Dynamic mobility of surfactant-stabilized nano-drops: unifying equilibrium thermodynamics, electrokinetics and Marangoni effects

Electrokinetic spectra of dilute surfactant-stabilized nano-emulsions

“…Nevertheless, both estimates suggest that, at the MHz forcing of an electroacoustic experiment, the adsorbed DS − is expected to behave as if it is irreversibly bound to the interface, as assumed by Hill & Afuwape (2020) who implicitly set k a = k d = 0 based on 'kinetic rates' being much smaller than ∼1 MHz. Here, the kinetic rate implied by Hill & Afuwape (2020) is more precisely…”

“…as pioneered for rigid spheres by Delacey & White (1981) (dielectric response) and Mangelsdorf & White (1992) (dynamic mobility). Section 3 (and appendix A) details how the internal, interfacial, and external regions are coupled in an efficient numerical method that solves this notoriously stiff numerical problem over a wide range of the parameter space (Hill, Saville & Russel 2003). This section also sets out notation (and non-dimensionalization), including the superposition of the U-and E-problems.…”

“…to capture the internal fluid dynamics, interfacial Marangoni effects (surface tension and lateral transport) and exchange kinetics. The concentration Marangoni number (Hill & Afuwape 2020)…”

“…compares interfacial diffusion and surface-tension relaxation times, whereas Ma ∼ 1 is a dimensionless combination of intrinsic interfacial properties (comparing interfacial and thermal energy). The dynamic electrophoretic mobility is computed by solving the equations for a stationary drop with U = 1 and E = 0 (U-problem), and E = 1 and U = 0 (E-problem), from which the far-field decay of the velocity field furnishes 'asymptotic coefficients' (Hill et al 2003)…”

“…To address the high surface charge (and accompanying high surface conductivity) and fluid characteristics of nano-drops in dynamic electrophoretic mobility experiments (O'Brien 1988(O'Brien , 1990, Hill & Afuwape (2020) recently proposed a thin-double-layer model for the dynamic mobility, valid at high frequencies for which there is no time for diffusive ion transport. They assumed that the adsorbed surfactant is bound to the interface while the drop is subjected to an oscillatory electric field.…”