Subrata Majhi, Somnath Bhattacharyya
Abstract
We investigate the diffusiophoresis of a non-polarizable droplet laden with soluble ionic surfactant, for which the surface charge arises from adsorption of surfactant at the fluid-fluid interface. Unlike previous studies that 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. Analytical expressions for the droplet mobility and interfacial velocity are derived for insoluble surfactants. We demonstrate that assuming uniform, immobile surface charge leads to unphysical predictions, including negative chemiphoresis and singular mobility, whereas allowing the surface charge to evolve through interfacial surfactant redistribution yields continuous and physically consistent droplet diffusiophoresis. Interfacial kinetic exchange is found to play a central role. Increasing the desorption rate enhances surfactant redistribution and Marangoni stress, weakens the negative mobility, reverses the direction of motion through competition between electrophoretic and chemiphoretic contributions, 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 of different salts further reveals how mixed electrolytes provides a robust means of tuning droplet motion. This study highlights the critical role of finite-rate surfactant dynamics and interfacial transport in determining the diffusiophoresis of fluid particles, with implications for manipulating droplets in microfluidic and varying-salinity environments.