The influence of net fluid flow on the low-frequency ac response of a microchannel-nanochannel interface under dc bias is studied theoretically using a simple 1D model based on the Poisson-Nernst-Planck-Stokes equations. The model describes cross-sectional averaged transport wherein the electro-osmotic flow is controlled by the magnitude of the dc bias and captures essential features of the problem related to the micro-nano interface, specifically geometric focusing effects and nanochannel control of the net fluid flow. This model predicts behavior which differs from that predicted by a purely electrodiffusive formulation. The high-frequency edge of the Warburg branch of the complex impedance plot has a slope which deviates from the π/4 Warburg value, decreasing with increasing bias, and there are corresponding changes in the overall phase as seen in the Bode plots. This can be attributed to a streaming contribution to the capacitive reactance of the device as well an increase in the conductance of the depleted region, both due to net fluid flow. The increase in conductance, corresponding to reduced interfacial depletion, also permits dc currents above the classical electrodiffusive limit.
|Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
|Published - 15 Nov 2012