Semi-analytical Galerkin modeling of glucose transport and reaction in glucose oxidase-immobilized SBA-15 mesoporous silica

The immobilization of glucose oxidase (GOx) in ordered mesoporous silica can provide a stable and efficient platform for glucose sensing and biocatalytic applications. This work examines a reaction-diffusion model governing glucose transport and enzymatic conversion inside GOx-loaded SBA-15 structures, with attention to both rod-shaped and cuboid particle geometries. Three coupled phenomena are incorporated into the model: intraparticle Fickian diffusion, Michaelis-Menten kinetics modified by competitive inhibition, and the dynamic exchange between glucose within the pore and in the surrounding bulk solution. The governing system of nonlinear PDE and ODE is solved in two complementary ways: the Method of Lines (MOL) and the semi-analytical Galerkin modal method. There is a high level of concordance between the semi-analytical and numerical solutions in a wide range of combinations in enzyme loadings and pore geometries shown in simulation findings. Absolute and relative errors remain minimal, particularly under diffusion-limited conditions at high enzyme loadings. Model predictions are further validated against experimental bulk depletion data reported in the literature, with mean absolute percentage error below 1% across the examined time window. A sensitivity analysis was performed to identify that the competitive inhibition constant has a more significant impact on glucose conversion within the parameters examined compared to the effective diffusivity. The semi-analytical galerkin formulation reduces the spatial problem to a small set of modal coefficients rather than the tens-to-hundreds of nodes required by Method of Lines, yielding a compact representation well-suited for parametric and sensitivity studies without loss of accuracy in the regimes examined. The results demonstrate that the semi-analytical Galerkin modal method offers a reliable alternative to conventional numerical approaches, yielding practical design guidance for mesoporous glucose biosensors on particle geometry, enzyme loading, and inhibition mitigation.