Prior Research (July 2008 Snapshot)

This page was taken verbatim from my former MIT math website in July 2008 and gives a summary of research in my group at MIT from roughly 2003 to 2008.


Induced-charge electro-osmosis

Image: Streaks of fluorescent tracer particles in ICEO flow around a gold post in a polymer microchannel, driven by an AC electric field. (Jeremy Levitan).

When a background electric field is applied to a polarizable object (metal or dielectric) immersed in a liquid electrolyte, its surface charge evolves in time and space to produce a nonuniform zeta potential. The resulting `induced-charge' electro-osmotic (ICEO) flow is very different from the case of normal `fixed-charge electro-osmosis' (with a fixed zeta potential). A long-range component of the flow develops, which sucks in fluid along the field axis and ejects it radially. The amplitude of such flows is generally proportional to the square of the field amplitude, and thus it is stronger than the usual linear dependence of classical electro-osmosis and persists in an AC field. Broken symmetries lead to the net pumping of fluid (for a fixed object) or "induced-charge electrophoresis" (motion of a colloidal particle) in uniform DC and AC fields. Non-uniform DC and AC applied fields also produce to electrophoretic motion, although the physical mechanism is surface-slip driven and time-dependent in a way that differs from basic dielectrophoresis.

ICEO flows have a number of special features, which make them potentially useful in applications. For example, induced-charge electrophoretic velocities are very sensitive to particle sizes and shapes, which allows for efficient colloidal manipulation and separation. We also are exploring a variety of novel designs for microfluidic pumps and mixers exploiting ICEO with AC applied fields. This includes an experimental effort to build real microfluidic devices in other labs at MIT. Our electrode-array pumps are currently the fastest available, operating at a small battery voltage. We are currently developing implantable drug infusion pumps and portable lab-on-a-chip medical diagnostic devices.

Our experiments (and others) reveal that existing theories of ICEO and related phenomena need to be modified to better explain "strongly nonlinear" behavior, when voltages larger than the thermal voltage (kT/e = 25mV) are applied across a charged nanolayer. The effects of solution chemistry (concentration, ion sizes, ion charge numbers,...) are also poorly understood. We are working on new theories to incorporate steric and viscoelectric effects in electrochemical transport and electro-osmotic flows to better explain the experiments.

For more information, see Nonlinear Electrokinetics @ MIT.

This work is supported by the Army Research Office via the MIT Institute for Soldier Nanotechnologies and by the National Science Foundation (DMS).

About this work:

Recent Papers

  1. Induced-charge electro-kinetic phenomena: Theory and microfluidic applications, M. Z. Bazant and T. M. Squires, Phys. Rev. Lett. 92, art. no. 066101 (2004). (Thompson Scientific indentified this paper as having created a Fast Moving Front.)
  2. Induced-charge electro-osmosis, T. M. Squires and M. Z. Bazant, J. Fluid. Mech. 509, 217-252 (2004).
  3. Experimental observation of induced-charge electro-osmosis around a metal wire in a microchannel, J. A. Levitan, S. Devasenathipathy, V. Studer, Y. Ben, T. Thorsen, T. M. Squires, and M. Z. Bazant, Colloids and Surfaces A 267, 122-132 (2005).
  4. Breaking symmetries in induced-charge electro-osmosis and electrophoresis, T. M. Squires and M. Z. Bazant, J. Fluid Mech. 560, 65-101 (2006).
  5. Theoretical prediction of fast 3D AC electro-osmotic pumps, M. Z. Bazant and Y. Ben, Lab on a Chip, 6, 1455-1461 (2006).
  6. Fast AC electro-osmotic pumps with non-planar electrodes, J. P. Urbanski, T. Thorsen, J. A. Levitan, and M. Z. Bazant, Applied Physics Letters 89, 143508 (2006).
  7. The effect of step height on the performance of AC electro-osmotic microfluidic pumps, J. P. Urbanski, J. A. Levitan, D. N. Burch, T. Thorsen, and M. Z. Bazant, Journal of Interface and Colloid Science 309, 332-341 (2007).
  8. Nonlinear electrokinetics at large voltages, M. Z. Bazant, M. S. Kilic, B. Storey, and A. Ajdari, preprint.
  9. Flow reversal of AC electro-osmotic pumps due to steric effects, B. Storey, L. R. Edwards, M. S. Kilic, and M. Z. Bazant.
  10. Induced-charge electrophoresis of metallo-dielectric particles, S. Gangwal, O. J. Cayre, M. Z. Bazant, and O. D. Velev, preprint.

Electrochemical dynamics

Image: Electrostatic potential and current lines for semi-infinite parallel-plate electrodes showing concentration polarization in a binary electrolyte at 90% of the limit current. (J. Choi).

We study the interplay of diffuse charge dynamics and reaction kinetics in electrochemical systems using continuum models, via asymptotic analysis and numerical simulations. Themes include limiting currents, geometrical effects, and time-dependent couplings of applied voltages to diffuse charge fluctuations and chemical reactions. Our work is motivated by applications to micro/nano-batteries (e.g. composed of thin films or nano-structured materials) and microfluidic devices, which test the limits of traditional macroscopic theories in electrochemistry. In this regard, we are working on modifications of Poisson-Boltzmann and Nernst-Planck equations.

Our current work on lithium rechargeable batteries focuses on developing transport models for charging/discharging of lithium battery materials, which can be strongly nonlinear and anisotropic, as in the case of lithium iron phosphate. We work with our CMSE collaborators doing atomistic simultions and experiments to guide the development of new models.

We are also interested in non-aqueous electrolytes, such as ionic liquids, solid thin films, and molten salts. These systems provide a testing ground for models of steric effects and correlations in highly charged and/or confined double layers.

This work is supported the NSF through Center for Materials Science and Engineering (IRG IV).

Recent Papers

  1. Diffuse-charge dynamics in electrochemical systems, M. Z. Bazant, K. Thornton, and A. Ajdari, Phys. Rev. E 70, 021506 (2004).
  2. Conformal mapping of some non-harmonic functions in transport theory, M. Z. Bazant, Proc. Roy. Soc. A. 460, 1433-1452 (2004).
  3. Current-voltage relations for electrochemical thin films,M. Z. Bazant, K. T. Chu, and B. J. Bayly, SIAM J. Appl. Math 65, 1463-1484 (2005).
  4. Electrochemical thin films at and above the classical limiting current, K. T. Chu and M. Z. Bazant, SIAM J. Appl. Math 65, 1485-1505 (2005).
  5. Nonlinear electrochemical relaxation around conductors, K. T. Chu and M. Z. Bazant, Phys. Rev. E 74, 011501 (2006).
  6. Steric effects in the dynamics of electrolytes at large applied voltages: I. Double-layer charging, M. S. Kilic, M. Z. Bazant, and A. Ajdari, Phys. Rev. E 75, 021502 (2007).
  7. Steric effects in the dynamics of electrolytes at large applied voltages: II. Modified Nernst-Planck equations, M. S. Kilic, M. Z. Bazant, and A.Ajdari, Phys. Rev. E 75, 021503 (2007).
  8. Surface conservation laws at microscopically diffuse interfaces, K. T. Chu and M. Z. Bazant, J. Colloid and Interface Science 315, 319-329 (2007).
  9. Intercalation dynamics in rechargeable battery materials: General theory and phase-transformation waves in LiFePO4, G. Singh, G. Ceder, and M. Z. Bazant, Electrochimica Acta (2008).

Granular flow

Image: Voronoi tesselation of a flowing dense sphere packing. (C. Rycroft).

In the Dry Fluids Group, we are developing new mathematical models and simulation techniques for particle dynamics in slow granular flows, e.g. during drainage from a silo, in coordination with real particle-tracking experiments. These non-equilibrium statistical models will describe flows at more coarse-grained level than molecular dynamics, but at a much finer scale that continuum models (which only describe the mean velocity). In some sense, the goal is to develop an analog of the random-walk theory of Brownian motion in gases for the very different case of granular drainage, which requires taking into account the cooperative nature of particle dynamics in dense random packings. A related goal is to develop new accelerated multiscale algorithms for simulations of realistic large-scale granular flows by combining the statistical model with occasional, brief, and localized relaxation taking into account inter-particle forces. We hope that such algorithms may also be applied to other amorphous materials, such as supercooled liquid and glasses.

We have created the MIT Dry Fluids Laboratory to do accurate particle-tracking experiments using a high-speed digital video camera and computer image processing. Our experimental data unambiguously rejects existing statisticals model of drainage, while supporting a new model we proposed (before the experiments), based on the idea that diffusing ``spots'' of free volume cause cooperative particle diffusion.

We have been doing simulations with the Spot Model to better understand its strengths and weaknesses: In our experiments, we have observed the spatial velocity-velocity correlations and mean velocity profiles predicted by the model, but the model typically leads to unphysical density fluctuations. We are also collaborating with Sandia National Lab on molecular dynamics simulations of granular flow as another source of "experimental data" for testing theoretical ideas. The simulations are performed in the Applied Mathematics Computational Laboratory.

Our current focus is to develop a general "stochastic flow rule" for classical plasticity theory to account for randomness and discreteness in amorphous materials. In this context, we view spots are localized regions of partial fluidization, where the yield criterion is locally violated, and plastic deformation occurs by random walks of spots biased along slip lines by imbalanced stresses. For granular materials, with the Mohr-Coloumb yield criterion, this seems to be the first model capable of describing a range of flows from gravity-driven silos to boundary-forced shear cells. With a different yield criterion, the same flow rule may also describe other amorphous materials.

In addition to advancing the basic science of granular materials, an equally important objective is to provide mathematical models and simulation tools for the engineering of pebble-bed nuclear reactors. We are working closely with MIT nuclear engineers on the Modular Pebble-Bed Reactor.

For more information, see the Dry Fluids Group.

This work has been supported by the Dept of Energy, NEC Corporation, and the Norbert Weiner Research Fund.

Recent Papers

  1. Diffusion and mixing in gravity-driven dense granular flows, J. Choi, A. Kudrolli, R. R. Rosales, and M. Z. Bazant, Phys. Rev. Lett. 92, 174301 (2004). (non-technical summary)
  2. Pebble flow experiments for pebble-bed reactors, A. C. Kadak and M. Z. Bazant, Proceedings of the International Meeting on High Temperature Reactor Technology, Beijing, China (2004).
  3. Velocity profile of granular flows in silos and hoppers, J. Choi, A. Kudrolli, and M. Z. Bazant, J. Phys.: Condens. Matter 17, S2533-S2548 (2005).
  4. The Spot Model for random-packing dynamics, M. Z. Bazant, Mechanics of Materials 38, 717-731 (2005).
  5. Dynamics of random packings in granular flow, C. H. Rycroft, M. Z. Bazant, J. Landry, and G. S. Grest, Physical Review E, 73, 051306 (2006).
  6. Analysis of granular flow in a pebble-bed nuclear reactor, C. H. Rycroft, G. S. Grest, M. Z. Bazant, and J. Landry, Phys. Rev. E, 74, 021306 (2006).
  7. Stochastic flow rule for granular materials, K. Kamrin and M. Z. Bazant, Phys. Rev. E 75, 041301 (2007).
  8. The Stochastic Flow Rule: A multiscale model for granular materials, K. Kamrin, C. H. Rycroft and M. Z. Bazant, Modeling and Simulation in Materials Science and Engineering 15, S449-S464 (2007).

Conformal mapping

Image: ADLA. A fractal aggregate growing by advection-diffusion in a flow (yellow streamlines). Colors show the evolving concentration field. The flow, concentration, and cluster surface are all obtained via a stochastic conformal map from the unit circle. (J. Choi)

Since the nineteenth century, conformal mapping has been used to solve Laplace's equation by exploiting the connection between harmonic and analytic functions. We exploit the fact that another special property of Laplace's equation -- its conformal invariance -- is not unique, but rather is shared by certain systems of nonlinear equations, whose solutions have nothing to do with analytic functions. This simple observation leads to some unexpected applications of conformal mapping in physics. For example, it generates a multitude of exact solutions to the Navier-Stokes equations of fluid mechanics and the Nernst-Planck equations of electrochemical transport. It also allows continuous and stochastic conformal-map dynamics for Laplacian growth (in models of viscous fingering and diffusion-limited aggregation, respectively) to be extended to a broad class of non-Laplacian growth phenomena, such as advection-diffusion- limited aggregation (DLA in a fluid flow). These models provide analytical insights into the effects of competing transport processes and the average shape of fractal clusters.

We have recently studied DLA on curved surfaces, such as stereographic projections of the plane, as well as interfacial dynamics in transport-limited dissolution, such as erosion of a solid in a fluid flow.


    General Theory
  1. Conformal mapping of some non-harmonic functions in transport theory, M. Z. Bazant, Proc. Roy. Soc. A. 460, 1433-1452 (2004).
  2. Conformal mapping methods for interfacial dynamics, M. Z. Bazant and D. Crowdy, in the Handbook of Materials Modeling, ed. by S. Yip et al., Vol. I, Art. 4.10 (Springer, 2005). (REVIEW ARTICLE)

    Continuous/Deterministic Problems
  3. Exact solutions of the Navier-Stokes equations having steady vortex structures, M. Z. Bazant and H. K. Moffatt, J. Fluid Mech. 541, 55-64 (2005).
  4. Steady advection-diffusion around finite absorbers in two-dimensional potential flows, J. Choi, D. Margetis, T. M. Squires, and M. Z. Bazant, J. Fluid Mech. 536, 155-184 (2005). SOFTWARE:
  5. Interfacial dynamics during tranport-limited dissolution, M. Z. Bazant, Phys. Rev. E 73, 060601 (2006).

    Discrete/Stochastic Problems
  6. Dynamics of conformal maps for a class of non-Laplacian growth phenomena, M. Z Bazant, J. Choi, and B. Davidovitch, Phys. Rev. Lett. 91, 045503 (2003). (non-technical summary).
  7. Transport-limited aggregation, M. Z. Bazant, J. Choi, B. Davidovitch, and D. Crowdy, Chaos 14, S6 (2004).
  8. Advection-diffusion-limited aggregation, M. Z. Bazant, J. Choi, and B. Davidovitch, Chaos 14, S7 (2004).
  9. The average shape of transport-limited aggregates, B. Davidovitch, J. Choi, and M. Z. Bazant, Phys. Rev. Lett. 95, 075504 (2005). counter image counter statistics