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Impacts of morphologies of both membrane and foulant on interaction energies related with adhesive fouling in a membrane bioreactor (MBR) were explored by thermodynamic analyses. Interaction energies in three possible interaction scenarios regarding different membrane and foulant morphologies under conditions in this study were quantified according to the thermodynamic methods. It was interestingly found that, strength of total interaction between soluble microbial products (SMPs) and rough membrane was over 20,000 times of that between sludge flocs and rough membrane under same conditions, indicating the extremely higher adhesion ability of SMPs than the large particulate foulants. This result plausibly explained the high fouling propensity of SMPs over sludge flocs. As compared with smooth surfaces, rough surfaces of both membrane and sludge flocs significantly reduced total interaction strength, alleviating adhesive fouling caused by the sludge flocs. Reduce in fractal dimension ( D f ) of membrane increased adhesive fouling caused by the SMPs, but alleviated adhesive fouling caused by the sludge flocs. These findings gave important implications to better understand and control membrane fouling in MBRs. [ABSTRACT FROM AUTHOR]

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]

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]

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]

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]