Multi-Scale Continuum Modeling of Mediated Electron Transfer in 3D Living Bio-Anodes

Bioelectrochemical systems, in which electroactive microbes transfer electrons across biological-abiotic interfaces, represent a vital technology for sustainable energy production, chemical synthesis, and environmental remediation. However, these systems are constrained by a two-dimensional design paradigm, with reactors achieving power densities 10–100-times lower than theoretical limits because conventional architectures restrict electron transfer to a single layer at the electrode surface. Here, we establish quantitative design rules that govern three-dimensional bio-electrochemical function driven by small-molecule electron transfer mediators. Through integrated theory, simulation, and engineered biofilm validation, we identify two distinct scale-dependent transport regimes: a macroscopic regime where bulk mediator availability governs active layer expansion and a microscopic regime where microbial packing geometry controls local redox cycling, both of which are fundamentally constrained by mass transport. We validate these scaling laws experimentally using agarose-encapsulated Shewanella oneidensis MR-1 and demonstrate that rational mediator loading and cellular packing can elevate current densities beyond 0.5 A m-2, exceeding two-dimensional performance ceilings. These design principles provide a generalizable blueprint for engineering high-performance biocatalytic systems and offer researchers studying natural biofilms a mechanistic framework to decode internal transport architecture.