Diffusiophoresis of a non-polar fluid droplet laden with soluble ionic surfactants

We investigate the diffusiophoresis of a non-polarizable droplet laden with soluble ionic surfactant, in which the surface charge arises from the adsorption of surfactant at the fluid–fluid interface. Unlike previous studies which assume either a fixed surface charge or instantaneous equilibrium between the interface and the adjacent electrolyte, we formulate the interfacial transport based on the mass-balance framework, incorporating Langmuir adsorption–desorption kinetics and finite surface diffusivity. The coupled electrokinetic problem is solved using a perturbation approach with imposed ionic concentration as a perturbation parameter. Analytical expressions for the droplet mobility and interfacial velocity are derived based on the Debye–Hückel approximation as well as the thin layer consideration for the insoluble surfactant, which are found to agree with the numerical results in the corresponding limits. We demonstrate that consideration of a uniform, immobile surface charge leads to an unphysical singular mobility, whereas allowing the surface charge to evolve through interfacial surfactant redistribution yields continuous and physically consistent droplet diffusiophoresis. Increasing the desorption rate enhances surfactant redistribution and Marangoni stress, which weakens the negative mobility created by the electrophoresis part, reverses the direction of motion by enhancing the chemiphoretic contribution, and subsequently leads to a strong enhancement of positive mobility before eventual saturation in the transport-limited regime. The dependence of mobility on viscosity ratio and electrolyte composition further reveals how mixed electrolytes provide a robust means of tuning droplet motion. This study underscores the crucial role of adsorption–desorption dynamics and interfacial transport of soluble ionic surfactants in governing the diffusiophoresis of fluid particles, with implications for droplet manipulation in microfluidic system in imposed salinity gradients.