Electrophoresis of Charged Dielectric Droplet With Ion Concentration Polarization Effect

Droplet electrophoresis is one of the most commonly used methods for measuring the charge at two-liquid interfaces. However, there is still a lack of analytical solutions that consider the ion concentration polarization mechanism with asymmetric ion distribution under high surface charge. Based on the thin electric double layer assumption, we construct the asymptotic form of the macroscopic model of dielectric droplet electrophoresis and establish the coarse-grained effective interface condition across the diffuse layer regions through the heuristic treatment extending the method of matched asymptotic expansion, revealing the coupling mechanism between ion concentration polarization and permittivity-induced inhomogeneous charging. An analytical solution under the weak-external-field limit is provided, demonstrating a nonmonotonic dependence of electrophoretic mobility on the $\zeta$ potential under weak external electric fields. By integrating previous experimental results on droplet electrophoresis, a concise and physically meaningful quantitative model of the charging mechanism for general nonpolar oil is established.