Quantitative evaluation of the interfacial interactions between a randomly rough sludge floc and membrane surface in a membrane bioreactor based on fractal geometry

- Randomly rough sludge surface can be well modeled by fractal geometry.
- A novel method to quantify interactions with randomly rough floc was developed.
- The proposed method was verified to be correct and feasible.
- The method had broad application prospect in membrane fouling research.

In this paper, a new method for quantification of interfacial interactions between a randomly rough particle and membrane surface was proposed. It was found that sludge flocs in a membrane bioreactor were of apparent fractal characteristics, and could be modeled by the modified two-variable Weierstrass-Mandelbrot (WM) function. By combining the surface element integration (SEI) method, differential geometry and composite Simpson's rule, the quantitation method for calculating such interfacial interactions was further developed. The correctness and feasibility of the new method were verified. This method was then applied to evaluate the interfacial interactions between a randomly rough particle and membrane surface. It was found that, randomly rough particle possesses stronger interaction strength than regularly rough particle but weaker strength than smooth particle with membrane surface, indicating significant effects of surface morphology and roughness. The proposed method in this study has broad application prospect in membrane fouling study.

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