Abstract
Quantitatively evaluating interaction energy between two randomly rough surfaces is the prerequisite to quantitatively understand and control membrane fouling in membrane bioreactors (MBRs). In this study, a new unified approach to construct rough topographies and to quantify interaction energy between a randomly rough particle and a randomly rough membrane was proposed. It was found that, natural rough topographies of both foulants and membrane could be well constructed by a modified two-variable Weierstrass-Mandelbrot (WM) function included in fractal theory. Spatial differential relationships between two constructed surfaces were accordingly established. Thereafter, a new approach combining these relationships, surface element integration (SEI) approach and composite Simpson’s rule was deduced to calculate the interaction energy between two randomly rough surfaces in a submerged MBR. The obtained results indicate the profound effects of surface morphology on interaction energy and membrane fouling. This study provided a basic approach to investigate membrane fouling and interface behaviors.
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