Abstract
The transport of ions in bulk electrolytes is governed by diffusion and convection, but the proximity of a charged surface introduces interfacial effects notably
electro-osmotic flow and surface conduction. In this paper, we describe a class of nonlinear electrokinetic phenomena that results from the competition between
bulk and interfacial transport in microstructures. First we consider the fundamental problem of steady state current through a dead-end microchannel with an ion perm-selective surface (membrane or electrode) at the end4 . The presence of charged side walls provides two new mechanisms for over-limiting current
(exceeding diffusion limitation) in addition to bulk electro-osmotic instability on the membrane, which dominates in thick channels. For very thin channels (<
1micron in water), over-limiting current is carried by surface conduction in the depleted region, and we provide simple analytical approximations for the ion profile and current-voltage relation. For intermediate channel thicknesses (1-20 microns), fast electro-osmotic flows on the sidewalls bring ions to the membrane via a pair of fast vortices, and we derive scaling relations and present
numerical solutions for this regime. Next, we consider dynamics at constant current. Mani, Zangle and Santiago1,2 recently showed that sharp concentration gradients can propagate away from a microchannel/nanochannel junction, analogous to shock waves in gases. Here, we elucidate the basic physics of
such ``desalination shocks" and develop a theory of shock existence, stability, and propagation in complex microstructures3 . The crucial dimensionless parameter in
our theory is the ratio of volume averaged surface charge to bulk counter-charge, which controls the importance of surface conduction. Via similarity solutions and
asymptotic analysis, we predict that desalination shocks accelerate and sharpen in narrowing channels and decelerate and weaken -- or even disappear -- in widening channels. Using volume-averaged transport equations for slowly varying microstructures, we predict that stable desalination shocks can also propagate in porous media. Experiment are underway in our group at MIT to test and apply these theoretical predictions.
electro-osmotic flow and surface conduction. In this paper, we describe a class of nonlinear electrokinetic phenomena that results from the competition between
bulk and interfacial transport in microstructures. First we consider the fundamental problem of steady state current through a dead-end microchannel with an ion perm-selective surface (membrane or electrode) at the end4 . The presence of charged side walls provides two new mechanisms for over-limiting current
(exceeding diffusion limitation) in addition to bulk electro-osmotic instability on the membrane, which dominates in thick channels. For very thin channels (<
1micron in water), over-limiting current is carried by surface conduction in the depleted region, and we provide simple analytical approximations for the ion profile and current-voltage relation. For intermediate channel thicknesses (1-20 microns), fast electro-osmotic flows on the sidewalls bring ions to the membrane via a pair of fast vortices, and we derive scaling relations and present
numerical solutions for this regime. Next, we consider dynamics at constant current. Mani, Zangle and Santiago1,2 recently showed that sharp concentration gradients can propagate away from a microchannel/nanochannel junction, analogous to shock waves in gases. Here, we elucidate the basic physics of
such ``desalination shocks" and develop a theory of shock existence, stability, and propagation in complex microstructures3 . The crucial dimensionless parameter in
our theory is the ratio of volume averaged surface charge to bulk counter-charge, which controls the importance of surface conduction. Via similarity solutions and
asymptotic analysis, we predict that desalination shocks accelerate and sharpen in narrowing channels and decelerate and weaken -- or even disappear -- in widening channels. Using volume-averaged transport equations for slowly varying microstructures, we predict that stable desalination shocks can also propagate in porous media. Experiment are underway in our group at MIT to test and apply these theoretical predictions.
| Original language | English GB |
|---|---|
| Title of host publication | ECS Meeting Abstracts |
| Pages | 1640 |
| Number of pages | 1 |
| State | Published - 2011 |