Electrohydrodynamic Forces on a Rigid Core Cylindrical Soft-Particle Close to an Inhomogeneously Charged Flat Electrode

Particles moving close to a planar wall undergo a considerable decrease in velocity, because of the viscous forces of the underlying fluid. The previous studies on electrophoretic migration very close to charged walls indicate an increase in the electrophoretic velocity as the particle approaches the wall, because of an increase in the electric field in the narrow lubrication region. However, analysis of the electrohydrodynamic forces acting on a particle in the vicinity of a planar wall/electrode has been conducted only for the case of a rigid particle. Soft particles or fuzzy particles that appear in biological systems consist of a polymer layer covering a rigid colloid, and the polymer layer upon compression leads to steric repulsion forces, due to its brushlike structure. In this study, the electrohydrodynamic forces acting on a soft particle deposited in the vicinity of an nonhomogeneously charged electrode with nonhomogeneous slip is considered. The fluid flow within the polymer layer of the soft particle follows a modified Brinkman equation that intrinsically depends on the polymer brush structure. The fluid flow within the thin lubrication region, which consists of the ordered porous layer and is bounded below the electrode wall, is modeled by the lubrication approximation. An added assumption of the large porosity of the polymer brush structure helps in arriving at an analytical approximation. The lubrication flow in the confinement and the electric field generated from the constant current emitting electrode leads to the development of nonzero forces and torques. The forces and the torques depend on the separation distance, the jump in the slip conditions, the nonhomogenous flow rates, and the porosity of the brush structure. The greater the compression of the polymer layer, the steric force, which is purely dependent on the compression, is found to increase, and along with it, the electrohydrodynamic lift forces are also found to increase. In cases of extreme compression, when D → 0, the magnitude of the forces goes to ∞, due to the singular nature of the forces. The analysis shows that forces and torques acting on a bare colloid and a soft colloid are dissimilar, which can be harnessed in the separation process of colloids with dissimilar structures.