Our study was designed to simulate the separation of oil/water emulsions using a crossflow ultrafiltration polysulfone/polyvinylpyrrolidone (PSF-PVP) membrane. The phase inversion method was used to produce the membrane, which consisted of a polysulfone (PSF) polymer base, a polyvinylpyrrolidone (PVP) additive, and a dimethylformamide (DMF) solvent. The oil phase included soybean oil at a constant concentration of 400 ppm in a liter of bi-distilled water. The experiments assessed the permeate flux and rejection variations over about 480 min. The data were analyzed to validate the model predictions. The process of membrane fouling was identified using a modified Hermia's model. By comparing the experimental data with Hermia's model, it is evident that fouling completely follows the complete blocking model. Hermia's modified model for complete blocking filtration in terms of time was used to simulate permeation and rejection variations. A complete pore-blocking resistance model was used to connect the rejection, feed, and permeate fluxes. Model estimations for transient permeate flux and rejection in turbulent flow regimes agree with the experimental observations. Finally, a time-step and mesh-independent model was developed to model the connection between flow rate and filtering time in an oil/water UF system. The modeling results show that increasing the transmembrane pressure (TMP) and temperature improves the permeate flux. However, TMP lowers oil rejection while increasing the temperature increases oil rejection. Additionally, TMP accelerates the fouling of membranes. Furthermore, a simple estimate of permeation using the average inlet/outlet pressures in the well-known Darcy equation corresponded well with the CFD results.

Graphical abstract

中文翻译：

---

使用有限元分析模拟横流超滤聚砜/聚乙烯吡咯烷酮膜分离以分离油/水乳液

我们的研究旨在使用交叉流超滤聚砜/聚乙烯吡咯烷酮 (PSF-PVP) 膜模拟油/水乳液的分离。采用相转化法生产膜，该膜由聚砜 (PSF) 聚合物基、聚乙烯吡咯烷酮 (PVP) 添加剂和二甲基甲酰胺 (DMF) 溶剂组成。油相包括在一升双蒸水中的恒定浓度为 400 ppm 的大豆油。实验评估了约 480 分钟内的渗透通量和截留率变化。分析数据以验证模型预测。使用修改后的 Hermia 模型确定膜污染过程。通过将实验数据与 Hermia 的模型进行比较，很明显结垢完全遵循完全阻塞模型。赫米娅 根据时间的完全阻塞过滤的修改模型用于模拟渗透和排斥变化。一个完整的孔隙阻塞阻力模型被用来连接排斥、进料和渗透通量。湍流状态下瞬态渗透通量和排斥的模型估计与实验观察结果一致。最后，开发了一个时间步长和网格无关的模型来模拟油/水 UF 系统中流速和过滤时间之间的联系。建模结果表明，增加跨膜压力 (TMP) 和温度会提高渗透通量。但是，TMP 会降低排油率，而升高温度会增加排油率。此外，TMP 会加速膜的污染。此外，

图形概要