Wavelet neural network modeling for the retention efficiency of sub-15 nm nanoparticles in ultrafiltration under small particle to pore diameter ratio

Abstract

Ultrafiltration (UF) using membranes with a small ratio of particle to pore diameter (PPD) would be very desirable for energy saving. The nanoparticle (NP) retention efficiency of membranes with a small PPD ratio depends on various physical and chemical properties of NPs, membranes and solutions as well as the filtration conditions. Until now, no simple model is available for the calculation of NP retention efficiency in UF membranes, besides, it is unlikely to conduct experiments covering all conditions for obtaining the efficiency. The artificial neural network (ANN) has been attracting much attention for studying the performance of a highly nonlinear system. In this study, a wavelet ANN model was developed to predict the NP retentions in membranes for the dead-ended UFs under different conditions. A total of 13 parameters, including the membrane features, particle properties, water solution characteristics, operating conditions, etc., are considered as ANN inputs and the NP retention efficiency as the output. A total of 200 datasets with high quality from literature were selected, in which 50% were for the model training, 30% for the model validation and the remaining 20% for the model testing. A high correlation between the output and inputs was obtained and the significance of the 13 parameters on the NP retention was ranked. A case study was performed to further validate the trained ANN model in the prediction of the retention efficiency of 10 nm gold NPs in a 50 nm pore sized polycarbonate track etched (PCTE) membrane at different pH conditions (5–9). Focusing on the variation of pH, an excellent agreement between the model prediction and the calculation by the modified extended Derjaguin Landau Verwey Overbeek-Maxwell (MEDLVO-Maxwell) model originating from classical and extended DLVO theory was obtained. The interaction energy in the MEDLVO-Maxwell model was based on the separation distance calculated by a quench molecular dynamics (MD) simulation. This study illustrates and validates the application of ANN modeling on the NP retention efficiency prediction in the UF with small PPD ratios.