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The model incorporates key factors of membrane such as permeability and resistance, feed concentration, fluid viscosity and pressure differentials. Special emphasis is placed on the fouling mechanisms, including pore blockage and cake layer formation, which significantly impact the efficiency of the filtration process.

In this study, we present a numerical analysis of permeate flux through a membrane, focusing on the intricate dynamics of fouling phenomena. Utilizing the Langevin model, we simulate the permeation process to understand how various operational parameters affect the flux rates.

Our results demonstrate that fouling not only reduces the permeate flux but also alters the membrane’s hydraulic resistance over time. The results show that the increasing of the diffusion process on membrane reduces the clogging phenomenon. Hence, the increases of the transmembrane pressure reduce exponentially blocking pore process.

By analyzing these changes, we provide insights into optimizing membrane performance and developing strategies to mitigate clogging membrane. This research contributes to the field of membrane technology by enhancing our understanding of permeate flux behavior under fouling conditions and offering potential pathways for improving long-term operational sustainability.