Modeling three-dimensional surface morphology of biocake layer in a membrane bioreactor based on fractal geometry

Bioresource Technology 222 (2016) 478–484

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Modeling three-dimensional surface morphology of biocake layer in a membrane bioreactor based on fractal geometry Leihong Zhao a, Lining Yang a, Hongjun Lin a,⇑, Meijia Zhang b, Haiying Yu a, Bao-Qiang Liao b, Fangyuan Wang a, Xiaoling Zhou a, Renjie Li a a b

College of Geography and Environmental Sciences, Zhejiang Normal University, Jinhua 321004, PR China Department of Chemical Engineering, Lakehead University, 955 Oliver Road, Thunder Bay, Ontario P7B 5E1, Canada

h i g h l i g h t s

g r a p h i c a l a b s t r a c t


Biocake layer surface illustrated

obvious fractal features.
Static light scattering method was

adopted to measure sludge fractal dimension.
Fractal Weierstrass-Mandelbrot function was feasible to model biocake surface.
Fractal dimension critically affected biocake surface topography and roughness.

a r t i c l e

i n f o

Article history: Received 25 August 2016 Received in revised form 5 October 2016 Accepted 6 October 2016 Available online 13 October 2016 Keywords: Membrane bioreactor Fractal dimension Surface morphology Biocake layer Membrane fouling

a b s t r a c t While the adsorptive fouling in membrane bioreactors (MBRs) is highly dependent of the surface morphology, little progress has been made on modeling biocake layer surface morphology. In this study, a novel method, which combined static light scattering method for fractal dimension (Df) measurement with fractal method represented by the modified two-variable Weierstrass-Mandelbrot function, was proposed to model biocake layer surface in a MBR. Characterization by atomic force microscopy showed that the biocake surface was stochastic, disorder, self-similarity, and with non-integer dimension, illustrating obvious fractal features. Fractal dimension (Df) of sludge suspension experienced a significant change with operation of the MBR. The constructed biocake layer surface by the proposed method was quite close to the real surface, showing the feasibility of the proposed method. It was found that Df was the critical factor affecting surface morphology, while other factors exerted moderate or minor effects on the roughness of biocake layer. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction With almost five decades’ development, membrane bioreactor (MBR) has been conceived as a well-established technology for wastewater treatment and reclamation (Lin et al., 2012; Wang ⇑ Corresponding author. E-mail address: [email protected] (H. Lin). http://dx.doi.org/10.1016/j.biortech.2016.10.020 0960-8524/Ó 2016 Elsevier Ltd. All rights reserved.

et al., 2014b). In spite of that, membrane fouling is inevitable, and still brings serious problems, such as increasing operating and maintenance costs, to MBR technology (Lin et al., 2014; Meng et al., 2009; Zhang et al., 2016). Membrane fouling in MBRs is generally caused by initial pore clogging followed by formation of biocake layer (Meng et al., 2009). Numerous studies have confirmed that formation of biocake layer is the major cause of membrane fouling (Liu et al., 2016; Low et al., 2016; Wang and Li, 2008).

L. Zhao et al. / Bioresource Technology 222 (2016) 478–484

Most studies reported that biocake resistance accounted for over 80% of total resistance in MBRs (Lin et al., 2009; Miura et al., 2007). Moreover, biocake layer would act as a secondary membrane once it formed. It is biocake layer rather than separation membrane that contact bulk sludge suspension, which actually governs the subsequent development of membrane fouling (Gao et al., 2011; Wang and Li, 2008; Zhou et al., 2014). Better understanding of biocake layer properties is essential to control membrane fouling and optimize MBR performance. Considerable efforts have been recently devoted into characterization of biocake layer (Gao et al., 2011; Meng et al., 2007; Su et al., 2013). However, most of these efforts focused on characterizing physical structure (Miura et al., 2007; Su et al., 2013), chemical composition (Meng et al., 2007; Yu et al., 2014) and microbial community (Gao et al., 2013; Zhang et al., 2011). Surface morphology/topography is an important property which may exert profound impacts on membrane fouling and other properties of biocake (Chen et al., 2012; Hoek and Agarwal, 2006; Jin et al., 2004; Zhao et al., 2015). For example, it is generally believed that surface morphology of biocake layer affects interfacial interactions between biocake layer and sludge foulants, and then critically affects subsequent adhesion of sludge foulants (Hong et al., 2013). It was also reported that biocake morphology was closely related with biocake permeability (Meng et al., 2005). Therefore, it is of great interest to characterize surface morphology of biocake layer, because such a work makes it possible to reconstruct its surface morphology, and based on that, physiochemical interactions between biocake layer and foulants in bulk sludge suspension could be quantified (Hong et al., 2016). This would really accelerate deep understanding of membrane fouling. However, pursuing the literature indicates that seldom studies have explored this issue. This situation may be attributed to lack of proper methods for characterization of biocake surface morphology. Although techniques, such as scanning electron microscopy (SEM), atomic force microscopy (AFM), have been used to characterize biocake surface morphology (Meng et al., 2010), they always fail to reflect real surface morphology because pretreatments of biocake samples are required before these measurements. Sample pretreatments such as drying would certainly damage biocake structure and surface morphology. Moreover, natural surfaces including biocake surface are irregular and disorder (Jaggard and Sun, 1990). These surfaces are named as fractals (Meng et al., 2005; Yan and Komvopoulos, 1998). A general feature related with fractals is self-similarity, which means that an object comprises sub-units on multiple levels that are statistically similar to the whole object structure (Jaggard and Sun, 1990). Obviously, biocake surface morphology cannot be properly described by either the conventional techniques or the Euclidean geometries. It was reported that, different from Euclidean geometry, fractal geometry, which was first proposed by Mandelbrot (1967), could well represent the fractal characteristics of some natural surfaces (Jaggard and Sun, 1990; Majumdar and Tien, 1990). Considering that biocake layer surface in MBRs is a kind of natural surface, it is envisaged that surface morphology of biocake layer can be constructed by fractal geometry, although such a hypothesis involves massive innovation, and has not been tested previously. This study, therefore, aims to model surface morphology of biocake layer by fractal theory. Accordingly, the biocake layer was characterized, and the fractal dimension was determined by the light scattering method. Thereafter, a fractal method represented by the modified two-variable Weierstrass-Mandelbrot (WM) function was proposed to model the surface morphology of biocake layer. Effects of various parameters including particularly fractal dimension on the simulated surface morphology were analyzed.

479

2. Materials and methods 2.1. Biocake layer samples A lab-scale submerged anaerobic MBR (SAnMBR) setup with 80 L effective volume was continuously operated in this study. A flat sheet polyvinylidene fluoride (PVDF) membrane module (SINAP, China) with effective area of 0.6 m2 was immerged in the SAnMBR. Detailed information regarding the SAnMBR system can refer to the previous study (Wang et al., 2014a). Continuous operation of the SAnMBR resulted in formation of a biocake layer on the membrane surface. The samples of biocake layer were obtained from the SAnMBR for characterization. 2.2. Fractal theory Regular objects such as points, curves, surfaces, and cubes can be described by Euclidean geometry with the integer dimensions of 0, 1, 2 and 3. Apart from these regular objects, lots of natural objects such as sludge, rivers and lakes are irregular and disordered. Apparently, these objects are not Euclidean geometries. Conception of ‘‘fractal geometry” was accordingly developed to describe these objects (Mandelbrot, 1967). Two of the most distinct features of fractal objects are self-similarity and non-integer dimension (fractal dimension). Self-similarity means that each part of a fractal object is similar to the whole object when it is divided into parts. For the rough surface, self-similarity property is represented by the multiscale which means the appearance of more small scales of similar roughness when the section of rough surface is magnified. Non-integer dimension is a measure of the complexity of fractal patterns or sets as a ratio of the change in detail to the change in scale (Mandelbrot, 1982). 2.3. Analytic methods 2.3.1. Particle size distribution Particle size distribution (PSD) of the sludge suspension samples was analyzed by a Mastersizer 2000 instrument (Malvern, UK). The biocake sludge sample for PSD measurement was prepared as follows: firstly, the biocake layer on membrane surface was carefully scraped off using a spatula, and then resuspended with the MBR permeate by mild shaking until no obvious sludge cluster could be visually observed. Similar preparing processes have been used in the literature (Lin et al., 2009; Wang and Li, 2008). Light scattering method was used for PSD measurement where the scattered light was detected by 31 photosensitive detectors which converted the light signal to a size distribution in volume. A peristaltic pump would continuously recycle the sludge suspension sample through a sample cell in the instrument. The detection range is 0.02–2000 lm. 2.3.2. Fractal dimension determination Mastersizer 2000 instrument can provide two sets of data for a sludge suspension sample, one is for the PSD, and the other is for the fractal dimension (Df). Static light scattering method was used to measure the Df value of a sludge liquor sample. For independently scattering aggregates, light intensity (I) is a function of the scatter vector (Q) and Df, which can be represented by (Guan et al., 1998):

I / Q Df

ð1Þ

Data of I and Q can be measured by the Malvern Mastersizer 2000 instrument. Df can be obtained by the slope of log I versus log Q by fitting a straight line. The sample for light scattering

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method was fresh without the pretreatments like drying. Therefore, light scattering method can well represent the real situation of biocake fractal characteristics. 2.3.3. AFM analysis A thin biocake layer on the membrane surface was taken from the reactor, and then immediately rinsed in phosphate buffer (pH 7.0) to remove loosely attached macromolecules. The treated biocake layer sample on membrane surface was placed into an alumina dish for freeze-drying. The alumina dish together with the sludge sample was placed in a freeze-dryer (Labconco Freezone 12, USA) until freeze-dried. An atomic force microscopy (AFM) (Multi-Mode AFM, Agilent Technologies, USA) operated in tapping mode was used to capture surface images. The images were analyzed by the NanoScope software by which surface roughness was obtained by calculating the arithmetic average and root mean square of the scanned surface. 2.3.4. Surface morphology modeling MATLAB 2013a was used to model biocake layer surface morphologies with different parameter values. This software provides a set of functions to generate three-dimensional images of an object. The main function for such a simulation in MATLAB is ‘‘meshz(x, y, z)”. The background knowledge regarding this function can refer to the instruction of MATLAB 2013. A program with the original codes was composed to effectively model the complicated surface morphology. 2.3.5. Surface roughness calculation RA is the arithmetic average of the absolute values of the surface height (Zi) deviations measured from the mean plane, which can be obtained by:

RA ¼

N 1X jZ i j N i¼1

ð2Þ

RRMS is the root mean square average of height deviations taken from the mean data plane, which is expressed as:

RRMS

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi PN 2 i¼1 Z i ¼ N

ð3Þ

Surface modeling would give the relevant height information, which can serve for surface roughness calculation.

by Df, nor to model/simulate biocake layer surface, due to the potential effects of sample pretreatment on the surface morphology in this study. In order to obtain Df value of the biocake layer, the biocake layer were resuspended in the permeate of MBR, and the PSD of the resuspended suspension was measured. The results together with the PSD of the sludge suspension in the MBR were provided in Fig. 1(a). While stemmed from the sludge suspension, biocake sludge consisted of more small particles (with radius <10 lm) as compared with sludge suspension. This result indicates easier adhesion of small particles to membrane surface than large ones. Similar results have been reported in the literature (Gao et al., 2011; Meng et al., 2007; Shen et al., 2015). Fig. 1(b) shows the plotting of log of the light scattering intensity versus log of the light scattering vector for the resuspended biocake sludge and the sludge suspension samples in the MBR. It was suggested that value of Df could be obtained by determining the linear slope of the plotting (Guan et al., 1998). Accordingly, Df was determined to be 2.205 and 2.190 for the biocake sludge and the sludge suspension samples, respectively. The values are representative for sludge suspension samples (Massé et al., 2006), indicating the feasibility of static light scattering method for Df measurement. Fig. 2 shows the variation of Df of the sludge suspension in the MBR with operational duration. It can be seen that Df of the sludge suspension first decreases from 2.37 to 1.88, and then increases to 2.21 during the operation period. Such a change trend was well correlated with the morphology change of sludge flocs in the reactor (for instance, the flocs became looser in the former stage of operational duration). Meanwhile, it was observed that biocake layer was more easily formed by the looser flocs. These observations suggested that Df may play important roles in floc morphology, biocake layer formation and membrane fouling in the MBR. In the literature, several methods such as image analysis (Ganczarczyk et al., 1992) and settling velocity measurement (Námer and Ganczarczyk, 1993) have been used to measure Df of sludge suspension. However, these methods are generally difficult to operate, time consuming and prone to error (Guan et al., 1998). In contrast, the method proposed herein for Df measurement is convenient and easy to follow. Moreover, this method allows instantaneous measurement of the average fractal dimension of sludge suspension as well as its evolution with time. These advantages together with the reliable results obtained by this method suggest the great significance of this method for surface morphology study.

3. Results and discussion 3.1. Biocake layer characterization Continuous operation of MBR resulted in foulant adhesion and an apparent formation of a biocake layer on membrane surface. Fig. S1 (provided in the Supporting Information) shows AFM images of the biocake layer formed on membrane surface at different scales. Although the drying pretreatment procedures might damage the original morphology of the biocake layer formed in the MBR to some extent, and the obtained image are highly dependent of resolution of the AFM instrument, these images could still provide some information. It can be seen that, the biocake surface is randomly rough at different scales. It is apparent that more small scales of roughness appear when the rough surface is magnified. Such a phenomenon is known as ‘‘multiscale property” or ‘‘selfsimilarity”. The AFM figures suggested that the biocake layer possessed typical fractal features. It should be noted that, although AFM provided visual images of the rough biocake layer surface with typical fractal features, these images were neither used to obtain the value of fractal features of the biocake layer represented

3.2. Biocake surface morphology modeling Although the randomly rough biocake surface eliminates a rigorous mathematical model to describe it, the apparent fractal characteristics of biocake surface can be satisfied by the modified twovariable Weierstrass-Mandelbrot (WM) function involved in the fractal geometry theory (Liu et al., 2015; Peng and Guo, 2007; Yan and Komvopoulos, 1998). This function is given by: zðx; yÞ ¼ L

 Df 2  1=2 X M n max X G ln g gðDf 3Þn L M m¼1 n¼0

 cos /m;n  cos

2pgn ðx2 þ y2 Þ L

1=2

 y pm  þ /m;n  cos tan1 x M

!!

ð4Þ

where L and G is the sample length and fractal roughness (the height scaling parameter independent of frequency), respectively. g is a parameter that determines the density of frequencies in the profile, M is the number of superposed ridges used to model a

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1

10

100

1000

Fig. 1. (a) Particle size distribution of the resuspended biocake sludge and the sludge suspension, (b) static light scattering data (log I versus log Q) for the resuspended biocake sludge and the sludge suspension in the MBR.

Table 1 Parameter values used for modeling rough biocake surface morphology. Parameter

Value

Unit

L G Df

5  106 1  1011 2.205 1.6 10 2  107 6 ½/1Mðnmax þ1Þ

m m – – – m – –

g

M Ls nmax /m,n

Fig. 2. Variation of Df of the sludge suspension in the MBR with operational duration.

surface, /m,n is the random phase. nmax is the highest frequency, which is defined as:

nmax ¼ intðlogðL=Ls Þ= log gÞ

ð5Þ

where Ls is the cutoff frequency, and int(. . .) is a function to obtain the maximum integer value of the number in the bracket. The WM function is well designed as it includes several parameters which would well reflect fractal characteristics of rough surface. For example, parameters Df and M denote non-integer dimension and multiscale characteristics, respectively. /m,n reflects the random process of rough surface. It is expected that this function can be used to describe the rough surface of biocake layer. The proposed method was then adopted to model biocake layer surface topography. Table 1 lists the data used to model a biocake surface morphology with area of 25 lm2 by Eq. (2). For most natural surfaces, G = 1  1011 m, g = 1.6, Ls = 1  106 m are typical (Komvopoulos and Yan, 1997; Xiao et al., 2015; Yan and Komvopoulos, 1998). For the biocake layer sample, Df = 2.205

was experimentally measured. M > 3 should be satisfied for a realistic surface. Herein, M = 10 was set. nmax was calculated to be 6 according to Eq. (5). A set of /m,n in range of [0, 2p] (provided in the Supporting Information) were generated by a random number generator, in order to prevent the coincidence of different frequencies at any point of the surface (Komvopoulos and Yan, 1997). Fig. 3 shows the constructed three-dimensional biocake layer surface in area of 25 lm2 by the fractal method represented by Eq. (4). Obviously, the constructed biocake surface is stochastic, disorder and natural. As compared with Euclidean geometries such as cubes and spheres, the constructed surface is more close to the reality. The roughness of the constructed biocake surface can be calculated according to Eqs. (2) and (3). Table 2 compares

Fig. 3. The constructed three-dimensional biocake layer surface by the fractal method.

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Table 2 Measured and reconstructed membrane statistical roughness parameters. Morphological parameter

Constructed surface

Real biocake surface

Deviation

Biocake layer area (lm2) RA (nm) RRMS (nm)

25 175.40 210.73

25 167.92 206.38

0% 4.45% 2.11%

the surface roughness in terms of RA and RRMS between the constructed biocake surface and the measured surface by AFM. It is evident that the constructed biocake surface possesses similar roughness to the AFM measured surface, indicating the feasibility of the proposed fractal method for rough biocake layer surface modeling. It worth noting that, the fractal characteristics (fractal dimension) of biocake layer for model simulation were determined by light scattering method rather than AFM measurement. Although the pre-treatment of the biocake sample for AFM measurement may cause certain difference between the measured average roughness and the real one, such a potential difference just causes certain value modification of the parameters involved in Eq. (4), but doesn’t affect the correctness and feasibility of the new method. Although regarded as an important research interest, rough surface modeling in the literature was generally conducted by randomly locating geometrically regular asperities as protrusions or depressions on a planar surface (Bhattacharjee et al., 1998; Hoek et al., 2003; Martines et al., 2008; Suresh and Walz, 1996). Such a method, however, failed to construct surface morphology close to the realistic surface. Recognizing the fractal features of biocake layer surface, this study introduced fractal method represented by the modified two-variable WM function into biocake layer surface modeling. This method well reflected stochastic, disorder, selfsimilarity, non-integer dimension and multiscale characteristics of the real rough biocake surface, showing the superiority of this method over the above-mentioned method. 3.3. Factors affecting the constructed morphology In order to assess factors affecting the constructed morphology, 6 sets of parameter data as shown in Table 3 were used to construct biocake surface morphology. These sets were set by means of changing the concerning parameter value while keeping the values of other parameters identical to set 1. Fig. 4 shows the constructed biocake surfaces by using the sets in Table 3 with Eq. (4). Table 4 lists the roughness information of the constructed biocake surfaces by using the sets in Table 3. Effects of concerning factors on the constructed surfaces can be evaluated by comparing the data resulted from sets 2–6 with the counterpart from set 1 in Fig. 4 and Table 4. It can be seen that, RA and RRMS of the constructed surface are changed from 2587.6 nm and 3020.2 nm to 14.1 nm and 17.4 nm, respectively, when Df is changed from 2.0 to 2.4, indicating that Df is a critical factor affecting roughness

Fig. 4. The constructed biocake surfaces by using (a) set 1, (b) set 2, (c) set 3, (d) set 4, (e) set 5, and (f) set 6 in Table 3.

of the constructed biocake surfaces although it doesn’t affect the location of asperities. Comparing Fig. 4(c) with Fig. 4(a) shows that parameter G has no effect on roughness value and location. Parameters g and Ls slightly affect the roughness value when comparing Fig. 4(d) with Fig. 4(a). Parameter M moderately affects the rough-

Table 3 6 Sets of parameter values used to simulate rough biocake surface morphology. Parameter

Set 1

Set 2

Set 3

Set 4

Set 5

Set 6

L (m) G (m) Df

1  105 1  1011 2.0 1.6 10 2  107 6 ½/1Mðnmax þ1Þ

1  105 1  1011 2.4 1.6 10 2  107 6 ½/1Mðnmax þ1Þ

1  105 1  109 2.0 1.6 10 2  107 6 ½/1Mðnmax þ1Þ

1  105 1  1011 2.0 1.8 10 1  107 6 ½/1Mðnmax þ1Þ

1  105 1  1011 2.0 1.6 4 2  107 6 ½/1Mðnmax þ1Þ

1  105 1  1011 2.0 1.6 10 2  107 6 ½/2Mðnmax þ1Þ

g

M Ls (m) nmax /m,n

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L. Zhao et al. / Bioresource Technology 222 (2016) 478–484 Table 4 Measured and reconstructed membrane statistical roughness parameters. Roughness

Set 1

Set 2

Set 3

Set 4

Set 5

Set 6

RA (nm) RRMS(nm)

2587.6 3020.2

14.1 17.4

2587.6 3020.2

2924.1 3417.4

3126.4 3267.9

1748.4 2197.3

variable Weierstrass-Mandelbrot (WM) function for fractal surface construction, was proposed for biocake layer surface modeling in this study. The cake layer surface was found to feature obvious fractal properties. Biocake layer surface constructed by the proposed method was rather similar to the reality. Continuous operation of a membrane bioreactor (MBR) experienced significant variation of Df of sludge suspension. Compared with other factors, Df critically affects the surface morphology and roughness of the constructed biocake layer. Acknowledgements

Fig. 5. Variation of the roughness of the constructed biocake surface with Df of biocake sludge.

ness value but highly affects the location and shape of asperities when comparing Fig. 4(e) with Fig. 4(a). Similar conclusion can be drawn on the effects of parameter /m,n from comparison of Fig. 4(f) with Fig. 4(a) when different values in the Supporting Information are assigned to /m,n. It can be concluded from these comparisons that, Df is the predominant factor governing the surface roughness. Effects of Df in a wide range of 1.9–2.5 on the roughness of the constructed biocake surface are shown in Fig. 5. It can be seen that the roughness of the constructed biocake surface exponentially decreases with Df in range of 1.9–2.5 although /m,n is randomly generated in this study. It was reported that biological aggregates typically exhibited fractal dimension values in the range of 1.8–2.5 (Massé et al., 2006). In this study, Df of the sludge suspension underwent a decrease from 2.37 to 1.88 (Fig. 2). This suggested that the biocake layer surface roughness might significantly change with operational time. Surface roughness has been reported to critically affect membrane fouling (Bhattacharjee et al., 1998; Hoek and Agarwal, 2006; Zhao et al., 2015). This study demonstrated the possibility to change surface roughness by changing Df of biocake sludge. It was reported that granular sludge generally possesses higher Df (Hao et al., 2015), indicating that granulation of sludge could improve sludge Df. It was summarized that sludge Df can be significantly changed by adding additives including coagulants, adsorbent agents and carriers into MBRs (Lin et al., 2014), providing the potential measures to control biocake layer surface morphology and membrane fouling. This study gave new insights into biocake layer surface modeling and membrane fouling. This study showed a significant change of Df of biocake during MBR operational period. Although the dynamism of this change is beyond the research scope of this paper (this study focused on development of a new method to model biocake layer surface), it deserves further study in future for better understanding of the fractal characteristics of biocake.

4. Conclusions A novel method, which combines static light scattering method for fractal dimension (Df) measurement with the modified two-

We thank the editor and the anonymous reviewers for their valuable comments and suggestions on revising and improving the work. This study was financially supported by National Natural Science Foundation of China (No. 51578509) and Natural Science Foundation of Zhejiang Province (Nos. Y17E080016, LQ16B060003). Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.biortech.2016.10. 020. References Bhattacharjee, S., Ko, C.-H., Elimelech, M., 1998. DLVO interaction between rough surfaces. Langmuir 14 (12), 3365–3375. Chen, L., Tian, Y., Cao, C.-Q., Zhang, J., Li, Z.-N., 2012. Interaction energy evaluation of soluble microbial products (SMP) on different membrane surfaces: role of the reconstructed membrane topology. Water Res. 46 (8), 2693–2704. Ganczarczyk, J.J., Zahid, W.M., Li, D.-H., 1992. Physical stabilization and embedding of microbial aggregates for light microscopy studies. Water Res. 26 (12), 1695– 1699. Gao, D., Fu, Y., Ren, N., 2013. Tracing biofouling to the structure of the microbial community and its metabolic products: a study of the three-stage MBR process. Water Res. 47 (17), 6680–6690. Gao, W.J., Lin, H.J., Leung, K.T., Schraft, H., Liao, B.Q., 2011. Structure of cake layer in a submerged anaerobic membrane bioreactor. J. Membr. Sci. 374 (1–2), 110– 120. Guan, J., Waite, T.D., Amal, R., 1998. Rapid structure characterization of bacterial aggregates. Environ. Sci. Technol. 32 (23), 3735–3742. Hao, T., Luo, J., Wei, L., Mackey, H.R., Liu, R., Rey Morito, G., Chen, G.-H., 2015. Physicochemical and biological characterization of long-term operated sulfate reducing granular sludge in the SANIÒ process. Water Res. 71, 74–84. Hoek, E.M.V., Agarwal, G.K., 2006. Extended DLVO interactions between spherical particles and rough surfaces. J. Colloid Interface Sci. 298 (1), 50–58. Hoek, E.M.V., Bhattacharjee, S., Elimelech, M., 2003. Effect of membrane surface roughness on colloidmembrane DLVO interactions. Langmuir 19 (11), 4836– 4847. Hong, H., Lin, H., Mei, R., Zhou, X., Liao, B.-Q., Zhao, L., 2016. Membrane fouling in a membrane bioreactor: a novel method for membrane surface morphology construction and its application in interaction energy assessment. J. Membr. Sci. 516, 135–143. Hong, H., Peng, W., Zhang, M., Chen, J., He, Y., Wang, F., Weng, X., Yu, H., Lin, H., 2013. Thermodynamic analysis of membrane fouling in a submerged membrane bioreactor and its implications. Bioresour. Technol. 146, 7–14. Jaggard, D.L., Sun, X., 1990. Fractal surface scattering: a generalized Rayleigh solution. J. Appl. Phys. 68 (11), 5456–5462. Jin, B., Wilén, B.-M., Lant, P., 2004. Impacts of morphological, physical and chemical properties of sludge flocs on dewaterability of activated sludge. Chem. Eng. J. 98 (1–2), 115–126. Komvopoulos, K., Yan, W., 1997. A fractal analysis of stiction in microelectromechanical systems. J. Tribol. 119 (3), 391–400. Lin, H., Gao, W., Meng, F., Liao, B.-Q., Leung, K.-T., Zhao, L., Chen, J., Hong, H., 2012. Membrane bioreactors for industrial wastewater treatment: a critical review. Crit. Rev. Environ. Sci. Technol. 42 (7), 677–740.

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