## 4 Conclusions  
In this paper, the micron particle aggregation during the membrane filtration process was simulated under different inlet velocities. The influence of inlet velocity on particle aggregation and water productivity was studied. The following conclusions were obtained:  
1. The porous media model can be used to simulate the flow across the semipermeable membrane, as long as accurate values for the coefficient of viscous resistance and the coefficient of inertial resistance are obtained, via experimental technology.
2. The particle concentration distribution was affected by different Reynolds numbers. When the Reynolds number is 19,000, the particle concentration near the surface of the porous media zone was higher, and the highest particle concentration reached 0.005 mg/um\({}^{3}\). With an increasing Reynolds number, the particle concentration near the surface of the porous media zone, gradually decreased. When the Reynolds number increased to 31,000, the particle concentration near the surface of the porous media zone was about 0.001 mg/um\({}^{3}\), which was due to the increased scour velocity near the surface. Particle deposition near the surface of the porous media zone was closely related to the Reynolds number. The larger the Reynolds number, the less particles were deposited on the surface of the porous media zone.
3. The motion of particles in a flow field is susceptible to gravity. When there is gravity, because the particle's own gravity can generate a velocity along the direction of gravity, the particle is easy to deposit and not easy to diffuse. When there is no gravity, particles are more likely to follow the fluid motion and diffuse more freely.
4. Comparing the three working conditions, when the Reynolds number reached 31,000, the flow velocity near the porous media zone was larger, resulting in a larger transmembrane pressure difference, which can promote higher water productivity.  
This topic only discusses the effect of particle deposition on water productivity at three velocities, and the conclusions obtained have certain limitations. It is hoped that there will be more extensive discussions in the future.  
Figure 11: Water productivity with different inlet velocities.  
**Author Contributions:** Conceptualization, P.L., Z.Z., Q.D. and B.C.; methodology, P.L.; software, X.X.; validation, X.X. and Q.W.; formal analysis, P.L., X.X. and Q.W.; investigation, X.X. and Q.W.; resources, P.L.; data curation, X.X.; writing--original draft preparation, X.X.; writing--review and editing, X.X., Q.W. and P.L.; visualization, X.X.; supervision, P.L.; project administration, P.L.; funding acquisition, P.L. All authors have read and agreed to the published version of the manuscript.  
**Funding:** The present work is financially supported by the Key R&D Program of Zhejiang Province (Grant No. 2020C03081), the Joint Funds of the National Natural Science Foundation of China (Grant No. U2006221), the National Natural Science Foundation of China (Grant No. 51676173), and 521 Talents Fostering Program Funding of Zhejiang Sci-Tech University of China. The supports are gratefully acknowledged.  
**Data Availability Statement:** The data that support the findings of this study are available from the corresponding author upon reasonable request.  
**Conflicts of Interest:** The authors declare no conflict of interest.