A charged dielectric particle in a viscous fluid confined by a spherical polarizable wall: Electrostatic force and the resultant dynamics

Electrostatic force on a charged dielectric particle in a viscous fluid confined by an initially uncharged spherical polarizable wall, and particle dynamics driven by this force were studied using numerical simulations. The charged particle interacts with the wall through electrostatics and low-Reynolds-number hydrodynamics. The electrostatic force is due to the Coulombic interaction between charges on the particle and induced charges on the cavity wall. The induced charges result from the dielectric polarization phenomenon when the dielectric permittivity of the fluid (ϵf) and that of the wall (ϵw) are not equal. Spherical, prolate, and oblate particles were considered, respectively, to study the effect of particle shape on the electrostatic force and particle dynamics. The ellipsoidal particle's axis of revolution is assumed to be along the particle–cavity line of centers. We varied particle–fluid and fluid–wall permittivity ratios (ϵp/ϵf and ϵf/ϵw), and calculated electrostatic forces on the particles as a function of the radial position of the particle center. It was found that ϵf/ϵw is more important than ϵp/ϵf in determining the electrostatic force on the particle; when ϵf/ϵw<1 (ϵf/ϵw>1), the force points toward (away from) the wall. Under the same permittivity ratios, radial position, particle charge, and particle volume, the electrostatic force on the prolate particle is the largest. We further analyzed particle velocities and trajectories under different particle shapes and sizes. Results suggest that permittivity ratios, particle shape, particle size, and particle charge can affect particle dynamics in the cavity. This study provides insights into the dynamics of charged particles under total confinement, and forms the basis for applications including intracellular delivery and microfluidic encapsulation technologies.