Analytical techniques for understanding biofilm modeling in indoor air quality management

This study presents a theoretical and mathematical framework for developing a dimensionless model to enhance the removal of volatile organic compounds (VOCs) through (botanical) biofiltration in indoor environments. Although biofiltration is a promising strategy for the control of indoor air pollution, the precise mechanism of VOC removal remains not well understood. The proposed model is formulated using nonlinear differential equations under specified boundary conditions to represent biofilm mass balance concentrations. To obtain approximate solutions, Homotopy perturbation and Akbari-Ganji analytical techniques are applied. In addition, numerical simulations are performed using MATLAB® and compared with analytical results to validate precision. The findings indicate that optimizing the biofilm thickness and reaction rates significantly enhances the removal efficiency of VOCs. Improves understanding of the behavior of biofilms through advanced mathematical analysis, contributing to the development of more effective biofiltration strategies for improved indoor air quality management. • Robust Analytical Solutions: Successfully employed Akbar-Ganji’s method and homotopy perturbation method for accurate modeling of VOC and oxygen dynamics in indoor biofiltration systems. • Validation Against Numerical Results: Strong correlation between analytical methods and numerical simulations, confirming their effectiveness and reliability in predicting system behavior. • AGM Enhanced Accuracy: AGM outperformed HPM in terms of accuracy and convergence speed, establishing it as the preferred method for complex biofiltration modeling.