Electrophoretic motion of a non-uniformly charged particle in a viscoelastic medium in thin electrical double layer limit

The electrophoretic motion of a non-uniformly charged particle in an Oldroyd-B fluid is analysed here in the limit of thin electrical double layers. To this end, we analytically derive expressions for the modified Smoluchowski slip velocity around the particle, carrying weak but otherwise arbitrary surface charge. Our analysis reveals that the modified Smoluchowski slip around a particle differs significantly in a viscoelastic medium as compared with Newtonian fluids. The flow field thus derived is applied to two special cases of non-uniformly charged particles to obtain a closed-form expression for their electrophoretic translational and rotational velocities. We show that the particle's velocity strongly depends on its size in a viscoelastic medium, even for weakly charged surfaces, which is in stark contrast to the well-established theory for Newtonian fluids for weakly charged particles with negligible surface conduction. We further demonstrate that the presence of non-uniform surface charge enhances the influence of the medium's viscoelasticity on the particle's translational as well as angular velocity and this effect strongly depends on the nature of surface charge distribution. Such a physical paradigm, which leads to a breaking of fore-aft symmetry that is unique to complex fluids despite operating in the regime of creeping flows. Our study provides new theoretical framework for understanding electrophoresis of charged entities (such as DNA or active matter) in complex fluids, including biologically relevant fluidic media.