Numerical Assessment of Elliptical Pore Orientation and Eccentricity Effects on Charge Transport in Anisotropic Functional Membranes

The transport efficiency of anisotropic functional membranes is largely dictated by the geometry and orientation of their internal pores. In this study, a numerical finite-volume framework was developed to evaluate how elliptical pore eccentricity (εcc) and orientation influence charge transport and effective conductivity (ek) within two-dimensional porous membrane microstructures. Canonical stochastic domains with controlled porosity were generated, considering parallel and perpendicular aligned configurations of the major pore axis relative to the imposed potential gradient. Results demonstrated a strong orientation dependence: under perpendicular alignment, the effective conductivity decreased by up to 70% as <i>εcc</i> increased from 0.5 to 0.999, while parallel alignment maintained at ek > 0.8 even for highly elongated pores. The aspect ratio (b/a) was identified as a secondary geometric modulator producing opposite conductivity trends depending on orientation. Through isotropy-error analysis, a critical morphological threshold at εcc ≈ 0.9 was found, indicating the onset of structural anisotropy and loss of isotropic transport. These results establish a quantitative structure-property relationship linking pore geometry to macroscopic transport performance. The proposed stochastic FVM-based approach provides a generalizable and computationally efficient tool for the design and optimization of anisotropic porous membranes used in electrochemical and energy-conversion devices.