Induced-charge electrokinetics at large voltages

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. 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. Thesis Supervisor: Martin Z. Bazant Title: Professor of Applied Mathematics Acknowledgements. I would like to take this opportunity to thank and modestly reciprocate all those who have supported me throughout my academic studies at MIT during the last five years. First, I must thank all the members of my thesis committee, Martin Z. Bazant, John Bush, Steven G. Johnson and Todd Thorsen for their participation, although I cannot thank Martin enough many times. Having Martin as my thesis advisor was the best thing that happened to me in a long time. This thesis would definitely not be completed without his efforts. Before I started working with him, I had been searching for an interesting and appropriate Ph.D. problem for the first two years at MIT. When I met him, he introduced me with not only many interesting problems but also ideas about how to solve them. I have always had a selection of projects to choose from. He has always been very generous about sharing his insights with me. He also taught me how to always be upbeat about my work, even when the problems seemed too hard or we just found out an old article solving that problem we have been working on for months. He is a source of positive energy and inspiration, who has changed my attitude towards life forever. Furthermore, Martin has been very supportive in every aspect of my life: be it academics or not. He has written reference letters for me in job search. He also let me intern during my summer and winter breaks. His contributions to my person extend well beyond this thesis research. I was also lucky to have Armand Ajdari as a visiting professor at MIT in the academic year 2005-06. I, Martin and him had many fruitful discussions from which a lot of ideas in this thesis came to existence. Armand was the first to suggest studying of the "modified PNP" equations, as well as the composite diffuse layer model among many other things. Having him in the department that year literally more than doubled our productivity, and made possible the completion of the work in chapters 4 and 5. Armand continued to give us feedback to us even after he became the director of R&D in Saint-Gobain. Needless to say, I am deeply indepted to Armand. I would like to thank Brian D. Storey, who has contributed a lot to our research, including to the numerical simulation of the ACEO pumps. He was actually the first one to discover the high-frequency flow reversal, one of the most elegant of our results. He has traveled from Olin College to MIT many times to join our group meetings. I have had a great fortnight in Sevilla, Spain during March 2008, thanks to Antonio Ramos. Besides showing hospitality, and generously buying dinner for us, he has suggested combining our models with specific adsorption and matching to real experimental data. During my stay, he took a lot of his precious time advising me every single day. Also, if it was not for him, we would have missed a number of crucial references. I must also thank Laurits Olesen for sharing his Comsol codes with me and writing a beautiful thesis on the simulation of ACEO pumps, which, by the way, is a great reference on the subject. I have learned how to impose periodic boundary conditions in Comsol from him as well. Also, his time-periodic solver has been useful in speeding up the 3-D ACEO pump calculations in chapter 6. I would like to also thank Ramkumar Krishnan, my advisor at Motorola during the summer internships in 2006 and 2007, for providing the opportunity to work on the modeling of the fuel cells. I have learned a lot from him, and I feel it is necessary to mention his name although most of that work did not end up in my thesis. I will also extend my thanks to Thomas Lane, at the MathWorks, who helped me improve my knowledge of Matlab and its statistics toolbox. Finally. I will acknnwlPdloP nmor TFi LVch; t-;n ,t fl+r If ';Al.1+ , -;+1 ~ I /±,i1, I