Electrohydrodynamic\nForces on a Rigid Core Cylindrical\nSoft-Particle Close to an Inhomogeneously Charged Flat Electrode

Particles moving close to a planar wall undergo a considerable\ndecrease in velocity, because of the viscous forces of the underlying\nfluid. The previous studies on electrophoretic migration very close\nto charged walls indicate an increase in the electrophoretic velocity\nas the particle approaches the wall, because of an increase in the\nelectric field in the narrow lubrication region. However, analysis\nof the electrohydrodynamic forces acting on a particle in the vicinity\nof a planar wall/electrode has been conducted only for the case of\na rigid particle. Soft particles or fuzzy particles that appear in\nbiological systems consist of a polymer layer covering a rigid colloid,\nand the polymer layer upon compression leads to steric repulsion forces,\ndue to its brushlike structure. In this study, the electrohydrodynamic\nforces acting on a soft particle deposited in the vicinity of an nonhomogeneously\ncharged electrode with nonhomogeneous slip is considered. The fluid\nflow within the polymer layer of the soft particle follows a modified\nBrinkman equation that intrinsically depends on the polymer brush\nstructure. The fluid flow within the thin lubrication region, which\nconsists of the ordered porous layer and is bounded below the electrode\nwall, is modeled by the lubrication approximation. An added assumption\nof the large porosity of the polymer brush structure helps in arriving\nat an analytical approximation. The lubrication flow in the confinement\nand the electric field generated from the constant current emitting\nelectrode leads to the development of nonzero forces and torques.\nThe forces and the torques depend on the separation distance, the\njump in the slip conditions, the nonhomogenous flow rates, and the\nporosity of the brush structure. The greater the compression of the\npolymer layer, the steric force, which is purely dependent on the\ncompression, is found to increase, and along with it, the electrohydrodynamic\nlift forces are also found to increase. In cases of extreme compression,\nwhen <i>D</i> → 0, the magnitude of the forces goes\nto ∞, due to the singular nature of the forces. The analysis\nshows that forces and torques acting on a bare colloid and a soft\ncolloid are dissimilar, which can be harnessed in the separation process\nof colloids with dissimilar structures.