Modeling of nanochannels in synthetic membranes

The behavior of a diluted electrolyte in a system of joint microchannel and nanochannel with charged dielectric walls under the action of external potential difference and external pressure is investigated numerically. The surface charge on the nanochannel walls prevents the ions of corresponding polarity from passing through it. Consequently, the system in question acquires ion-selective properties and can, under certain assumptions, be viewed as a fragment of an ion-selective membrane, including one synthesized by creating nanopores in a dielectric material. Such systems are used in experiments to control the movement of charged particles through concentration polarization. The objective of the work is to investigate the influence of a single pore on electrolyte flow and the possibilities to control that flow by changing the geometric and physical properties of the pore. The investigation relies on the specially developed simplified models based on cross-section-averaged Nernst-Planck, Poisson and Stokes equations that are subsequently reduced to a single nonlinear differential equation. The simplified models allow identifying the impact of different physical mechanisms of electrolyte movement: pressure-based (generated by the external mechanical action) and electroosmotic (generated by the electric field). A finite-difference method with semi-implicit time integration is used for the numerical solution of equations. It has been found that the behavior of the system qualitatively matches the behavior of a cell based on a non-ideally-selective ion-exchange membrane. In particular, the model correctly predicts the underlimiting and limiting electric current regimes, as well as vortex formation near the nanochannel inlet due to concurrency between electrolyte movement mechanisms. The proposed models can be extended to describe a channel with arbitrary geometry and an electrolyte with arbitrary number of charged species.