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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. [ABSTRACT FROM AUTHOR]

Quantification of interfacial interactions between two rough surfaces represents one of the most pressing requirements for membrane fouling prediction and control in membrane bioreactors (MBRs). This study firstly constructed regularly rough membrane and particle surfaces by using rigorous mathematical equations. Thereafter, a new method involving surface element integration (SEI) method, differential geometry and composite Simpson’s rule was proposed to quantify the interfacial interactions between the two constructed rough surfaces. This new method were then applied to investigate interfacial interactions in a MBR with the data of surface properties of membrane and foulants experimentally measured. The feasibility of the new method was verified. It was found that asperity amplitude and period of the membrane surface exerted profound effects on the total interaction. The new method had broad potential application fields especially including guiding membrane surface design for membrane fouling mitigation. [ABSTRACT FROM AUTHOR]

Fractal roughness is one of the most important properties of a fractal surface. In this study, it was found that, randomly rough membrane surface was a fractal surface, which could be digitally modeled by a modified two-variable Weierstrass-Mandelbrot (WM) function. Fractal roughness of membrane surfaces has a typical power function relation with the statistical roughness of the modeled surface. Assessment of interfacial interactions showed that an increase in fractal roughness of membrane surfaces will strengthen and prolong the interfacial interactions between membranes and foulants, and under conditions in this study, will significantly increase the adhesion propensity of a foulant particle on membrane surface. This interesting result can be attributed to that increase in fractal roughness simultaneously improves separation distance and interaction surface area for adhesion of a foulant particle. This study gives deep insights into interfacial interactions and membrane fouling in MBRs. [ABSTRACT FROM AUTHOR]