Impact of charged polarizable core on mobility of a soft particle embedded in a hydrogel medium

Electrophoresis of a soft particle with a charged polarizable core is analyzed theoretically. The soft particle is embedded in an uncharged hydrogel medium. The hydrodynamics in both the gel medium and the soft layer encapsulating the hard core are governed by the Darcy-Brinkman model. We have considered the numerical model based on the conservation principle of mass, momentum, and ion flux, leading to a coupled set of partial differential equations. A simplified approach under the weak field and low charge density consideration is also proposed. The subtle nonlinear effects arising due to the polarization and relaxation of the double layer and the convective transport of counterions induced by the immobile charge of soft layer are elucidated. These nonlinear effects have negligible impact when the bulk ionic concentration becomes high. The simplified model under the weak field consideration is independent of the core dielectric permittivity. However, the numerical model shows a strong dependence on core permittivity when the applied electric field is moderate. We have also addressed the ion partitioning effect when the dielectric permittivity of the soft layer is different from the gel medium. This creates a counterion saturation in the soft layer, and hence an augmentation in the electrophoresis.