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Microfluidic designs require the effort to understand the flow pattern depending on the channel geometry. An in-depth analysis based on the theoretical model is presented for the pressure-driven electrokinetic microflows in curved rectangular channels by applying the finite volume scheme with a SIMPLE ͑semi-implicit method for pressure-linked equations͒ algorithm. The external body force originated from between the nonlinear Poisson-Boltzmann field around the channel wall and the flow-induced electric field is employed in the Navier-Stokes equation, and the Nernst-Planck equation is taken into further consideration. Unknown pressure terms of the momentum equation are solved by using the continuity equation as the pressure-velocity coupling achieves convergence. Attention is focused on the geometry effect on the fluid velocity profile at the turn of charged rectangular channels with ranging complementary channel aspect ratios ͑i.e., H / W = 0.2-5.0͒. Simulation results exhibit that the streamwise axial velocity at the turn skews the profile to the inner region of the microchannel. This is due to the stronger effect of spanwise pressure gradient arising from a sufficiently low Dean number. The skewed pattern in the velocity profile becomes greater with decreasing channel aspect ratio as well as degree of the channel curvature. Quantitative predictions for the decreasing velocity due to the electrokinetic interaction were also provided in both cases of shallow and deep microchannels. FIG. 11. ͑Color online͒ The axial velocity profiles at different positions of channel height with H / W of ͑a͒ 0.2 ͑shallow channel͒ and ͑b͒ 5.0 ͑deep channel͒, where solid, dashed, and dotted curves are obtained by different electrokinetic conditions of ⌿ s = 1 and −1 = 9.7 nm, ⌿ s = 2 and −1 = 965 nm, and ⌿ s = 4 and −1 = 965 nm, respectively. 052004-9The geometry effect on steady electrokinetic flows Phys. Fluids 22, 052004 ͑2010͒

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In our recent Brownian dynamics (BD) simulation study, the structure and dynamics of anionic polyelectrolyte xanthan in bulk solution as well as confined spaces of slitlike channel were examined by applying a coarse-grained model with nonlinear bead-spring discretization of a whole chain [J. Jeon and M.-S. Chun, J. Chem. Phys. 126, 154904 (2007)]. This model goes beyond other simulations as they did not consider both long-range electrostatic and hydrodynamic interactions between pairs of beads. Simulation parameters are obtained from the viscometric method of rheology data on the native and sonicated xanthan polysaccharides, which have a contour length less than 1 microm . The size of the semiflexible polyelectrolyte can be well described by the wormlike chain model once the electrostatic effects are taken into account by the persistence length measured at a long length scale. For experimental verifications, single molecule visualization was performed on fluorescein-labeled xanthan using an inverted fluorescence microscope, and the motion of an individual molecule was quantified. Experimental results on the conformational changes in xanthan chain in the electrolyte solution have a reasonable trend to agree with the prediction by BD simulations. In the translational diffusion induced by the Debye screening effect, the simulation prediction reveals slightly higher values compared to those of our measurements, although it agrees with the literature data. Considering the experimental restrictions, our BD simulations are verified to model the single polyelectrolyte well.