Optimizing diffusion-limited transport, with applications to electrochemical systems
Abstract
Transport in certain systems fails when diffusion cannot replenish or remove material from a boundary rapidly enough, causing the boundary concentration to reach a critical minimum or maximum. Motivated by experiments in electrochemical systems that demonstrate this diffusion-limited failure of charge transport, we determine dynamic current protocols that maximize charge transfer subject to a prescribed concentration constraint. The optimal protocol has a "bang-ride" structure: the maximum feasible current is used until the boundary concentration reaches its critical value, after which the current is progressively reduced to maintain that value. For semi-infinite domains, we derive the optimal currents analytically and obtain system-independent upper bounds on their improvement over constant-current operation. We also extend the framework to finite and multilayer domains and show that the same formulation applies to both charging and discharging.
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BibTeX
@misc{mannattil2026optimizing,
title = {{Optimizing diffusion-limited transport, with applications to electrochemical systems}},
author = {Manu Mannattil and L. Mahadevan},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.00849},
eprint = {2609.00849},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.00849},
}
RIS
TY - UNPB
TI - Optimizing diffusion-limited transport, with applications to electrochemical systems
AU - Manu Mannattil
AU - L. Mahadevan
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.00849
UR - https://arxiv.org/abs/2609.00849
AB - Transport in certain systems fails when diffusion cannot replenish or remove material from a boundary rapidly enough, causing the boundary concentration to reach a critical minimum or maximum. Motivated by experiments in electrochemical systems that demonstrate this diffusion-limited failure of charge transport, we determine dynamic current protocols that maximize charge transfer subject to a prescribed concentration constraint. The optimal protocol has a "bang-ride" structure: the maximum feasible current is used until the boundary concentration reaches its critical value, after which the current is progressively reduced to maintain that value. For semi-infinite domains, we derive the optimal currents analytically and obtain system-independent upper bounds on their improvement over constant-current operation. We also extend the framework to finite and multilayer domains and show that the same formulation applies to both charging and discharging.
ER -