The COVID-19 pandemic has highlighted the critical need to improve indoor air quality (IAQ) through efficient air filtration, especially in heating, ventilation, and air-conditioning (HVAC) systems. While dedicated high-performance filters are effective, their high-pressure drops result in significant energy consumption when used in HVAC systems. Herein, we report the application of machine learning (ML) models to predict filtration efficiency and pressure drop, enabling the design and optimisation of filter media in HVAC. Specifically, three ML models, Gaussian process regression (GPR), artificial neural network (ANN), and decision tree (DT), have been trained on a dataset obtained from the literature. The dataset comprised key structural parameters of a wide range of filter media. The GPR model emerged as the most reliable predictor, exhibiting the highest coefficient of determination (R2) and lowest root mean squared error (RMSE) in predicting filtration efficiency and pressure drop, rendering it the most reliable predictor for small and uncertain datasets. The robustness of the GPR model is further confirmed via validation with commercially available filter media. In addition, the ML models accurately capture the established relationship between filtration efficiency and its characteristic drop at the most penetrating particle size (MPPS).

Percolation is a geometric phase transition in which formerly local clusters spontaneously form a system-spanning cluster, also referred to as a percolating cluster, facilitating efficient charge transport in conductive materials. Here, a combinatorial approach is developed that integrates a theoretical framework with Monte Carlo simulations to investigate the percolation behavior of penetrable rectangles by systematically exploring the effects of aspect ratio and anisotropic orientation distributions. A theoretical model incorporating a modified expression for the average excluded area is proposed, with both the model and simulations providing rigorous validation and correcting the errors in the original work. With the aid of predictive modeling and simulations, the critical area fraction and bond number have been computed by considering the aspect ratio of rectangles with a specified degree of anisotropy. These results demonstrate that the bond number in isotropic networks remains within 3.6–4.5 across a wide aspect ratio range (1–1000), in strong agreement with established benchmarks reporting convergence to 3.6 for aspect ratios above 20. Using the predicted critical area fractions, the electrical conductivity trends of two-dimensional (2D) conductive networks are modeled by fitting power-law curves to the reported simulation and experimental results. 

Engineering liquid-repellent textiles through tailored multi-scale surface morphology and controlled surface chemistry opens pathways to a broad spectrum of advanced technological applications. Woven fabrics exemplify intrinsically rough surfaces with hierarchical topography governed by mesoscale weave geometry and the microscale organization of fibers within the yarn structure. Herein, we systematically investigate the wetting behavior of woven fabrics by establishing structure–property relationships between the apparent water contact angle and multi-scale structural hierarchy along with the equilibrium contact angle of the fiber. Guided by the design principles of multi-scale organization, we predict the apparent contact angles of three distinct woven fabrics comprising polyester, a Kevlar/polytetrafluoroethylene (PTFE) hybrid, and carbon using yarn- and structure-level parameters obtained via X-ray microcomputed tomography (micro-CT) analysis. The predicted apparent contact angle values show good agreement with experimental measurements, particularly when evaluating (an)isotropy of droplet behavior from four different directions. Intriguingly, polyester fabric exhibits the fastest wetting transition, enabled by its tightly packed weave and moderate hydrophilicity of the constituent fibers. Parametric analysis demonstrates that tuning yarn- and structure-level parameters, along with the equilibrium (apparent) contact angle of individual fibers (yarn), can induce superhydrophobic behavior in woven fabrics and predict lower roll-off angles. These findings highlight the pivotal role of multi-scale structural design in governing fabric wettability.