Electrokinetic Effects on Flow and Ion Transport in Charge-Patterned Corrugated Nanochannels

Abstract: This study explores how the distribution of surface charge along corrugated nanochannels affects flow rates and influences ionic currents and charge selectivity in a pressure gradient-driven flow. We numerically solve the coupled Poisson-Nernst-Planck-Stokes (PNPS) equations for periodic aperture profiles and explore how changes in the Debye screening length and the degree of symmetry between surface charge and geometry, and the magnitude of an applied pressure gradient affect the velocity profile. We identify three regimes of flow: I. At low (no) pressure gradients, the inhomogeneous distribution of surface charge generates a nonlinear torque that drives recirculating flow. Placing surface charge asymmetrically with respect to the geometry produces a net axial flow. II. At moderate pressure gradients, the flow rate is proportional to the mechanical driving force, though is significantly diminished relative to channels absent of surface charge inhomogeneity. Throughput is inhibited by the electrostatic force that opposes the displacement of ions from the diffuse part of the electric double layer. III. At high pressure gradients, we demonstrate a transition between electrostatically and mechanically controlled flow regimes, where -- under appropriate choice of parameters -- a marginal increase in the applied pressure gradient triggers an abrupt, orders-of-magnitude increase in the mean velocity. By incorporating the computed velocity and electric fields from the PNPS equations into a random walk particle tracking algorithm, we provide a detailed quantitative characterization of the transport dynamics of the ions, demonstrating the ability to selectively control the flux of charge and moderate the rate of ion dispersion.