Inertial migration of an electrophoretic rigid sphere in a two-dimensional Poiseuille flow

Abstract

There has been a recent interest in integrating external fields with inertial microfluidic devices to tune particle focusing. In this work, we analyze the inertial migration of an electrophoretic particle in a 2-D Poiseuille flow with an electric field applied parallel to the walls. For a thin electrical double layer, the particle exhibits a slip-driven electrokinetic motion along the direction of the applied electric field, which causes the particle to lead or lag the flow (depending on its surface charge). The fluid disturbance caused by this slipdriven motion is characterized by a rapidly decaying source-dipole field which alters the inertial lift on the particle. We determine this inertial lift using the reciprocal theorem.Assuming no wall effects, we derive an analytical expression for a phoretic-lift which captures the modification to the inertial lift due to electrophoresis. We also take wall effects into account at the leading order, using the method of reflections. We find that for a leading particle, the phoretic-lift acts towards the regions of high shear (i.e. walls), while the reverse is true for a lagging particle. Using an order-of-magnitude analysis, we obtain different components of the inertial force and classify them on the basis of the interactions from which they emerge. We show that the dominant contribution to the phoretic-lift originates from the interaction of source-dipole field (generated by the electrokinetic slip at the particle surface) with the stresslet field (generated due to particle's resistance to strain in the background flow). Furthermore, to contrast the slip-driven phenomenon (electrophoresis) from a force-driven phenomenon (buoyancy) in terms of their influence on the inertial migration, we also study a non-neutrally buoyant particle. We show that the gravitational effects alter the inertial lift primarily through the interaction of the background shear with the buoyancy induced stokeslet field.

Electrokinetically enhanced cross-stream particle migration in viscoelastic flows

“…This is identical to that obtained for a Newtonian fluid (Choudhary et al 2019). However, the pressure exhibits a variation in the lateral direction for SOF…”

“…(3.8a−d) Since the migration time scale is much larger than the convective time scale (a * /κU * max ), we analyse the migration in quasi-steady-state (Becker, McKinley & Stone 1996;Choudhary et al 2019). Also, we neglect inertial effects (i.e.…”

“…Since the potential distribution is not affected by the fluid rheology, the Maxwell force on the particle in a second-order fluid is identical to that in a Newtonian fluid (Yariv 2006). Following our previous analysis (Choudhary et al 2019), we use the method of reflections to determine the potential distribution in the particle-wall configuration (Brenner 1962). Since our aim is to obtain qualitative insights and analytical results, we restrict the analysis to small particles i.e.…”

“…The other disturbances (terms multiplying F 1 , G 1 , H 1 ) are further singularities in the multipole expansion which arise due to the curvature (γ ) in the background flow field. The evaluation of higher-order reflections can be found using Faxén transformation (Faxén 1922) and is identical to our previous analysis (Choudhary et al 2019); the details of evaluation are provided in the supplementary material. We shall later show (in § 3.4.4) that the higher reflections of the velocity field (i.e.…”

“…Recent studies have shown that cancer cells exhibit a highly negative charge on their surface which can be used to separate them from the bloodstream by applying external electric fields (Chen et al 2016;Le et al 2019). In our previous study (Choudhary, Renganathan & Pushpavanam 2019), we studied the effects of electric fields on the inertial migration in pressure driven flow of a Newtonian fluid. Since most biological fluids exhibit non-Newtonian behaviour, it is important to understand the influence of electrokinetics on the migration in complex fluids.…”