  Percolation phenomena are pervasive in nature, ranging from capillary flow,
crack propagation, ionic transport, fluid permeation, etc. Modeling percolation
in highly-branched media requires the use of numerical solutions, as problems
can quickly become intractable due to the number of pathways available. This
becomes even more challenging in dynamic scenarios where the generation of
pathways can quickly become a combinatorial problem. In this work, we develop a
new constriction percolation paradigm, using cellular automata to predict the
transport of oxygen through a stochastically cracked Zr oxide layer within a
coupled diffusion-reaction framework. We simulate such branching trees by
generating a series porosity-controlled media. Additionally, we develop an
analytical criterion based on compressive yielding for bridging the transition
state in corrosion regime, where the percolation threshold has been achieved.
Our model extends Dijkstras shortest path method to constriction pathways and
predicts the arrival rate of oxygen ions at the oxide interface. This is a
critical parameter to predict oxide growth in the so-called post-transition
regime, when bulk diffusion is no longer the rate-limiting phenomenon.
