Electrophoresis of cell membrane-coated nanoparticles: an analytical theory

The present article deals with the electrophoresis of biomimetic core-shell structured nanoparticles. Such particles featuring a cell membrane-like peripheral shell are of increasing interest for targeted drug delivery and other biomedical applications. The membrane is taken as a two-dimensionally oriented viscous liquid with a low dielectric permittivity relative to the surrounding aqueous medium. These membranes further often harbor mobile charges -arising from free lipid molecules or ionic surfactants- that impart a surface charge density to the outer surface of the nanoparticle. The current model systematically incorporates collective ion partitioning effects arising from dielectric permittivity gradients, steric hindrance, and Donnan electrostatic equilibrium. Moreover, the theoretical formulation is here refined to account for the nanoparticle's curvature, which significantly modulates the electric double layer (EDL) structure compared to planar interfacial models. In this work, we derive an original analytical expression for the electrophoretic mobility of such a generic composite particle type within the Debye-Hückel approximation under weak field strength conditions. In addition, we demonstrate that the electrophoretic mobility of a liquid droplet containing internal mobile ions can be viewed as a limiting case of our generalized formulation. This limit further successfully recovers established results for droplets devoid of internal ions, as reported in several seminal studies. Finally, we illustrate the sensitivity of the electrophoretic mobility to various relevant electrohydrodynamic descriptors of the nanoparticles. This analytical framework provides a foundation for developing advanced models to optimize nanoparticle transport in biological environments.