Abstract:
Electrophoresis in complex (non-Newtonian) fluidic media is becoming increasingly prominent owing to its applications in a wide variety of separation processes. Although most particles that undergo electrophoresis carry nonuniform surface charge, their motion in complex fluidic media has been addressed only recently, while many other separation processes also use externally imposed flows. Despite this, the impact of external flows on the electrophoretic motion of such particles in non-Newtonian fluids still remains largely unexplored. To address this, here we develop a semianalytical framework using a combination of matched asymptotic expansion and regular perturbation to examine the trajectories of nonuniformly charged particles suspended in a viscoelastic medium, subject to imposed shear flow and electric field. We assume the particle's surface charge to be weak but otherwise arbitrary, the electrical double layer to be thin, the suspending medium to obey the Oldroyd-B constitutive relation, and the overall flow to be weakly viscoelastic. Our results reveal that in the presence of imposed flows, any particle carrying a nonuniform surface charge will likely undergo cross-stream migration when the suspending medium is viscoelastic. It is shown that the very nature of a particle's trajectory and the extent of its migration will strongly depend on whether the imposed flow or the electrophoretic propulsion dominates particle motion. This is further supported by a reduced order model derived for Newtonian fluids, using which particles' velocities and their trajectories may be deduced without a detailed knowledge of the flow field. We demonstrate that in the limit of weak viscoelasticity, the general conclusions from this reduced order model may indeed be extended beyond the realm of Newtonian fluids. Our framework may be useful towards improving particle separation relevant to many biochemical applications.