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Below is a summary of my current research in chemical engineering and applied mathematics.

For more details on some of these topics and others, see
my
Prior Research (July 2008
Snapshot) taken from my former MIT math website.

- Fundamental theory of nonlinear "induced-charge" electrokinetics at large applied voltages in concentrated solutions.
- Design and fabrication of AC electro-osmotic micropumps
- Electrokinetic manipulation of polarizable colloids in microfluidic devices

For more information, see Nonlinear Electrokinetics @ MIT

Supported by the National Science Foundation under contract DMS-0707641.

The standard approach to modeling Li-ion batteries, based on porous electrode theory, assumes Butler-Volmer reaction kinetics, isotropic diffusion of intercalated ions, and an open circuit voltage (OCV) vs. composition fitted to experiments. In spite of many successes, it is not clear how to apply this approach to phase-separating materials with voltage plateaus. Certain materials of this type are promising for high power density, so a more robust model is needed for the engineering of faster charging batteries. Fundamental scientific questions about ion intercalation dynamics also remain to be answered.

We are developing a modeling framework based on statistical
thermodynamics, which coherently describes the OCV, intercalation, and
phase separation. The theory is based on the Cahn-Hilliard equation,
where the homogeneous free energy in the Cahn-Hilliard equation is
related to the OCV, and a new boundary condition is proposed for
intercalation kinetics, which depends on the full chemical potential,
including the gradient term. For phase-separating materials, such as
LiFePO_{4} the model predicts various
features of recent experiments: (i) the phase boundary aligns with the
crystal axis of greatest lattice-mismatch strain; (ii) intercalation
proceeds as a nonlinear wave along the crystal surface, filling it
layer by layer; (iii) a composite electrode in the miscibility gap
undergoes a ``mosaic instability'' , where reservoir crystals
spontaneously phase separate and fill with ions, one by one; and (iv)
``ultrafast'' battery charging can be
attained with surface coatings that distribute ions across each active
crystal facet.

Spotlight on graduate student, Todd Ferguson

Supported by the National Science Foundation under contracts DMS-6920068 and DMS-0842504 and by the MIT Energy Initiative.

We are developing new electrochemical approaches to desalination, based on theory, simulations, and experiments.

- Fundamental theory of diffuse-charge dynamics
- "Desalination shocks" (propagating sharp salt concentration gradients) in microchannels, microfluidic electrodialysis
- Capacitive desalination by porous electrodes

- Diffuse charge in thin films and membranes
- General theory of electrochemical reaction rates in non-ideal solutions

- Tensorial hydrodynamic slip and transverse flows for superhydrophobic surfaces
- Electrokinetics of high-slip, polarizable surfaces

- Statistical theory of failure of structures
- Dielectric breakdown of ultrathin films
- Capacity fade and lifetime of rechargeable batteries

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