Curvature-induced secondary microflow motion in steady electro-osmotic transport with hydrodynamic slippage effect

Abstract

In order to exactly understand the curvature-induced secondary flow motion, the steady electro-osmotic flow (EOF) is investigated by applying the full Poisson-Boltzmann/Navier-Stokes equations in a whole domain of the rectangular microchannel. The momentum equation is solved with the continuity equation as the pressure-velocity coupling achieves convergence by employing the advanced algorithm, and generalized Navier’s slip boundary conditions are applied at the hydrophobic curved surface. Two kinds of channels widely used for lab-on-chips are explored with the glass channel and the heterogeneous channel consisting of glass and hydrophobic polydimethylsiloxane, spanning thin to thick electric double layer (EDL) problem. According to a sufficiently low Dean number, an inward skewness in the streamwise velocity profile is observed at the turn. With increasing EDL thickness, the electrokinetic effect gets higher contribution in the velocity profile. Simulation results regarding the variations of streamwise velocity depending on the electrokinetic parameters and hydrodynamic fluid slippage are qualitatively consistent with the predictions documented in the literature. Secondary flows arise due to a mismatch of streamline velocity between fluid in the channel center and near-wall regions. Strengthened secondary flow results from increasing the EDL thickness and the contribution of fluid inertia (i.e., electric field and channel curvature), providing a scaling relation with the same slope. Comparing with and between the cases enables us to identify the optimum selection in applications of curved channel for enhanced EOF and stronger secondary motion relevant to the mixing effect.

Effects of Micromachining Processes on Electro-Osmotic Flow Mobility of Glass Surfaces

“…The relation was modified for non-wetting charged surfaces by considering the fluid slip effect [65], which was experimentally validated [66]. Surface roughness is another factor that needs to be taken into consideration.…”

Electrostatic Potential Analysis in Polyelectrolyte Brush-Grafted Microchannels Filled with Polyelectrolyte Dispersion

“…To provide an insight for realistic predictions, rigorous values of material parameters are required. In the case of bare channel without covering the brush, the value of surface potential of PDMS for various pH can be obtained from the literature [27,36,37]. The molecular weight (Mw) of PAA for PE dispersion is 45 kDa, whereas the PAA brush is considered as the Mw of 30 kDa and the Kuhn segment length b K of 0.64 nm [38][39][40].…”

“…Previous studies on PE brush-grafted nanochannel employed the Poisson-Boltzmann (PB) equation to estimate the electrostatic potential, assuming that the ion concentration within the brush layer follows the Boltzmann distribution [15][16][17][18]. This PB equation has been widely employed in the literature concerning microfluidics in microchannels [26][27][28]. However, the ion concentration within the brush layer depends on the monomer density profile, and the ion concentrations predicted by the Boltzmann distribution can approach infinity with increasing electrostatic potential or surface charge.…”