Title: Optimal design of a model energy conversion device,
Abstract: Fuel cells, batteries, thermochemical and other energy conversion devices
involve the transport of a number of (electro-)chemical species through
distinct materials so that they can meet and react at specified multi-material
interfaces. Therefore, morphology or arrangement of these different materials
can be critical in the performance of an energy conversion device. In this
paper, we study a model problem motivated by a solar-driven thermochemical
conversion device that splits water into hydrogen and oxygen. We formulate the
problem as a system of coupled multi-material reaction-diffusion equations
where each species diffuses selectively through a given material and where the
reaction occurs at multi-material interfaces. We express the problem of optimal
design of the material arrangement as a saddle point problem and obtain an
effective functional which shows that regions with very fine phase mixtures of
the material arise naturally. To explore this further, we introduce a
phase-field formulation of the optimal design problem, and numerically study
selected examples.