MATHEMATICAL MODELING OF TRANSPORT PHENOMENA THROUGH M EMBRANES: PORE-FLOW MODELS (REVIEW)

Today, water scarcity and energy shortages are a significant issue for many societies, and according to the United Nations report and the International Water Management Institute, Iran will face water scarcity in the coming years. Therefore, it is crucial to develop and find optimal utilization and increase drinking water resources. One of these methods is the use of a membrane for water desalination. In addition, membrane technology is used in various wastewater treatment processes (Nikazar and Jamshidi ۲۰۰۸) and water desalination (Marjani ۲۰۱۷). Furthermore, it is used in the food industry (Garcia-Castello, McCutcheon, and Elimelech ۲۰۰۹) and power generation (Achilli, Cath, and Childress ۲۰۰۹). Simultaneously with the development of membrane processes, various models and mechanisms to study transfer material through the membrane have been developed. For example, in Solution-Diffusion (SD) mechanisms, first, soluble and solvent must be dissolved in the dense layer of the membrane, then because the gradient of the concentration penetrates to the other side of the membrane. Also, in the Pore-flow (PF) mechanism, the material will be separated by a pressure convective flow through tiny pores. The cause of this separation is the ability of pores to repel certain particulate materials and absorb some others (Mehdizadeh ۱۹۹۰). In this paper, the mathematical modeling of pore-flow models has been studied. These models, which are most commonly used in the classification of porous transport models (Fig. ۱), have also been used to model the transfer of materials through ultrafiltration and reverse osmosis membranes (J. G. Wijmans and Baker ۱۹۹۵).