On the effect of hydrodynamic slip on the polarization of a nonconducting spherical particle in an alternating electric field

The polarization of a charged, dielectric, spherical particle with a hydrodynamically slipping surface under the influence of a uniform alternating electric field is studied by solving the standard model (the Poisson–Nernst–Planck equations). The dipole moment characterizing the strength of the polarization is computed as a function of the double layer thickness, the electric field frequency, the particle’s surface charge, and the slip length. Our studies reveal that two processes contribute to the dipole moment: ion transport inside the double layer driven by the electric field and the particle’s electrophoretic motion. The hydrodynamic slip will simultaneously impact both processes. In the case of a thick double layer, an approximate analytical expression for the dipole moment of a weakly charged particle with an arbitrary slip length and a small zeta potential $\zeta$ [normalized with the thermal voltage $\left(\sim 25\text{mV}\right)$ ], accurate within $O\left({\zeta }^2\right)$ , shows that the polarization is dominated by the particle’s electrophoretic motion and the enhancement of the polarization due to the hydrodynamic slip is primarily attributed to the enhancement of the electrophoretic mobility from the slip. In contrast, for a thin double layer, the dipole moment is governed by ion transport inside the double layer. Asymptotical analytical models conclude that the hydrodynamic slip has more complicated influence on the polarization. At the high-frequency range where the surface conduction is important, the dipole moment is predicted to increase for any zeta potential. On the contrary, at the low-frequency range where the bulk diffusion is significant, the enhancement of the dipole moment due to the slip is lost at large zeta potentials.