Electrophoresis of non-uniformly charged particles in viscoelastic fluids: The weak field limit

Electrophoresis of charged particles in polymeric (viscoelastic) fluids remains important in various separation processes, although their theoretical analysis is rather scarce in the literature. The ones which do investigate this topic use simplifying assumptions, especially that of thin Electrical Double Layers (EDLs) and weak surface charge on the particles, which are often assumed to be uniform in nature. In contrast, this article seeks to move beyond such conventional analytical boundaries, by probing the electrophoretic motion of a non-uniformly (but axisymmetrically) charged particle in an Oldroyd-B fluid, accounting for arbitrary EDL thickness and surface potential. The only restriction is that of a weak external electric field (the so-called “weak field limit”), which enables us to use regular perturbation expansions to deduce the particle's electrophoretic velocity. Our results reveal that the excess polymeric stresses in a viscoelastic medium tend to significantly impact the particle's velocity only when the EDL is sufficiently thin. At the same time, increasing the magnitude of the surface potential (or charge) tends to augment the impact of viscoelasticity. We find that depending on the precise distribution of the particle's surface potential, the medium's viscoelasticity may either speed up or slow down the particle, when compared to a Newtonian fluid. Overall, the inhomogeneity in the surface potential enhances the influence of viscoelasticity, and this enhancement is more pronounced for smaller particles as compared to larger ones.