Optimizing diffusion-limited transport, with applications to electrochemical systems

Manu Mannattil; L. Mahadevan

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arXiv · 2609.00849

Optimizing diffusion-limited transport, with applications to electrochemical systems

Manu Mannattil·L. Mahadevan

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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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Manu Mannattil, L. Mahadevan. 2026-09-01. Optimizing diffusion-limited transport, with applications to electrochemical systems. https://arxiv.org/abs/2609.00849

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