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While membrane bioreactor (MBR) technology is generally considered as one of the most promising technologies for wastewater treatment and recovery, membrane fouling remains the major obstacle limiting its applications. Interfacial interactions, which critically determine adhesion process and membrane fouling, were investigated in this study. It was found that, natural membrane surface was of a Gaussian surface obeying Gaussian distribution. A Gaussian approach integrating Fourier transform technique, Gaussian distribution and spectrum method was deduced to simulate rough surface topography of membrane. Thereafter, surface element integral (SEI) method, together with composite Simpson rule and triangulation of Gaussian surface was proposed to calculate interfacial interactions. By using the unified method, quantification of interfacial interactions with a Gaussian membrane surface was realized for the first time to date. It was further found that, membrane surface topography had profound impacts on interfacial interactions and adhesive fouling in the MBR. The deduced method can be used to address impacts of various factors on interfacial interactions and adhesive fouling, posing in-depth thermodynamic insights into membrane fouling and pointing towards its widespread potential in fouling research in MBRs. [ABSTRACT FROM AUTHOR]

Quantification of interfacial interactions between particles provides a way to regulate the interface behaviors of particles related with adhesion, aggregation, flotation, flocculation, membrane fouling, etc. Existing methods are based on assumptions of smooth particles although real particle surfaces are rather rough. This study proposed a new method to quantify interfacial interactions between two rough particles. In this study, a rigorous mathematical equation was firstly introduced to construct surface topography. In the framework of surface element integration (SEI) method, the spatial relationship between two rough particles was significantly explored, resulting in establishment of a formula of double integrals for interaction quantification. Thereafter, surface properties of the microbial aggregations obtained from a membrane bioreactor (MBR) were experimentally measured. With these data, the interfacial interactions between two rough microbial aggregations were numerically quantified according to composite Simpson’s rule. The new method was compared with Derjaguin approximation (DA) method. It was found that ripple frequency and particle radius had profound effects on the total interfacial interaction. This method has extensive application foreground in interfacial behavior research. [ABSTRACT FROM AUTHOR]