Identify the time-dependent or interface-coupled mobility governing the nickel enrichment zone

Identify a mobility function of unknown form that can reproduce the approximately constant nickel-enrichment-zone width observed between 72 and 480 hours, while remaining physically consistent with transport at the receding metal/barrier-layer interface.

Background

The measured nickel-enrichment-zone widths remain approximately flat across a factor of 6.7 in exposure time, whereas the tested constant-mobility transport model predicts monotonic growth. Two proposed one-parameter extensions—a defect-flux-coupled mobility and a finite-capacity interfacial-trapping closure—failed the synthetic identifiability gate or did not produce a satisfactory quantitative improvement.

The paper therefore concludes that the unresolved modeling target is not another constant mobility value but a time-dependent or interface-coupled mobility law. Such a closure must explain the observed zone-shape behavior and be constrained by denser exposure-time data and the transport equations.

References

A third is sharper: the nickel zone rejects every constant-mobility description these data can test, so the quantity actually wanted is a mobility function of unknown form, which a neural representation can carry as an unknown closure constrained by the transport equation while a classical solver must first commit to a parametric guess.

— Sparse data limit what a mechanistic corrosion model can predict  (2609.11869 - Feugmo, 10 Sep 2026) in Section 4, Discussion, final paragraph on the inversion framework