Realization of quantifying interfacial interactions between a randomly rough membrane surface and a foulant particle

•Randomly rough membrane surface can be well reconstructed by fractal geometry.•A novel method for calculation of interactions with rough surface was developed.•First realization of quantifying energy with randomly rough surface was provided.•Membrane surface topography significantly affected interaction energy.

Quantification of interfacial interaction with randomly rough surface is the prerequisite to quantitatively understand and control the interface behaviors such as adhesion, flocculation and membrane fouling. In this study, it was found that membrane surface was randomly rough with obvious fractal characteristics. The randomly rough surface of membrane could be well reconstructed by the fractal geometry represented by a modified Weierstrass-Mandelbrot function. A novel method, which combined composite Simpson's approach, surface element integration method and approximation by computer programming, was developed. By using this method, this study provided the first realization of quantifying interfacial energy between randomly rough surface of membrane and a foulant particle. The calculated interactions with randomly rough surface of membrane were significantly different from those with smooth surface of membrane, indicating the significant effect of surface topography on interactions. This proposed method could be also potentially used to investigate various natural interface environmental phenomena.

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