A mathematical elucidation of separation membrane operations and technology of chemical and physical processes: An advanced review

Reviving mathematical elucidation of separation membrane setups, and analyzing actual processes (chemical and physical processes), and illustrating situations that happened during the operations have been interpreted here. Mathematical elucidation defines operations, as well as a broad range of processes used in chemistry and chemical technology concerned with heat, mass and momentum transfer, phase transition, chemical reactions, adsorption, desorption, which were also discoursed. The strategies were engaged to determine the numerous claims that persisted in the mathematical interpretation of separation membrane operations of chemical and physical processes. The illustrations of mathematical elucidation of various processes help in solving various complications that existed in engineering tasks, process simulation, and designing methodologies, controlling the processing, optimization, determination of parameters, experiment prediction, planning, and diagnosis and troubleshooting. Without doing these exercises, researchers cannot be unambiguously dignified queries and cannot do feasibility revisions. Therefore, all mathematical elucidation of numerous models were employed to redefine membrane technology. Innovative arenas concerned with membrane technology and engineering were presented because their concerned elucidated equations can be employed for the separation as unit operations. The specific potential of these revealed mathematical operations is based on mathematical interpretation concerning the basic needs, and particular aspects that have potential applications in ecological growth and an upgraded lifestyle. Several efforts have been done and applied to expose the role of membrane engineering in foremost technology such as water desalination or purifications. The authors provide a high grade practical and industry-relevant approach to the subject by highlighting mathematical elucidation of separation membrane technology. This review summarized the poles apart aspects of numerous models such as Schofield’s model, Tomaszewska’s model, Lawson-Lloyd model, Lagana’s model, Yu’s model, Hayer’s model, Eleiwi’s dynamic model, Response surface model, Ali’s model, and Cheng’s model applied in separation membrane technology, physical and chemical operations