Interfacial Adsorption–Desorption of Ionic Surfactants and Charge-Density Inversion in Droplet Electrophoresis with Multivalent Electrolytes

The electrophoresis of a viscous droplet coated with sodium dodecyl sulfate (SDS), an anionic surfactant, in a nonamphiphilic electrolyte containing valence-asymmetric salts is investigated. The lateral mobility and kinetic exchange of surfactant molecules at the droplet interface lead to a nonuniform surfactant distribution, generating Marangoni stresses and enhancing electric double-layer (EDL) polarization. Consequently, the electrophoretic response of the droplet differs from predictions based on the conventional assumption of a constant and immobile surface charge density. To account for these effects, we develop a modified electrokinetic model incorporating finite-sized and electrostatically correlated ions. The finite size of ions introduces steric effects and modifies the effective viscosity of the suspending medium, while correlations among ions modify the ion distribution in the EDL. The electrostatic correlations are described using a nonlocal electrostatic framework. The modified model agrees well with existing experimental observations, including the reversal of electrophoretic mobility at high electrolyte concentrations. Based on this modified model, we investigate the influence of multivalent counterions on the adsorption–desorption dynamics of SDS at the droplet interface and their consequences for droplet electrophoresis. Our analysis demonstrates the formation of an ionic layered structure within the EDL and the associated mobility reversal in the strong coupling regime. The formation of multilayer structures at the air–electrolyte interface in anionic surfactant systems upon the addition of multivalent counterions has been reported in previous experimental studies and is corroborated by the findings of the present study. This layered structure reverts to a monolayer structure at a higher concentration of LaCl3. We find that the solubility of the ionic surfactant attenuates the droplet mobility and promotes the mobility reversal in trivalent counterions compared to insoluble surfactants. Higher interfacial surfactant coverage reduces the effective surfactant desorption rate.