Inertial migration of an electrophoretic rigid sphere in an electroosmotic-Poiseuille flow

Inertial focusing is the phenomenon of cross-stream migration of particles in the presence of finite inertia. This physics is employed to sort cells and droplets in microfluidic devices. To gain an enhanced control over this migration, recently a few experimental studies have applied an external electric field to sort particles based on their intrinsic properties such as charge density. We have analytically studied the migration of a rigid spherical particle in a two-dimensional Poiseuille flow, subjected to an externally imposed electric field. The particle and wall both have a uniform zeta potential and are assumed to have a thin electrical double layer. The electrostatic potential and velocity disturbances are evaluated by using the method of reflections. A semi-analytical expression for the lift force as a function of particle size (κ), zeta potential (ζ_p) and an electric Reynolds number (Re_E) is obtained. To obtain an insight on this migration, we find the magnitude of the constituents of the lift force and draw a comparison with the buoyancy induced Saffman-lift. It is found that the leading-order modification (~O(κ Re_E ζ_p) higher) in this lift is due to interaction of the additional ‘force-free phoretic’ disturbance with the background parabolic flow profile.