(Ion Power Poster Award Winner) Analytical Model for the Interdigitated Flow Field
The flux of a species through the IDFF channel can be described by the Nernst-Planck equation in porous media, which is a conformally invariant mathematical function5. Thus, it is possible to achieve an analytical expression for reactant flux and / or streamlines through the IDFF via the method of conformal mapping5. Through this strategy, the combined migration-diffusion-advection problem can first be solved in a straight channel, and then the straight-channel solution is mapped (Figure 1) to the more complicated IDFF geometry by exploiting the Schwarz-Christoffel transformation5. The original numerical 2-D model by Kazim et al. is solved in this work, analytically2; Figure 2 shows a representative velocity magnitude profile for an IDFF electrode cross section. Due to unwieldy equations which arise from the analytical construction, dimensionless numbers are developed to provide an intuitive understanding of transport relationships in the IDFF, and limiting cases of electrode thickness are considered. Ultimately a convenient framework for IDFF design rules is developed by analytically solving the transport equations, allowing for greater insight to system design.
We would like to acknowledge the financial support of the Joint Center for Energy Storage Research and the United States National Science Foundation Graduate Research Fellowship program.
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