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Influences of fractal dimension ( D f ) of membrane surface on interfacial interactions related to membrane fouling in a membrane bioreactor were investigated based on thermodynamic methods. It was found that membrane surface had significant fractal features, and its fractal dimension could be characterized by the power spectrum method. The modified Weierstrass-Mandelbrot (WM) function was found to be effective to model the fractal membrane surface, and higher D f corresponded to higher number of fine asperities in the modeled surface. Moreover, the modeled surface roughness exponentially decreased with D f . Interaction calculations according to a novel method showed that the interactions for fractal membrane surface were elongated and weakened as compared with smooth membrane surface. It was interestingly found that the absolute value of total interaction monotonically decreased with D f of membrane surface. As D f is a measure of substance stiffness, this result indicates that softer surface is more susceptible to adhesion by sludge foulant. The results offered new insights into membrane fouling mechanisms and alleviation. [ABSTRACT FROM AUTHOR]

Interfacial interactions between foulants and membrane directly determine foulant adhesion and membrane fouling. In this study, surface of sludge foulant particles (flocs) was found to be rough, and could be modeled by a sinusoidal sphere function. A novel method, which combined surface element integration (SEI) method, differential geometry and composite Simpson’s rule, was developed to quantify the interfacial interactions between the modeled rough floc surface and membrane surface. Application of the novel method in a membrane bioreactor (MBR) provides broad profiles of quantitative interactions with rough floc surface with separation distance. It is also found that increase in the scaled amplitude of floc surface significantly reduced the interaction strength. Derjaguin’s approximation (DA) can be regarded as a special case of the novel method, indicating the extensive application prospect of the novel method. The novel method for interaction calculation was verified to be correct and feasible. Finally, roles of the novel method in membrane fouling research were discussed. [ABSTRACT FROM AUTHOR]