In this work, a non-isothermal pore network (PN) model with quasi-steady vapor transport and transient heat transfer is presented for the first time for the application of primary freeze drying. The pore-scale resolved model is physically based and allows for the investigation of correlations between spatially distributed structure and transport conditions. The studied examples were regular PN lattices with a significantly different structure, namely a spatially homogeneous PN, also denoted as monomodal PN, and a PN with significant structure variation, referred to as bimodal PN because of its bimodal pore size distribution. The material properties selected for the solid skeleton in this study are equivalent to those of maltodextrin. The temperature ranges applied here were −28 °C to −18 °C in the PN and −42 °C in the surrounding environment. The environmental vapor pressure was 10 Pa. The PNs were dried with constant temperature boundary conditions, and heat was transferred at the top side by the vapor leaving the PN. It is shown how the structural peculiarities affect the local heat and mass transfer conditions and result in a significant widening of the sublimation front in the case of the bimodal PN. The possibility of spatially and temporally resolved front structures is a unique feature of the PN model and allows the study of situations that are not yet described by classical continuum approaches, namely heterogeneous frozen porous materials. As demonstrated by the thin layers studied here, the pore-scale simulations are of particular interest for such situations, such as in lyomicroscopes or collagen scaffolds, where a length-scale separation between dry and ice-saturated regions is not possible.

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.

Gas transport within biomass particles is a key factor controlling volatile release, secondary reactions, and product formation during pyrolysis. However, the influence of the anisotropic microstructure and its evolution during thermal conversion remains insufficiently understood. In this study, we combine high resolution X-ray micro-computed tomography with a pore network model (PNM) to compute the anisotropic gas permeability of beech wood at different stages of pyrolysis. Darcy permeabilities are obtained for the three major anatomical directions (radial, tangential, and longitudinal). Pore-resolved computational fluid dynamics (CFD) simulations on the same porous domains are used to derive a geometric correction factor for gas transport in the PNM. This correction brings the PNM close to the accuracy of the pore-resolved CFD simulations at significantly reduced computational cost. The PNM is then applied to quantify the contribution of the different cell types of the wood microstructure to gas transport. The results show that gas transport occurs predominantly in vessels larger than 15 μm. The estimated permeability of the extracted network of interconnected, mostly longitudinally oriented vessels is in the range 10–11 m2 to 10–10 m2 and is nearly unaffected by pyrolysis, whereas the network of fibers smaller than 15 μm yields values of 10–17 m2 to 10–14 m2. A detailed pore-scale analysis reveals that the opening and enlargement of smaller pores have a negligible effect in the longitudinal direction, where flow is dominated by the larger vessels. Perpendicular to this main transport direction, however, permeability increases substantially, as thermal decomposition enhances pore connectivity, particularly among the fibers. By linking microstructural evolution to directional transport properties, the method supports the parameterization of predictive multiscale models for biomass pyrolysis.

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