Lie symmetry analysis of effluent dispersion over oxytactic-laden porous domain: a mathematical insight on pollutant dynamics

The escalating contamination of water bodies presents a critical threat to environmental integrity and public health. Effluents laden with complex pollutants underscore the urgent need for advanced treatment techniques aiding towards the United Nations Sustainable Development Goals (SDGs) 6 and 9. Developing and implementing efficient effluent treatment and water filtration technologies mitigate these significant risks and ensure widespread access to clean and safe water resources, thus contributing to SDGs 3, 6, 9, 14, and 15. Most previous studies have overlooked the integrated effect of microbial activity, porous drag, pollutant transport, radiative and electromagnetic effects, and multi-physical mass transfer phenomena creating an important gap that has been covered here. The novel strength of the present work is that several physical mechanisms are unified in one framework, offering a more comprehensive effluent treatment model than existing studies. The modelled partial differential equations have been scaled to nondimensional ordinary differential equations using Lie group analysis and then resolved numerically. Quantities like heat and pollutant transfer rates, microbe and oxygen density numbers, and drag coefficient have been scrutinized. The pollutant transfer rate is maximum for higher values of the electric field and lower values of the Soret parameter. Per unit change in the electric field parameter enhances the drag coefficient by 15.64% and 13.69% for Casson and Newtonian fluid, respectively. Further, an inclined microbial density number was noted for higher microbial and oxygen Lewis numbers.