Induced-charge electrokinetics at large voltages

Abstract

The classical transport theory cannot explain the experimental behavior of electrochemical systems in the extreme operating conditions required by modern microfluidics devices. Some experimental puzzles include strange behavior of colloidal particles, high-frequency flow reversal in microfluidic ACEO pumps, and concentration dependence of electrokinetic slip. Theoretical developments would help not only in exploiting poorly understood effects favorably, but also in building more efficient microfluidics devices. The goal of this thesis is to explore possible mechanisms and modifications of the current theory that would enable us to interpret the experimental data. The following is a brief summary of the contributions of this thesis to the subject: Colloidal Particles. A new invention in colloidal science is the Janus particle, which is a two-faced spherical particle where one face is polarizable, and the other non-polarizable. These particles have potential applications in drug delivery, building of nanowires and solar energy. Experiments show that Janus particles strongly interact with boundaries: they approach walls, swim along walls, or sometimes jump away from walls. We show, by conducting numerical simulations of this truly 3D problem, that at least some of those observations can be explained within the classical linear theory. Finite Size Effects in Electrolytes. The classical Poisson-Boltzmann (PB) theory of electrolytes assumes a dilute solution of point charges with mean-field electrostatic forces. Even for very dilute solutions, however, it predicts absurdly large ion concentrations (exceeding close packing) for surface potentials of only a few tenths of a volt, which are often exceeded, e.g., in microfluidic pumps and electrochemical sensors. Since the 1950s, there have been numerous attempts in the literature to incorporate steric effects into the standard models.

(cont.) Most of those theories are complex, and require non-trivial numerical methods even for a simple problem. For this reason, they have not found applications in other contexts such as electrokinetics. In contrast, we focus on qualitative finite size effects, and incorporate only the essential elements of ion-crowding, using a lattice-gas model based statistical mechanical approach. Nonetheless, we are able to reach many conclusions about how steric effects play a role in electrochemical systems at large applied voltages. While dilute solution theory predicts that the differential double layer capacitance is exponentially increasing, steric effects predict that it varies non-monotonically: the differential capacitance always decays to zero after an initial increase. In addition, the net salt adsorption by the double layers in response to the applied voltage is greatly reduced, and so is the tangential "surface conduction" in the diffuse layer, to the point that it can often be neglected, compared to bulk conduction. This explains why, contrary to PB theory, limiting current is rarely attained in experiments. It has been shown that an asymmetric array of electrodes can be used to pump fluids in micro devices. These pumps operate only with AC voltage. Experiments have demonstrated that, when the AC frequency is high enough, the fluid flow supplied by such pumps reverses. This reversal, while not predicted by any of the standard theories, can be explained using our steric theory. We also generalize our steric models to the time-dependent case, deriving the first modified Poisson-Nernst-Planck (MPNP) equations, which incorporate finite size effects into the PNP equations. The modified equations should be used instead of PNP when the thin double layer approximation fails and the ion concentrations are high enough to make steric effects important.