Nicole Vorhauer-Huget

We present a pore network approach for the simulation and study of biofilm growth inside porous structures under various limiting conditions. The proposed pore-scale model allows us to resolve the interrelationship between growth and diffusive transport based on the solution of coupled ordinary differential equations. Special focus of this study is on diffusion as well as on metabolically limited conditions, which is realized with different second Damköhler numbers. Instead of relying on idealized geometries, the pore network structures are generated using the effective transport properties of thin sintered particles and fibrous felt porous layers derived from high-resolution X-ray micro-CT scans. The great differences in pore sizes and porosities of the regarded structures result in significantly different effective diffusivities. In addition to that, competitive substrate consumption and inhibition is achieved using the experiment-based kinetic model for S. oneidensis from Tang et al. (Tang et al., Biotechnol. Bioeng. 96:125–133, 2007). The primary nutrients are lactate and oxygen. Acetate is both, a by-product and a potential substrate, theoretically enabling dynamic shifts in substrate utilization. With the chosen parameters and conditions, the second Damköhler number can be varied with a significant impact on biomass distribution inside of the two selected pore networks, especially in dependence on oxygen availability in single pores. The simulation results show that biofilm growth is limited by the transport of dissolved oxygen. Interestingly, significantly more biomass per m ³ is produced in the sintered structure because of the generally higher pore utilization degree. Graphical Abstract

The efficiency of an electrolyzer is significantly influenced by mass, heat, and charge transport within its porous transport layer (PTL). The infeasibility of measuring them in-situ makes it challenging to study their influence experimentally, leading to the adoption of various modeling approaches. This study applies pore network (PN) modeling to investigate mass transport properties and capillary invasion behavior in three commercial titanium felt PTLs commonly used in proton exchange membrane water electrolyzers (PEMWEs). One PTL has a graded structure. Reconstructed PNs were derived from microcomputed X-ray tomography (µ-CT) data, allowing for a detailed analysis of pore size distributions, absolute and relative permeabilities, capillary pressure curves, and residual liquid saturations. The results from the PN approach are compared to literature correlations. The absolute permeability of all PTLs is between 1.1 × 10⁻¹⁰ m² and 1.5 × 10⁻¹⁰ m², with good agreement between PNM results and predictions from the Jackson and James model and the Tomadakis and Sotirchos model, the two latter involving the fiber diameter as a model parameter. The graded PTL, with fiber diameters varying between 25 µm and 40 µm, showed the best agreement with literature correlations. However, the capillary pressure curves exhibited significant deviations from the Leverett and Brooks–Corey equations at low and high liquid saturations, emphasizing the limitations of these correlations. In addition, residual liquid saturation varied strongly with PTL structure. The thicker PTL with a slightly narrower pore size distribution, demonstrated a lower residual liquid saturation (19%) and a more homogeneous invasion compared to the graded PTL (64%), which exhibited significant gas fingering. The results suggest that higher gas saturation could enhance gas removal, with much higher relative permeabilities, despite the greater PTL thickness. In contrast, the graded PTL achieves the highest relative liquid permeability (~70%) while maintaining a relative gas permeability of ~30%. These findings highlight the impact of microstructure on invasion and transport properties and suggest PN modeling as a powerful tool for their study.