Electrokinetic secondary-flow behavior in a curved microchannel under dissimilar surface conditions

Abstract

The curved channel appears to be indispensable for the lab-on-chips systems because it provides a convenient scheme for increasing the channel length per unit chip area in the direction of net flow. A secondary Dean flow in curved rectangular microchannels is examined by applying the finite-volume scheme with a semi-implicit method for pressure-linked equations (SIMPLE) algorithm for the pressure-driven electrokinetic transport. This framework is based on the theoretical model coupled with the full Poisson-Boltzmann, Navier-Stokes, and the Nernst-Planck principles of net charge conservation [Yun et al., Phys. Fluids 22, 052004 (2010)]. The effect of a dissimilar wall condition on the secondary flow at the turn is explored by considering different configurations of channel wall having complementary aspect ratios (i.e., ratio of the channel height to the channel width, H/W = 0.25 and 4.0) with combinations of hydrophilic glass and hydrophobic polydimethylsiloxane surfaces. Simulation results exhibit that, contrary to the case of general narrow-bore channels, the streamwise axial velocity tends to shift toward the inner wall caused by a stronger effect of the spanwise pressure gradient, according to a sufficiently low Dean number. The increasing rate of this shift with increasing curvature ratio is more significant in the shallow (or low-aspect-ratio) channel, due to the effect of greater distance traveled by the fluid along the outer wall. The curvature introduces the presence of pairs of counter-rotating vortices perpendicular to the flow direction. Comparing between shallow and deep (or high-aspect-ratio) channels allows us to identify that the patterns of axial velocity and vorticity are altered by the heterogeneity effect of surfaces occupying a large area. The total magnitude of vorticity at the cross section of the channel increases with increasing slip length, due to the contribution of enhanced axial velocity driven by the slip, while there is no fluid-slip dependency for the slip length of less than about 50 nm.