to the engineering of emulsions, which are a cornerstone of many technological applications ranging from oil recovery and separations to food science and cell biology. Recent experiments [Birrer et al., ChemRxiv (2025)] have revealed that the flux of a soluble surfactant partitioning from an aqueous solution into a clean oil micro-droplet can mechanically destabilize the interface and produce its disintegration. Here, we investigate theoretically the possible pathways to this interfacial instability. Using linear stability analysis, we first illustrate that surfactants alone cannot produce the unstable deformation of a quiescent, planar fluid interface in Stokes flow (i.e. with no fluid inertia). We then incorporate fluid curvature into the analysis, and examine the different regimes under which instability may be possible depending on the relative importance of physicochemical effects like surfactant bulk diffusion, adsorption/desorption kinetics, and the viscosities of the two liquid phases. We also discuss the effect of non-ideal equations of state and kinetic fluxes, which are known to play a role in virtually all practically relevant processes with realistic surfactant concentrations.