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Taking account of the effect of double-layer polarization, we modeled the sedimentation of a pH-regulated nanoparticle in a generalized field. The influences of the radius and the density of the functional groups of the particle, the pH, and the bulk salt concentration of the liquid phase and the Reynolds number Reon the sedimentation behavior of the particle are examined in detail. We found that as Reincreases, because more counterions are dragged away from the particle surface, its averaged charge density decreases accordingly. The smaller the particle, the thicker the double layer so that double-layer polarization is more significant and the distribution of the surface charge density is more nonuniform. Interestingly, the smaller the particle, the higher the averaged surface charge density, but the smaller the electric force acting on it. If the particle is sufficiently large (300 nm in radius), its averaged surface charge density is insensitive to Reas it varies from 0.0025 to 0.04 but can have an appreciable difference (ca. 10%) if it is small (75 nm).

Inspired by biological ion channels, many artificial nanopores are fabricated for regulating ion transport based on functionality of discriminating ion types. It is expected that the transport of ions in these nanopores is influenced by their physicochemical nature such as their geometry and the conditions of the liquid phase such as the salt concentration. Taking account of possible presence of electroosmotic flow, these influences are investigated comprehensively in this work. Three types of salt are considered: KCl, NaCl, and LiCl. Several interesting behaviors are observed, and the associated mechanisms are discussed in detail. For example, if the bulk salt concentration is low and the cone angle is sufficiently small, then the rectification ratio of the salts examined ranks as LiCl > NaCl > KCl. However, this trend could be reversed at a larger applied voltage bias if the bulk salt concentration is sufficiently high or the cone angle is sufficiently large. This can be attributed to the fact that the degree of ion enrichment arising from the applied voltage bias is quite different for the types of salt examined. In addition, the behavior of ion selectivity as the applied voltage bias varies depends largely on the level of bulk salt concentration. In particular, if the bulk salt concentration is sufficiently low, then the selectivity decreases monotonically with increasing applied voltage bias, and if it is sufficiently high and the cone angle is sufficiently large, then the selectivity shows both a local minimum and a local maximum.