Nanocapillary Membrane Devices: A Study in Electrokinetic Transport Phenomena

There is considerable interest in developing micro-total analysis systems, also known as lab-on-a-chip devices, for applications in chemical and biological analysis. These devices often employ electrokinetic transport phenomena to move, mix, concentrate and separate dissolved species. The details of these phenomena in micro- and nanometer scale geometries are not fully understood; consequently, the basic principles of device operation are often unclear. For example, nanocapillary membranes (NCM) and other nanometer-sized passages can exhibit charge-selectivity and rectification effects similar to those observed in biological membranes. This dissertation addresses several issues related to ion transport in these membranes. Leading-order 1D steady-state models for diffusion-layer modulated transport through non-ideal membranes are used to study ionic rectification in geometrically asymmetric devices. These models provide qualitative explanations of the operation of a variety of fluidic rectifiers and experimentally observed hysteresis effects. By taking the first steps in the full boundary-layer analysis of the model, it is shown that non-ideal membranes do not maintain local electro-neutrality under passage of electric current. This is in contrast to the usual assumption of membrane local electro-neutrality, but is compatible with the existence of the non-equilibrium macroscopic space charge known to appear in the flanking electrolyte and the requirement of overall charge conservation. Lastly, the problem of electrokinetic instability due to non-equilibrium electro-osmotic slip is considered for the case of an electrolyte-membrane interface inside a 2D channel