Mixing in a rotating soft microchannel under electrical double layer effect: A variational calculus approach

In this work, we investigate the mixing dynamics of fluid streams in the rotating narrow-fluidic channel having grafted polyelectrolyte layer on its inner wall surfaces. We invoke the variational calculus approach for solving the coupled nonlinear system of transport equations, which is integrated with the non-homogeneous boundary conditions pertinent to this analysis. We obtain the velocity distribution in the asymptotic limit of geostrophic plug flow and then demonstrate the mixing dynamics from the perspective of qualitative assessment as well as quantitative evaluation. Performing the Poincare map analysis, we predict the mixing of fluid streams from the qualitative assessment, while for the quantification of underlying mixing, we focus on the entropy of mixing analysis. We show that the grafted polyelectrolyte layer at the channel walls modulates the electrical double layer phenomenon following the involved electrostatics. This phenomenon in the presence of an external electric field strengthens the electroosmotic pumping in the fluidic channel non-trivially. Results show that the effects stemming from a larger thickness of the grafted polyelectrolyte layer, that is, the stronger electroosmotic pumping together with a relatively larger magnitude of friction drag, modulate the rotational force-driven primary as well as the secondary flows in the channel. The correlative-cooperative effects of the grafted polyelectrolyte layer on the rotational electrohydrodynamics lead to the formation of the dumbbell-shaped vortex and results in an enhancement in the underlying mixing.