New insight into pore characteristics for cake layers formed on nanocomposite membranes: Effect of membrane surface fractality

Over the past two decades, there has been extensive research that attempts to relate membrane's performance to its surface roughness. However, applicability of this approach to nanocomposite membranes is questionable, given the highly diverse membrane structures. In this study, three types of carbon nanotube composite membranes (CNT_S, CNT_M, and CNT_L) were prepared and used to filter fluorescent polystyrene particles under favorable surface interaction conditions. The resulting cake structures were imaged using laser confocal microscopy and analyzed for pore characteristics. It was found that cake layers with lower porosity and smaller average pore size also had more tortuous and complex pore channels, leading to lower water permeability. Moreover, simulations of the cake layers with a pore network model reveal that pore radius and throat length are key factors affecting water permeability. Further application of the machine learning (ML) model accurately predicts cake permeability based on the 3D fractal dimension (2.44–2.81), anisotropy (0.64–0.81) and porosity (0.3–0.71) of the pore space and R² of the test set reaches 0.96. Finally, the Weierstrass-Mandelbrot equation is applied to describe the self-similar fractal surfaces possessed by the CNT membranes. The respective fractal dimensions of three membrane surfaces (D_f) are 2.31, 2.11 and 2.57. At a D_f value of 2.31, the cake layer exhibits greater pore homogeneity and connectivity, and thus higher water permeability. Overall, this study revealed the fractal nature of CNT membrane surface and its relevance to pore structure and water permeability of the cake layers.