One-dimensional axial simulation of electric double layer overlap effects in devices combining micro- and nanochannels

Abstract

This paper presents a numerical steady-state model of ion transport in micro- and nanofluidic devices with widely varying geometric scale, such as transitions between micro- and nanochannels. Finite element or finite volume simulation of such problems is challenging, due to the number of elements needed to produce a satisfactory mesh. Here, only the lengthwise channel dimension is meshed; standard analytical approximations are used to incorporate cross-channel properties. Singularly perturbed cases are built up by continuation. The method is shown to reproduce our previously reported measurements of electric double-layer effects on conductivity, ion concentration, and ion enhancement and depletion. Comparison with 2-D simulations reported in the literature shows that effects on accuracy due to the 1-D approximation are small. The model incorporates analytical models of surface charge density taken from the literature. This enables predictive simulation with reasonable accuracy using published parameter values, or these values may be tuned based on experiment to give improved results. Use of the model for iterative design and parameter estimation is demonstrated.