A One-Dimensional Model Capturing Selective Ion Transport Effects in Nanofluidic Devices

Abstract

This paper presents a numerical model of one-dimensional, steady-state, multi-species, ion transport along a channel of variable width and depth. It is intended for computationally efficient simulation of devices with large variations in characteristic length scale—for example those incorporating both micro- and nanochannels. The model represents both volume charge in the fluid and surface charge on the channel walls as equivalent linear charge densities. The relative importance of the surface terms is captured by a so-called “overlap parameter” that accounts for electric double-layer effects, such as selective ion transport. Scale transitions are implemented using position-dependent area and perimeter functions. The model is validated against experimental results previously reported in the literature. In particular, model predictions are compared to measurements of fluorescent tracer species in nanochannels, of nanochannel conductivity, and of the relative enhancement and depletion of negatively and positively charged tracer species in a device combining micro- and nanochannels. Surface charge density is a critical model parameter, but in practice it is often poorly known. Therefore it is also shown how the model may be used to estimate surface charge density based on measurements. In two of the three experiments studied the externally applied voltage is low, and excellent results are achieved with electroosmotic terms neglected. In the remaining case a large external potential (∼ 1 kV) is applied, necessitating an additional adjustable parameter to capture convective transport. With this addition, model performance is excellent.