  Solid-oxide fuel cells produce electric current from energy released by a
spontaneous electrochemical reaction. The efficiency of these devices depends
crucially on the microstructure of their electrodes and, in particular, on the
three-phase boundary (TPB) length, along which the energy-producing reaction
occurs. We present a systematic maximisation of the TPB length as a function of
four readily-controllable microstructural parameters, for any given mean
hydraulic radius, which is a conventional measure of the permeability to gas
flow. We identify the maximising parameters and show that the TPB length can be
increased by a factor of over 300% compared to current common practices. We
support this result by calculating the TPB of several numerically simulated
structures. We also compare four models for a single intergranular contact in
the sintered electrode and show that the model commonly used in the literature
is oversimplified and unphysical. We then propose two alternatives.
