# Constriction Percolation Model for Coupled Diffusion-Reaction Corrosion of Zirconium in PWR

## TL;DR

This paper introduces a novel constriction percolation model using cellular automata to predict oxygen transport in cracked zirconium oxide layers, advancing understanding of corrosion processes in nuclear reactors.

## Contribution

The work develops a new percolation paradigm and analytical criterion for corrosion transition, extending shortest path algorithms to model complex branching pathways in dynamic media.

## Key findings

- Predicts oxygen ion arrival rates at oxide interfaces.
- Identifies percolation threshold in corrosion regimes.
- Extends percolation modeling to dynamic, branched structures.

## Abstract

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.