The nanofiltration (NF) process becomes the most recently used technologies for the desalination of seawater and brackish water. The porous media transport properties are first related to the geometrical complexity of the product. However, the membrane transport models used in desalination process constitute approximatively the less understood process. The objective of this work is to address modeling and numerical study of the desalination process of the water and ions fluxes by using a porous membrane with nanoparticles. Our filtration system used is constituted by two different zones that the membrane sheets are sandwiched. The fluid undergoes a first simple filtration and a second NF process by the injected nanoparticles. The impacts of the permeability [Formula: see text] and porosity [Formula: see text] of the membrane under the effect of a pressure [Formula: see text] were discussed. Our findings are obtained in the framework of the dynamic Langevin approach based on the competitiveness between the stochastic process and dissipation. The results show that the performance of the rejection membrane is significant as the nanoparticle concentration decreases, and increases as a power law with the ratio of the viscosity of the salty fluid to the pure fluid.

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To understand and improve the performance of membrane separation surface used in the water desalination water process, we have studied the effect of friction coefficient on the morphological properties of retentate deposits particles on the surface membrane separation. The investigation is made in the framework of the Langevin equation model based on the competition between stochastic and particle dissipation mechanisms. The noise coefficient, the friction coefficient, and the constant flow rate are remarkable parameters that influence the average velocity and the average distance between the particles. The results show that the temporal evolution of the mean velocity of retentate deposits particles presents an exponential profile with two different regimes. However, the scaling dynamic studies show that the studied system is governed by scaling exponents more consistent with the Family–Vicsek model.

The desalination process using membrane distillation (MD) has recently attracted wide attention in the last few years around the world. Especially, membranes that have an asymmetric geometry, for their performance to filtrate the salt water and the high salt rejection. In this paper, the Langevin dynamics model was adopted as a simulation method to investigate the transport of salt water through the sloping membrane under a pressure drop. The surface of the used membrane is considered as a hydrophilic sloping surface. Thus, the pressure drop effect on the fluid flux was observed, which leads to attracting the salt water into pores that are randomly distributed. The influence of deposition and accumulation of the ions into pores, the incline angle of the membrane surface, and the thickness of the formed layer on the surface were investigated. In addition, the impact of biofouling is caused by the accumulation and the variation of the fluid velocity as a function of pressure drop values. The obtained results show that the relationship between the fluid velocity and the pressing force is a power law. Moreover, the increase in fluid flow velocity in the porous medium is severe in the earlier time regime, but it becomes almost constant in the second regime. However, the time desalination process increases linearly with the pressure drop. Moreover, the accumulation and deposition of ions into the pores cause a decrease in the water flow through the pores resulting in a higher pressure drop in the less inclined direction. Finally, the influence of deposition and accumulation of the salt phase into the pores on the membrane performance was remarked, resulting in a high desalination rate. The obtained results explain the salt water behavior through a porous membrane, which provides ideas for making a high membrane performance.