{"paper":{"title":"Scaling and Analytical Approximation of Porous Electrode Theory for Reaction-limited Batteries","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"A lean model governed by four dimensionless numbers simplifies porous electrode theory for reaction-limited batteries.","cross_cats":["cs.SY"],"primary_cat":"eess.SY","authors_text":"Martin Z. Bazant, Shakul Pathak","submitted_at":"2026-04-17T18:28:17Z","abstract_excerpt":"Porous electrode theory (PET) provides essential insights into electrochemical states, but its computational complexity hinders real-time control and obscures scaling relations. To bridge the gap between high-fidelity simulations and reduced-order models, we present a framework of scaling analysis and analytical approximations. By assuming high-performance electrodes minimize transport limitations and overpotentials, we derive a simplified \"lean model\" governed by four dimensionless numbers: (i) a traditional Damk\\\"ohler number, $Da$, scaling the characteristic reaction rate to the diffusion r"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"By assuming high-performance electrodes minimize transport limitations and overpotentials, we derive a simplified 'lean model' governed by four dimensionless numbers... For batteries, we derive analytical solutions for standard protocols... our formulae show excellent agreement at negligible computational cost.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The assumption that high-performance electrodes minimize transport limitations and overpotentials, which is invoked to justify collapsing the full porous electrode theory into the lean model (stated in the abstract).","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Scaling analysis produces a lean porous electrode model with four Damkohler numbers (Da, Da_p, Da_w, Da_c) and closed-form solutions for battery protocols that match full simulations.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A lean model governed by four dimensionless numbers simplifies porous electrode theory for reaction-limited batteries.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"8c920002715590aeae11677f12b4c6c2de8caafcd9b18e4d8ec7a657e49afec6"},"source":{"id":"2604.16627","kind":"arxiv","version":2},"verdict":{"id":"b9b78683-b65e-41f2-b9b8-7f423c056462","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-10T07:20:25.554597Z","strongest_claim":"By assuming high-performance electrodes minimize transport limitations and overpotentials, we derive a simplified 'lean model' governed by four dimensionless numbers... For batteries, we derive analytical solutions for standard protocols... our formulae show excellent agreement at negligible computational cost.","one_line_summary":"Scaling analysis produces a lean porous electrode model with four Damkohler numbers (Da, Da_p, Da_w, Da_c) and closed-form solutions for battery protocols that match full simulations.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The assumption that high-performance electrodes minimize transport limitations and overpotentials, which is invoked to justify collapsing the full porous electrode theory into the lean model (stated in the abstract).","pith_extraction_headline":"A lean model governed by four dimensionless numbers simplifies porous electrode theory for reaction-limited batteries."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.16627/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}