A Multi-scale Modelling Strategy to Evaluate Permeability in Diagnostic Paper Membranes

Paper-based materials exhibit distinctive qualities such as being lightweight, biodegradable, and cost-effective, making them particularly attractive for point-of-care diagnostics. To design such diagnostic devices accurately, precise fluid flow modeling is essential, which requires accurate determination of hydraulic properties of these paper materials. In this context, our work presents a relatively simple and efficient method to calculate the anisotropic permeability of paper-based substrates. The current study introduces a novel modelling approach that incorporates anisotropic features by analyzing micrographs acquired via field emission scanning electron microscopy (FESEM). Our approach exploits the geometric details of the paper by combining the mathematical homogenization, incorporating 3D geometric effects in the 2D images, and solving the Stokes equation extended to the full domain, including the solid substrate, with the fictitious domain method. The post-processing of the Stokes solution provides robust, quantitative, anisotropic permeability measurements. This bypasses the conventional meshing and connects the microstructural features with macroscopic behavior. The absolute permeability can be used for macroscopic calculations for the paper using Darcy’s law or Richards’ equation. Furthermore, the permeability values obtained were compared against experimentally measured fluid velocities, demonstrating the predictive fluid transport capabilities of paper substrates. The determination of hydraulic properties enables the design of optimized, predictive paper-based platforms.