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A novel approach for quantitative evaluation of the physicochemical interactions between rough membrane surface and sludge foulants in a submerged membrane bioreactor
Bioresource Technology 171 (2014) 247–252
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A novel approach for quantitative evaluation of the physicochemical interactions between rough membrane surface and sludge foulants in a submerged membrane bioreactor Hongjun Lin a,⇑, Meijia Zhang a, Rongwu Mei b, Jianrong Chen a, Huachang Hong a b
College of Geography and Environmental Sciences, Zhejiang Normal University, Jinhua 321004, PR China Environmental Science Research and Design Institute of Zhejiang Province, Hangzhou 310007, PR China
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
A new method to quantitatively
foulant
assess physicochemical interactions was proposed. Membrane surface morphology highly affected the interaction energies with foulant. The method could serve as a primary tool for membrane fouling study in MBRs.
combined approach R
SEI method
m em br an e
composite Simpson’s rule
a r t i c l e
i n f o
Article history: Received 10 July 2014 Received in revised form 12 August 2014 Accepted 16 August 2014 Available online 23 August 2014 Keywords: Membrane bioreactor Membrane fouling Physicochemical interaction Rough membrane surface
physicochemical interactions
a
MATLAB programming
application in a MBR
rough surface
a b s t r a c t This study proposed a novel approach for quantitative evaluation of the physicochemical interactions between a particle and rough surface. The approach adopts the composite Simpson’s rule to numerically calculate the double integrals in the surface element integration of these physicochemical interactions. The calculation could be achieved by a MATLAB program based on this approach. This approach was then applied to assess the physicochemical interactions between rough membrane surface and sludge foulants in a submerged membrane bioreactor (MBR). The results showed that, as compared with smooth membrane surface, rough membrane surface had a much lower strength of interactions with sludge foulants. Meanwhile, membrane surface morphology significantly affected the strength and properties of the interactions. This study showed that the newly developed approach was feasible, and could serve as a primary tool for investigating membrane fouling in MBRs. Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction With 4 decades development, membrane bioreactor (MBR) has been actively employed in various wastewater treatment and reuse due to its outstanding advantages over conventional activated sludge (CAS) system (Robles et al., 2012; Wu and He, 2012; Abdollahzadeh Sharghi et al., 2014). Nevertheless, ⇑ Corresponding author. Tel./fax: +86 579 82282273. E-mail address: [email protected] (H. Lin). http://dx.doi.org/10.1016/j.biortech.2014.08.074 0960-8524/Ó 2014 Elsevier Ltd. All rights reserved.
effects of surface morphology
membrane fouling, which will rise operating cost and reduce membrane life span, still remains one of the most serious challenges for application of MBR technology (Khan et al., 2009; Lin et al., 2011). Therefore, there have been longstanding interests to study the factors, mechanisms and control strategies of membrane fouling in MBRs. Membrane fouling is directly related with adhesion of sludge matters on membrane surface in MBRs (Yeo et al., 2007; Lin et al., 2014). In disturbed systems like MBRs, hydrodynamic forces resulted from aeration could forward sludge matters nearby
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H. Lin et al. / Bioresource Technology 171 (2014) 247–252
membrane surface. However, the eventual adhesion of these matters to form a foulant layer on membrane surface is determined by the physicochemical interactions between sludge matters and membrane (van Oss, 1994; Hong et al., 2013; Wang et al., 2013). It is therefore of primary importance to quantitatively assess these physicochemical interactions for a given MBR. Generally, physicochemical interactions between two solid surfaces in aqueous medium could be characterized within the framework of the extended Derjaguin–Landau–Verwey–Overbeek (XDLVO) theory, which accounts for Vander Waals (LW), electrostatic double layer (EL), and acid–base (AB) interaction energies (van Oss, 1993). The XDLVO approach allows to quantitatively calculate these three types of interaction energies between two infinite parallel flat plates (van Oss, 1994). However, sludge foulant is generally assumed to be a global particle. In order to calculate the physicochemical interactions between a sphere and an infinite flat plate, Derjaguin approximation (DA) method, which treats sphere surface as a series of concentric rings, was applied (Derjaguin, 1934). While emerging as a convenient calculation approach, this method has several limitations. For example, DA is simply an approximation and is not valid in a strictly mathematical sense (Dantchev and Valchev, 2012). Moreover, this method does not include the effect of geometry of interacting surfaces (Bhattacharjee and Elimelech, 1997; Dantchev and Valchev, 2012). Actually, the surface of membranes used in MBRs was very rough as illustrated by atomic force microcopy (AFM) observation (Hoek et al., 2003; Brant and Childress, 2004; Mahendran et al., 2011; Chen et al., 2012). The limitations of DA method, together with the rough property of membrane surface, give significant impetus to the development of surface element integration (SEI) method (Bhattacharjee and Elimelech, 1997). The SEI method, which integrates the interaction energy per unit area between opposing differential planar elements over the entire surfaces, can circumvent the limitations of DA method (Bhattacharjee and Elimelech, 1997; Dantchev and Valchev, 2012), and thus is expected to enable to quantitatively assess the physicochemical interactions between a sludge foulant and a rough membrane surface. Unfortunately, due to the complicated morphology of membrane surface, it is basically impossible in practice to obtain the antiderivative of integrals in SEI method (Hoek et al., 2003; Hoek and Agarwal, 2006; Chen et al., 2012). This problem highly limits its real application. Particularly, to the best of our knowledge, there has been no specific study investigating the application of SEI method in MBRs. Therefore, it is quite desirable to develop an effective approach to quantitatively assess the physicochemical interactions between a sludge foulant and a rough membrane surface. The primary goal of this study is to develop a combined method which enables to quantitatively compute the physicochemical interactions between sludge foulants and rough membrane surface. In this study, a novel method which combined SEI method with composite Simpson’s rule was firstly established. In order to improve the computational efficiency and accuracy, MATLAB software was applied to complete the mass data computation. Thereafter, this method was applied to calculate the interactions between sludge foulants and membranes with different surface morphologies in a lab-scale MBR. Effects of roughness on the physicochemical interactions were also briefly discussed. 2. Methods 2.1. Analytical methods Sludge samples were taken from sludge suspension in a stablyrunning lab-scale submerged MBR treating synthetic municipal wastewater. The details regarding the MBR system and the
wastewater composition have been reported in a previous study (Zhang et al., 2014). The membrane (0.3 lm normalized pore size) used in the MBR was made of PVDF material, and provided by Shanghai SINAP Co., Ltd. Zeta potentials of sludge foulants and membrane were measured by a Zetasizer Nano ZS (Malvern Instruments Ltd., UK) and A Zeta 90 Plus Zeta Potential Analyzer (Brookhaven Instruments, UK), respectively. Three measurements were performed for each sample. Samples including virgin PVDF membrane and sludge foulants were first treated according to the methods described in Wang et al. (2014). Thereafter, a contact angle meter (Kino industry Co., Ltd., USA) based on the sessile drop method was adopted to determine static contact angles of three probe liquids (ultra-pure water, glycerol and diiodomethane) on these prepared samples. The morphology of the virgin membrane surface was observed by AFM (NT-MDT). Particle size distribution (PSD) of sludge suspension samples was measured through a Malvern Mastersizer 2000 instrument. Calculation of double integrals based on composite Simpson’s rule was executed using MATLAB v5.3. 2.2. XDLVO approach Thermodynamic interactions including LW, EL and AB interaction between sludge foulant and membrane in water can be described by XDLVO theory (van Oss, 1994). The individual XDLVO interaction energy per unit area (DGLW(h), DGAB(h) and DGEL(h)) between two infinite planar surfaces is given by:
DGLW ðhÞ ¼
AH 12ph
ð1Þ
2
DGAB ðhÞ ¼ DGAB D0 exp
h0 h k
DGEL ðhÞ ¼ er e0 jff fm
ð2Þ
! f2f þ f2m 1 ð1 coth jhÞ þ sinh jh 2ff fm
ð3Þ
where h is the separation distance between two planar surfaces; 2
AH (¼ 12ph0 DGLW h0 ) is Hamaker constant; Contact of two planar surfaces is assumed to occur at a hypothetical minimum equilibrium cut-off distance (minimum separation distance (h0), assigned to be 0.158 nm) (Meinders et al., 1995); k (=0.6 nm) is the decay length of AB energy in water; ere0 is the permittivity of sludge suspension; ff and fm are the surface zeta potential of foulant and memAB brane, respectively; j is the reciprocal Debye length; DGLW h0 , DGh0
and DGEL h0 are the LW, AB and EL interaction energy per unit area between two infinite planar surfaces at the minimum separation distance, respectively, which are given by Eqs. 4–6, respectively:
DGLW h0 ¼ 2
qffiffiffiffiffiffiffiffi
cLW m
qffiffiffiffiffiffiffiffiqffiffiffiffiffiffiffiffi
cLW w
cLW f
qffiffiffiffiffiffiffiffi
cLW w
ð4Þ
hpffiffiffiffiffiffipffiffiffiffiffiffi pffiffiffiffiffiffi pffiffiffiffiffiffi pffiffiffiffiffiffiqffiffiffiffiffiffi pffiffiffiffiffiffi pffiffiffiffiffiffi DGAB cþw cf þ cm cw þ cw cþf þ cþm cþw h0 ¼ 2 qffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffii cf cþm cþf cm ð5Þ
DGEL h0
¼
e0 er j 2
" ðn2f
þ
n2m Þ
1 cothðjh0 Þ þ
2nf nm n2f þ n2m
# cschðjh0 Þ
ð6Þ
where cLW, c+ and c are the surface tension parameters of foulant (subscript f), water (subscript w) and membrane (subscript m). The surface tension parameters of a solid material can be calculated by solving a set of three Young’s equations (van Oss, 1994), provided that the contact angle (h) data of three probe liquids (their surface tension parameters are known) on the solid material are measured.
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H. Lin et al. / Bioresource Technology 171 (2014) 247–252
ð1 þ cos hÞ Tol cl ¼ 2
qffiffiffiffiffiffiffiffiqffiffiffiffiffiffiffiffi
cLW cLW þ s l
ffi pffiffiffiffiffi ffipffiffiffiffiffi þ
cl
cs þ
qffiffiffiffiffiffipffiffiffiffiffiffi
cþl cs
ð7Þ
Eqs. 1–3 are only applicable for planar surfaces. Derjaguin approximation (DA) method provides a solution to calculate the interaction AB EL energy components (U LW fwm ðDÞ; U fwm ðDÞ and U fwm ðDÞ) between a spherical object (foulant particle) and planar membrane surface (Derjaguin, 1934). This method can be expressed as Eqs. 8–10: 2
LW U LW fwm ðDÞ ¼ 2pDGh0
h0 R D
ð8Þ
AB U AB fwm ðDÞ ¼ 2pRDDGh0 exp
h0 D k
where D is the closest distance between a particle and membrane surface; R is the particle radius. 3. Results and discussion 3.1. Development of the combined method According to SEI method, the interaction energy between two subjects can be calculated by integrating the interaction energy per unit area (DG(h)) between two differential planar elements over the entire surface:
DGðhÞdA
ð11Þ
where h is the separation distance between two differential surface elements; dA is the differential surface area. Fig. 1 shows the schematics of a foulant particle in the vicinity of a rough membrane surface. As shown in Fig. 1(a), by applying cylindrical coordinate system for the spherical surface of foulant, the total interaction energy can be obtained by integrating differential interaction energies between a series of differential circular rings and rough membrane surface with different vertical distance (h). It can be seen from Fig. 1(a), the differential area of a circular arc in the circular ring can be expressed as:
dA ¼ rdhdr
ð12Þ
where r is the circular ring radius, dh is the differential angle corresponding to the differential circular arc. The vertical distance (h)
(a)
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R2 r 2 f ðr; hÞ
ð13Þ
where la is the height of asperity on membrane surface; f(r, h) is local amplitude directly below the circular arc as a function of the position defined by r and h. Combining Eqs. 1–3 with Eqs. 11–13 could yield equations for calculation of LW, AB and EL interaction energy between sludge foulant and rough membrane surface:
U LW fwm ¼
ð10Þ
Z Z
h ¼ D þ R þ la
ð9Þ
1 þ ejD 2 2 2jD þ n ln 1 e U EL ðDÞ ¼ p e e R 2n n ln þ n r 0 f m f m fwm 1 ejD
UðhÞ ¼
between the differential circular arc and rough membrane surface would vary with both of circular ring position and membrane surface morphology (Fig. 1(b)). The relation can be described as:
U AB fwm ¼
U EL fwm ¼
Z 2p Z 0
ð14Þ
R
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi DGAB D þ R þ la R2 r 2 f ðr; hÞ rdrdh
ð15Þ
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi DGEL D þ R þ la R2 r 2 f ðr; hÞ rdrdh
ð16Þ
0
Z 2p Z 0
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi DGLW D þ R þ la R2 r 2 f ðr; hÞ rdrdh
0
Z 2p Z 0
R
R
0
Because f(r, h) is related with both of r and h, it is generally impossible to get antiderivative of integrals shown in Eqs. 14–16, and thus, unable to quantitatively calculate the physicochemical interactions. In this study, the composite Simpson’s rule was applied to numerically estimate these double integrals. As for double integral, certain point x1 = a, xi = x1 + ih (i = 1, 2, . . ., 2m + 1) and y1 = b, yj = y1 + jk (j = 1, 2, . . ., 2n + 1) were used to subdivide the interval [a, b] of variable x and the interval [c, d] of variable y, respectively. Herein, h = (b a)/2m, and k = (d c)/2n. Defining fi,j as the function value of f(xi, yj), the double integral could be obtained as follows:
Rb Rd a
c
f ðx; yÞdxdy ¼
m X n X Rx
2i
x2i2
R y2j y2j2
f ðx; yÞdxdy hk 9
i¼1 j¼1
m X n X ðf 2i2;2j2 i¼1 j¼1
þ f 2i;2j2 þ f 2i;2j þ f 2i2;2j Þ þ 4ðf 2i1;2j2 þ f 2i;2j1 þ f 2i1;2j þ f 2i2;2j1 Þ þ16f 2i1;2j1 ð17Þ Generally, the greater the value of m and n, the higher the accuracy of the computation. Although the composite Simpson’s rule is an approximate method, it is possible to get results with high accuracy through setting high value of m and n. Detailed calculations showed that, setting m = n = 1600 or above could make the
(b)
Fig. 1. Schematics of a foulant particle on top of rough membrane surface: (a) outline view and (b) side view.
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H. Lin et al. / Bioresource Technology 171 (2014) 247–252
calculation error negligible. However, such an operation would result in an enormous computation amount such that the help of computers has to be sought. MATLAB software was adopted in this study because it could implement the operation much easier as compared with other languages. A MATLAB program with the original code for calculating these double integrals was provided in the Supplementary Data. It was confirmed that, by performing this program in MATLAB software, the three types of interaction energies in a certain separation distance could be obtained. A lot of experimental studies and practical operations have demonstrated the importance of physicochemical interactions in foulant adhesion and foulant layer formation process (Hoek et al., 2003; Brant and Childress, 2004; Chen et al., 2012; Wang et al., 2013; Lin et al., 2014). Quantitative assessment of the physicochemical interactions is of great interest for research community. Some researchers have been attempting to develop methods for quantitative calculation of the physicochemical interactions between foulant and rough membrane surface. For example, Hoek and Agarwal (2006) treated these interactions as sum of sphere–asperity interactions and sphere–flat surface interactions. However, strictly speaking, such a treatment is incorrect, and cannot be applied in real situations. Martines et al. (2008) suggested that these interactions can be calculated by summing the interactions of projected elements on the patterned surface with the projected sphere elements of both hemispheres. Due to the complicated membrane surface morphology, this method is infeasible in operation. So far, no practicable method for quantitative calculation of the physicochemical interactions between foulant and rough membrane surface is available. This study provided a complete set of solution for the quantitative calculation of the physicochemical interactions with rough surface. As long as the surface properties including surface tensions and zeta potential of foulant and membrane are measured, and membrane surface morphology is defined, the physicochemical interactions between foulant and rough membrane surface could be easily computed. Such a combined method also provided a useful tool for membrane selection, membrane fabrication and fouling control for MBR systems. Therefore, the establishment of such a method was of great significance for the development of membrane separation technology as well as MBR technology. 3.2. Application of the combined method 3.2.1. Characterization of surfaces of foulant and membrane The MBR was continuously run for over 300 days. During this period, the synthetic wastewater had a COD concentration of 300 mg/L, while the effluent COD generally leveled at approximately 10 mg/L with a COD removal of over 96%. An apparent cake layer would form on membrane surface in 30–50 days during this period. The cake layer formation resulted in a high rise of transmembrane pressure (TMP), and thus was the main cause of membrane fouling in this study. Table 1 shows the surface properties (including zeta potential and contact angle) of sludge foulant and membrane. Their surface tensions can be calculated based on the data in Table 1, and the results are shown in Table 2. For the sludge samples, c component and absolute value of zeta potential was relatively high. These data
are comparable with those reported in literature (Feng et al., 2009; Su et al., 2013), demonstrating the representativeness of the sludge samples in this study for MBRs. The morphology of membrane surface was characterized by AFM scan (Fig. 2). It can be seen that, a series of asperities (protrusions) and valleys (depressions) with different amplitude and spacing distributing on the membrane surface. The primary parameters characterizing an asperity or valley are its height (la) and radius (ra) (Fig. 2). According to Fig. 2, the average height and radius were estimated to be 92 nm and 106 nm, respectively, in this study. Previous studies (Choi and Ng, 2008; Mahendran et al., 2011; Chen et al., 2012) also reported similar roughness size for the membranes used in MBRs. As a matter of fact, almost all the commercial membranes used in MBRs have a significantly rough surface (Lin et al., 2013). Therefore, assessment of interactions with rough surface is particularly important. PSD analysis showed that a majority of foulant particles in sludge suspension based on number were leveled at a size of about 10 lm. 3.2.2. Physicochemical interactions between foulant and rough membrane Fig. 3 shows the simulated rough membrane surface and distribution of local amplitude directly below the differential circular ring with different roughness. The local amplitude directly below the differential circular ring (f(r, h)) varies significantly with the position defined by r and h. It should be more realistic to define f(r, h) as a sine function rather than a semicircle. Previous studies also demonstrated the feasibility of assigning a sine function for reproducing 1-D structures of membrane surface (Whitehead and Verran, 2006; Verran et al., 2010). There were two types of sine functions assigned for f(r, h) in this study. One (termed as ‘‘morphology 1’’, Eq. (18)) was suggested by literature studies (Whitehead and Verran, 2006; Verran et al., 2010), the other (termed as ‘‘morphology 2’’, Eq. (19)) was proposed in this study:
f ðr; hÞ ¼ la sinðpr cos h=2r a þ /Þ
ð18Þ
f ðr; hÞ ¼ la sinðpr=2r a þ /Þ sinðprh=2r a þ /Þ
ð19Þ
where / is a phase shift of the sine function (assumed to be zero for simplicity in this study). By using this combined method, the interaction energies between foulant and rough membrane surface in the entire short-ranged separation distance range can be computed. Fig. 4 shows the interaction energy profiles for foulant-rough membrane surface combinations and foulant-smooth membrane surface combination. It is notable that there exists a repulsive energy barrier in the profile of total interaction energy with separation distance. Existence of an energy barrier suggested that, only those foulants with energy higher than the energy barrier have the opportunity to adhere to membrane surface. Hydrodynamic forces could render foulants different kinetic energies, and then take a role in the foulant adhesion process. Meanwhile, hydrodynamic forces could affect detachment of foulants on membrane surface based on the ‘‘peeling’’ or ‘‘rolling’’ effects which would rise the leverage and separation distance (van Oss, 1997; Hong et al., 2014). As shown in Fig. 4, as compared with smooth membrane, rough membrane surfaces possess weaker interaction strength with foulant particle. This result indicates that, under the conditions of this study,
Table 1 Contact angle and zeta potential data for membrane and sludge foulant. Materials
PVDF membrane Sludge foulant
Contact angle (°)
Zeta potential (mV)
Water
Glycerol
Diiodomethane
59.59 (±1.34) 69.77 (±0.61)
52.30 (±1.74) 70.50 (±1.84)
22.00 (±1.07) 43.17 (±0.34)
31.30 (±1.10) 21.93 (±1.76)
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H. Lin et al. / Bioresource Technology 171 (2014) 247–252 Table 2 Surface tensions, LW, AB and EL interaction energy per unit area (mJ m2) at contact for membrane and sludge foulant. Materials
cLW
c+
c
cAB
cTol
DGLW h0
DGAB h0
DGEL h0
PVDF membrane Sludge foulant
47.17 37.98
0.22 0.04
16.31 17.72
3.78 1.74
50.95 36.24
6.57
18.33
0.16
(a)
300 Total interaction
height
radius
Interaction energy (kT)
200
Fig. 2. AFM image of the rough surface membrane and illustration of an asperity.
(a)
Interaction energy (kT)
(b)
EL interaction
100
Energy barrier
Secondary energy minimum
0 -100
LW interaction AB interaction
-200 100 -300 0
2
4
50
6 8 10 12 14 16 Separation distance (nm) EL interaction
18
20
22
24
Total interaction Secondary energy minimum Energy barrier
0
-50
LW interaction AB interaction
(b)
Interaction energy (kT)
(c)
2500 -100 2000 0 1500
2
4
6
Total interaction
8 10 12 14 16 Separation distance (nm) EL interaction
18
20
22
24
1000 Energy barrier
500
Secondary energy minimum
0 -500 LW interaction
-1000 -1500
AB interaction
-2000 -2500 0
Fig. 3. Simulated rough membrane surface and distribution of local amplitude directly below the differential circular ring with different roughness.
existence of roughness on the membrane surface remarkably reduces interaction strength. Won et al. (2012) observed that the sludge cake formation on the rough membrane surface was significantly reduced compared to that on the smooth membrane surface. The calculation results based on the newly developed method in this study can serve as a theoretical explanation for this experimental observation. The interaction energy profiles for the two types of membrane surface morphologies are also significantly different (Fig. 4(a) and (b)), indicating that the surface morphology significantly affects the interaction energies. As indicated in this study, since membrane surface roughness and morphology significantly affected foulant adhesion process, it is possible to quantitatively design surface morphology for improving the antiadhesion ability of membrane. The combined method established in this study could serve for this purpose. A comprehensive study
2
4
6
8 10 12 14 16 Separation distance (nm)
18
20
22
24
Fig. 4. Profiles of interaction energies between (a) foulant particle and rough membrane with morphology 1, (b) foulant particle and rough membrane with morphology 2, and (c) foulant particle and smooth membrane (asperity height = 92 nm, asperity radius = 106 nm, particle radius = 10 lm, ionic strength = 0.01 mol/L NaCl, pH = 7.0).
regarding how to design membrane surface morphology is very desirable, and will be conducted in near future. 4. Conclusion This study proposed a novel approach which combined surface element integration (SEI) method and composite Simpson’s rule. This approach was successfully applied to quantitatively evaluate the physicochemical interactions between rough membrane surface and sludge foulant in a submerged membrane bioreactor. It was found that, the interaction energies were significantly affected by membrane surface roughness and morphology. This study demonstrated the feasibility of this approach. The newly developed approach had many potential uses in membrane fouling mitigation and membrane design, showing the fundamental significance of this approach for membrane fouling study.
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H. Lin et al. / Bioresource Technology 171 (2014) 247–252
Acknowledgements Financial support of National Natural Science Foundation of China (No. 51108424), Zhejiang Provincial Project of Construction of Science and Technology Infrastructure (No. 2012F10019), and Zhejiang Provincial Environmental Protection Scientific Research Project (No. 2013A024) is highly appreciated.
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.2014.08. 074.
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Khan, S.J., Visvanathan, C., Jegatheesan, V., 2009. Prediction of membrane fouling in MBR systems using empirically estimated specific cake resistance. Bioresour. Technol. 100 (23), 6133–6136. Lin, H., Peng, W., Zhang, M., Chen, J., Hong, H., Zhang, Y., 2013. A review on anaerobic membrane bioreactors: applications, membrane fouling and future perspectives. Desalination 314, 169–188. Lin, H., Wang, F., Ding, L., Hong, H., Chen, J., Lu, X., 2011. Enhanced performance of a submerged membrane bioreactor with powdered activated carbon addition for municipal secondary effluent treatment. J. Hazard. Mater. 192 (3), 1509–1514. Lin, H., Zhang, M., Wang, F., Meng, F., Liao, B.-Q., Hong, H., Chen, J., Gao, W., 2014. A critical review of extracellular polymeric substances (EPSs) in membrane bioreactors: characteristics, roles in membrane fouling and control strategies. J. Membr. Sci. 460, 110–125. Mahendran, B., Lin, H., Liao, B., Liss, S.N., 2011. Surface properties of biofouled membranes from a submerged anaerobic membrane bioreactor after cleaning. J. Environ. Eng. 137 (6), 504–513. Martines, E., Csaderova, L., Morgan, H., Curtis, A.S.G., Riehle, M.O., 2008. DLVO interaction energy between a sphere and a nano-patterned plate. Colloids Surf. A 318 (1–3), 45–52. Meinders, J.M., van der Mei, H.C., Busscher, H.J., 1995. Deposition efficiency and reversibility of bacterial adhesion under flow. J. Colloid Interface Sci. 176 (2), 329–341. Robles, A., Ruano, M.V., García-Usach, F., Ferrer, J., 2012. Sub-critical filtration conditions of commercial hollow-fibre membranes in a submerged anaerobic MBR (HF-SAnMBR) system: the effect of gas sparging intensity. Bioresour. Technol. 114, 247–254. Su, X., Tian, Y., Li, H., Wang, C., 2013. New insights into membrane fouling based on characterization of cake sludge and bulk sludge: an especial attention to sludge aggregation. Bioresour. Technol. 128, 586–592. van Oss, C.J., 1993. Acid–base interfacial interactions in aqueous media. Colloids Surf. A 78, 1–49. van Oss, C.J., 1997. Hydrophobicity and hydrophilicity of biosurfaces. Curr. Opin. Colloid Interface Sci. 2 (5), 503–512. van Oss, C.J., 1994. Interfacial Forces in Aqueous Media. Marcel Dekker, New York. Verran, J., Packer, A., Kelly, P., Whitehead, K.A., 2010. The retention of bacteria on hygienic surfaces presenting scratches of microbial dimensions. Lett. Appl. Microbiol. 50 (3), 258–263. Wang, F., Zhang, M., Peng, W., He, Y., Lin, H., Chen, J., Hong, H., Wang, A., Yu, H., 2014. Effects of ionic strength on membrane fouling in a membrane bioreactor. Bioresour. Technol. 156, 35–41. Wang, Q., Wang, Z., Zhu, C., Mei, X., Wu, Z., 2013. Assessment of SMP fouling by foulant–membrane interaction energy analysis. J. Membr. Sci. 446, 154–163. Whitehead, K.A., Verran, J., 2006. The effect of surface topography on the retention of microorganisms. Food Bioprod. Process. 84 (4), 253–259. Won, Y.J., Lee, J., Choi, D.C., Chae, H.R., Kim, I., Lee, C.H., Kim, I.C., 2012. Preparation and application of patterned membranes for wastewater treatment. Environ. Sci. Technol. 46 (20), 11021–11027. Wu, J., He, C., 2012. Effect of cyclic aeration on fouling in submerged membrane bioreactor for wastewater treatment. Water Res. 46 (11), 3507–3515. Yeo, Y., Jang, N., Cho, J., Kim, K.S., Kim, I.S., 2007. Identification of the effect of extracellular polymeric substances on bacterial adhesion to the membrane surface in a membrane bioreactor using Pseudomonas fluorescens. Water Sci. Technol. 55 (1–2), 35–42. Zhang, Y., Zhang, M., Wang, F., Hong, H., Wang, A., Wang, J., Weng, X., Lin, H., 2014. Membrane fouling in a submerged membrane bioreactor: effect of pH and its implications. Bioresour. Technol. 152, 7–14.
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Bioresource Technology journal homepage: www.elsevier.com/locate/biortech
A novel approach for quantitative evaluation of the physicochemical interactions between rough membrane surface and sludge foulants in a submerged membrane bioreactor Hongjun Lin a,⇑, Meijia Zhang a, Rongwu Mei b, Jianrong Chen a, Huachang Hong a b
College of Geography and Environmental Sciences, Zhejiang Normal University, Jinhua 321004, PR China Environmental Science Research and Design Institute of Zhejiang Province, Hangzhou 310007, PR China
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
A new method to quantitatively
foulant
assess physicochemical interactions was proposed. Membrane surface morphology highly affected the interaction energies with foulant. The method could serve as a primary tool for membrane fouling study in MBRs.
combined approach R
SEI method
m em br an e
composite Simpson’s rule
a r t i c l e
i n f o
Article history: Received 10 July 2014 Received in revised form 12 August 2014 Accepted 16 August 2014 Available online 23 August 2014 Keywords: Membrane bioreactor Membrane fouling Physicochemical interaction Rough membrane surface
physicochemical interactions
a
MATLAB programming
application in a MBR
rough surface
a b s t r a c t This study proposed a novel approach for quantitative evaluation of the physicochemical interactions between a particle and rough surface. The approach adopts the composite Simpson’s rule to numerically calculate the double integrals in the surface element integration of these physicochemical interactions. The calculation could be achieved by a MATLAB program based on this approach. This approach was then applied to assess the physicochemical interactions between rough membrane surface and sludge foulants in a submerged membrane bioreactor (MBR). The results showed that, as compared with smooth membrane surface, rough membrane surface had a much lower strength of interactions with sludge foulants. Meanwhile, membrane surface morphology significantly affected the strength and properties of the interactions. This study showed that the newly developed approach was feasible, and could serve as a primary tool for investigating membrane fouling in MBRs. Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction With 4 decades development, membrane bioreactor (MBR) has been actively employed in various wastewater treatment and reuse due to its outstanding advantages over conventional activated sludge (CAS) system (Robles et al., 2012; Wu and He, 2012; Abdollahzadeh Sharghi et al., 2014). Nevertheless, ⇑ Corresponding author. Tel./fax: +86 579 82282273. E-mail address: [email protected] (H. Lin). http://dx.doi.org/10.1016/j.biortech.2014.08.074 0960-8524/Ó 2014 Elsevier Ltd. All rights reserved.
effects of surface morphology
membrane fouling, which will rise operating cost and reduce membrane life span, still remains one of the most serious challenges for application of MBR technology (Khan et al., 2009; Lin et al., 2011). Therefore, there have been longstanding interests to study the factors, mechanisms and control strategies of membrane fouling in MBRs. Membrane fouling is directly related with adhesion of sludge matters on membrane surface in MBRs (Yeo et al., 2007; Lin et al., 2014). In disturbed systems like MBRs, hydrodynamic forces resulted from aeration could forward sludge matters nearby
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H. Lin et al. / Bioresource Technology 171 (2014) 247–252
membrane surface. However, the eventual adhesion of these matters to form a foulant layer on membrane surface is determined by the physicochemical interactions between sludge matters and membrane (van Oss, 1994; Hong et al., 2013; Wang et al., 2013). It is therefore of primary importance to quantitatively assess these physicochemical interactions for a given MBR. Generally, physicochemical interactions between two solid surfaces in aqueous medium could be characterized within the framework of the extended Derjaguin–Landau–Verwey–Overbeek (XDLVO) theory, which accounts for Vander Waals (LW), electrostatic double layer (EL), and acid–base (AB) interaction energies (van Oss, 1993). The XDLVO approach allows to quantitatively calculate these three types of interaction energies between two infinite parallel flat plates (van Oss, 1994). However, sludge foulant is generally assumed to be a global particle. In order to calculate the physicochemical interactions between a sphere and an infinite flat plate, Derjaguin approximation (DA) method, which treats sphere surface as a series of concentric rings, was applied (Derjaguin, 1934). While emerging as a convenient calculation approach, this method has several limitations. For example, DA is simply an approximation and is not valid in a strictly mathematical sense (Dantchev and Valchev, 2012). Moreover, this method does not include the effect of geometry of interacting surfaces (Bhattacharjee and Elimelech, 1997; Dantchev and Valchev, 2012). Actually, the surface of membranes used in MBRs was very rough as illustrated by atomic force microcopy (AFM) observation (Hoek et al., 2003; Brant and Childress, 2004; Mahendran et al., 2011; Chen et al., 2012). The limitations of DA method, together with the rough property of membrane surface, give significant impetus to the development of surface element integration (SEI) method (Bhattacharjee and Elimelech, 1997). The SEI method, which integrates the interaction energy per unit area between opposing differential planar elements over the entire surfaces, can circumvent the limitations of DA method (Bhattacharjee and Elimelech, 1997; Dantchev and Valchev, 2012), and thus is expected to enable to quantitatively assess the physicochemical interactions between a sludge foulant and a rough membrane surface. Unfortunately, due to the complicated morphology of membrane surface, it is basically impossible in practice to obtain the antiderivative of integrals in SEI method (Hoek et al., 2003; Hoek and Agarwal, 2006; Chen et al., 2012). This problem highly limits its real application. Particularly, to the best of our knowledge, there has been no specific study investigating the application of SEI method in MBRs. Therefore, it is quite desirable to develop an effective approach to quantitatively assess the physicochemical interactions between a sludge foulant and a rough membrane surface. The primary goal of this study is to develop a combined method which enables to quantitatively compute the physicochemical interactions between sludge foulants and rough membrane surface. In this study, a novel method which combined SEI method with composite Simpson’s rule was firstly established. In order to improve the computational efficiency and accuracy, MATLAB software was applied to complete the mass data computation. Thereafter, this method was applied to calculate the interactions between sludge foulants and membranes with different surface morphologies in a lab-scale MBR. Effects of roughness on the physicochemical interactions were also briefly discussed. 2. Methods 2.1. Analytical methods Sludge samples were taken from sludge suspension in a stablyrunning lab-scale submerged MBR treating synthetic municipal wastewater. The details regarding the MBR system and the
wastewater composition have been reported in a previous study (Zhang et al., 2014). The membrane (0.3 lm normalized pore size) used in the MBR was made of PVDF material, and provided by Shanghai SINAP Co., Ltd. Zeta potentials of sludge foulants and membrane were measured by a Zetasizer Nano ZS (Malvern Instruments Ltd., UK) and A Zeta 90 Plus Zeta Potential Analyzer (Brookhaven Instruments, UK), respectively. Three measurements were performed for each sample. Samples including virgin PVDF membrane and sludge foulants were first treated according to the methods described in Wang et al. (2014). Thereafter, a contact angle meter (Kino industry Co., Ltd., USA) based on the sessile drop method was adopted to determine static contact angles of three probe liquids (ultra-pure water, glycerol and diiodomethane) on these prepared samples. The morphology of the virgin membrane surface was observed by AFM (NT-MDT). Particle size distribution (PSD) of sludge suspension samples was measured through a Malvern Mastersizer 2000 instrument. Calculation of double integrals based on composite Simpson’s rule was executed using MATLAB v5.3. 2.2. XDLVO approach Thermodynamic interactions including LW, EL and AB interaction between sludge foulant and membrane in water can be described by XDLVO theory (van Oss, 1994). The individual XDLVO interaction energy per unit area (DGLW(h), DGAB(h) and DGEL(h)) between two infinite planar surfaces is given by:
DGLW ðhÞ ¼
AH 12ph
ð1Þ
2
DGAB ðhÞ ¼ DGAB D0 exp
h0 h k
DGEL ðhÞ ¼ er e0 jff fm
ð2Þ
! f2f þ f2m 1 ð1 coth jhÞ þ sinh jh 2ff fm
ð3Þ
where h is the separation distance between two planar surfaces; 2
AH (¼ 12ph0 DGLW h0 ) is Hamaker constant; Contact of two planar surfaces is assumed to occur at a hypothetical minimum equilibrium cut-off distance (minimum separation distance (h0), assigned to be 0.158 nm) (Meinders et al., 1995); k (=0.6 nm) is the decay length of AB energy in water; ere0 is the permittivity of sludge suspension; ff and fm are the surface zeta potential of foulant and memAB brane, respectively; j is the reciprocal Debye length; DGLW h0 , DGh0
and DGEL h0 are the LW, AB and EL interaction energy per unit area between two infinite planar surfaces at the minimum separation distance, respectively, which are given by Eqs. 4–6, respectively:
DGLW h0 ¼ 2
qffiffiffiffiffiffiffiffi
cLW m
qffiffiffiffiffiffiffiffiqffiffiffiffiffiffiffiffi
cLW w
cLW f
qffiffiffiffiffiffiffiffi
cLW w
ð4Þ
hpffiffiffiffiffiffipffiffiffiffiffiffi pffiffiffiffiffiffi pffiffiffiffiffiffi pffiffiffiffiffiffiqffiffiffiffiffiffi pffiffiffiffiffiffi pffiffiffiffiffiffi DGAB cþw cf þ cm cw þ cw cþf þ cþm cþw h0 ¼ 2 qffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffii cf cþm cþf cm ð5Þ
DGEL h0
¼
e0 er j 2
" ðn2f
þ
n2m Þ
1 cothðjh0 Þ þ
2nf nm n2f þ n2m
# cschðjh0 Þ
ð6Þ
where cLW, c+ and c are the surface tension parameters of foulant (subscript f), water (subscript w) and membrane (subscript m). The surface tension parameters of a solid material can be calculated by solving a set of three Young’s equations (van Oss, 1994), provided that the contact angle (h) data of three probe liquids (their surface tension parameters are known) on the solid material are measured.
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H. Lin et al. / Bioresource Technology 171 (2014) 247–252
ð1 þ cos hÞ Tol cl ¼ 2
qffiffiffiffiffiffiffiffiqffiffiffiffiffiffiffiffi
cLW cLW þ s l
ffi pffiffiffiffiffi ffipffiffiffiffiffi þ
cl
cs þ
qffiffiffiffiffiffipffiffiffiffiffiffi
cþl cs
ð7Þ
Eqs. 1–3 are only applicable for planar surfaces. Derjaguin approximation (DA) method provides a solution to calculate the interaction AB EL energy components (U LW fwm ðDÞ; U fwm ðDÞ and U fwm ðDÞ) between a spherical object (foulant particle) and planar membrane surface (Derjaguin, 1934). This method can be expressed as Eqs. 8–10: 2
LW U LW fwm ðDÞ ¼ 2pDGh0
h0 R D
ð8Þ
AB U AB fwm ðDÞ ¼ 2pRDDGh0 exp
h0 D k
where D is the closest distance between a particle and membrane surface; R is the particle radius. 3. Results and discussion 3.1. Development of the combined method According to SEI method, the interaction energy between two subjects can be calculated by integrating the interaction energy per unit area (DG(h)) between two differential planar elements over the entire surface:
DGðhÞdA
ð11Þ
where h is the separation distance between two differential surface elements; dA is the differential surface area. Fig. 1 shows the schematics of a foulant particle in the vicinity of a rough membrane surface. As shown in Fig. 1(a), by applying cylindrical coordinate system for the spherical surface of foulant, the total interaction energy can be obtained by integrating differential interaction energies between a series of differential circular rings and rough membrane surface with different vertical distance (h). It can be seen from Fig. 1(a), the differential area of a circular arc in the circular ring can be expressed as:
dA ¼ rdhdr
ð12Þ
where r is the circular ring radius, dh is the differential angle corresponding to the differential circular arc. The vertical distance (h)
(a)
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R2 r 2 f ðr; hÞ
ð13Þ
where la is the height of asperity on membrane surface; f(r, h) is local amplitude directly below the circular arc as a function of the position defined by r and h. Combining Eqs. 1–3 with Eqs. 11–13 could yield equations for calculation of LW, AB and EL interaction energy between sludge foulant and rough membrane surface:
U LW fwm ¼
ð10Þ
Z Z
h ¼ D þ R þ la
ð9Þ
1 þ ejD 2 2 2jD þ n ln 1 e U EL ðDÞ ¼ p e e R 2n n ln þ n r 0 f m f m fwm 1 ejD
UðhÞ ¼
between the differential circular arc and rough membrane surface would vary with both of circular ring position and membrane surface morphology (Fig. 1(b)). The relation can be described as:
U AB fwm ¼
U EL fwm ¼
Z 2p Z 0
ð14Þ
R
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi DGAB D þ R þ la R2 r 2 f ðr; hÞ rdrdh
ð15Þ
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi DGEL D þ R þ la R2 r 2 f ðr; hÞ rdrdh
ð16Þ
0
Z 2p Z 0
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi DGLW D þ R þ la R2 r 2 f ðr; hÞ rdrdh
0
Z 2p Z 0
R
R
0
Because f(r, h) is related with both of r and h, it is generally impossible to get antiderivative of integrals shown in Eqs. 14–16, and thus, unable to quantitatively calculate the physicochemical interactions. In this study, the composite Simpson’s rule was applied to numerically estimate these double integrals. As for double integral, certain point x1 = a, xi = x1 + ih (i = 1, 2, . . ., 2m + 1) and y1 = b, yj = y1 + jk (j = 1, 2, . . ., 2n + 1) were used to subdivide the interval [a, b] of variable x and the interval [c, d] of variable y, respectively. Herein, h = (b a)/2m, and k = (d c)/2n. Defining fi,j as the function value of f(xi, yj), the double integral could be obtained as follows:
Rb Rd a
c
f ðx; yÞdxdy ¼
m X n X Rx
2i
x2i2
R y2j y2j2
f ðx; yÞdxdy hk 9
i¼1 j¼1
m X n X ðf 2i2;2j2 i¼1 j¼1
þ f 2i;2j2 þ f 2i;2j þ f 2i2;2j Þ þ 4ðf 2i1;2j2 þ f 2i;2j1 þ f 2i1;2j þ f 2i2;2j1 Þ þ16f 2i1;2j1 ð17Þ Generally, the greater the value of m and n, the higher the accuracy of the computation. Although the composite Simpson’s rule is an approximate method, it is possible to get results with high accuracy through setting high value of m and n. Detailed calculations showed that, setting m = n = 1600 or above could make the
(b)
Fig. 1. Schematics of a foulant particle on top of rough membrane surface: (a) outline view and (b) side view.
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H. Lin et al. / Bioresource Technology 171 (2014) 247–252
calculation error negligible. However, such an operation would result in an enormous computation amount such that the help of computers has to be sought. MATLAB software was adopted in this study because it could implement the operation much easier as compared with other languages. A MATLAB program with the original code for calculating these double integrals was provided in the Supplementary Data. It was confirmed that, by performing this program in MATLAB software, the three types of interaction energies in a certain separation distance could be obtained. A lot of experimental studies and practical operations have demonstrated the importance of physicochemical interactions in foulant adhesion and foulant layer formation process (Hoek et al., 2003; Brant and Childress, 2004; Chen et al., 2012; Wang et al., 2013; Lin et al., 2014). Quantitative assessment of the physicochemical interactions is of great interest for research community. Some researchers have been attempting to develop methods for quantitative calculation of the physicochemical interactions between foulant and rough membrane surface. For example, Hoek and Agarwal (2006) treated these interactions as sum of sphere–asperity interactions and sphere–flat surface interactions. However, strictly speaking, such a treatment is incorrect, and cannot be applied in real situations. Martines et al. (2008) suggested that these interactions can be calculated by summing the interactions of projected elements on the patterned surface with the projected sphere elements of both hemispheres. Due to the complicated membrane surface morphology, this method is infeasible in operation. So far, no practicable method for quantitative calculation of the physicochemical interactions between foulant and rough membrane surface is available. This study provided a complete set of solution for the quantitative calculation of the physicochemical interactions with rough surface. As long as the surface properties including surface tensions and zeta potential of foulant and membrane are measured, and membrane surface morphology is defined, the physicochemical interactions between foulant and rough membrane surface could be easily computed. Such a combined method also provided a useful tool for membrane selection, membrane fabrication and fouling control for MBR systems. Therefore, the establishment of such a method was of great significance for the development of membrane separation technology as well as MBR technology. 3.2. Application of the combined method 3.2.1. Characterization of surfaces of foulant and membrane The MBR was continuously run for over 300 days. During this period, the synthetic wastewater had a COD concentration of 300 mg/L, while the effluent COD generally leveled at approximately 10 mg/L with a COD removal of over 96%. An apparent cake layer would form on membrane surface in 30–50 days during this period. The cake layer formation resulted in a high rise of transmembrane pressure (TMP), and thus was the main cause of membrane fouling in this study. Table 1 shows the surface properties (including zeta potential and contact angle) of sludge foulant and membrane. Their surface tensions can be calculated based on the data in Table 1, and the results are shown in Table 2. For the sludge samples, c component and absolute value of zeta potential was relatively high. These data
are comparable with those reported in literature (Feng et al., 2009; Su et al., 2013), demonstrating the representativeness of the sludge samples in this study for MBRs. The morphology of membrane surface was characterized by AFM scan (Fig. 2). It can be seen that, a series of asperities (protrusions) and valleys (depressions) with different amplitude and spacing distributing on the membrane surface. The primary parameters characterizing an asperity or valley are its height (la) and radius (ra) (Fig. 2). According to Fig. 2, the average height and radius were estimated to be 92 nm and 106 nm, respectively, in this study. Previous studies (Choi and Ng, 2008; Mahendran et al., 2011; Chen et al., 2012) also reported similar roughness size for the membranes used in MBRs. As a matter of fact, almost all the commercial membranes used in MBRs have a significantly rough surface (Lin et al., 2013). Therefore, assessment of interactions with rough surface is particularly important. PSD analysis showed that a majority of foulant particles in sludge suspension based on number were leveled at a size of about 10 lm. 3.2.2. Physicochemical interactions between foulant and rough membrane Fig. 3 shows the simulated rough membrane surface and distribution of local amplitude directly below the differential circular ring with different roughness. The local amplitude directly below the differential circular ring (f(r, h)) varies significantly with the position defined by r and h. It should be more realistic to define f(r, h) as a sine function rather than a semicircle. Previous studies also demonstrated the feasibility of assigning a sine function for reproducing 1-D structures of membrane surface (Whitehead and Verran, 2006; Verran et al., 2010). There were two types of sine functions assigned for f(r, h) in this study. One (termed as ‘‘morphology 1’’, Eq. (18)) was suggested by literature studies (Whitehead and Verran, 2006; Verran et al., 2010), the other (termed as ‘‘morphology 2’’, Eq. (19)) was proposed in this study:
f ðr; hÞ ¼ la sinðpr cos h=2r a þ /Þ
ð18Þ
f ðr; hÞ ¼ la sinðpr=2r a þ /Þ sinðprh=2r a þ /Þ
ð19Þ
where / is a phase shift of the sine function (assumed to be zero for simplicity in this study). By using this combined method, the interaction energies between foulant and rough membrane surface in the entire short-ranged separation distance range can be computed. Fig. 4 shows the interaction energy profiles for foulant-rough membrane surface combinations and foulant-smooth membrane surface combination. It is notable that there exists a repulsive energy barrier in the profile of total interaction energy with separation distance. Existence of an energy barrier suggested that, only those foulants with energy higher than the energy barrier have the opportunity to adhere to membrane surface. Hydrodynamic forces could render foulants different kinetic energies, and then take a role in the foulant adhesion process. Meanwhile, hydrodynamic forces could affect detachment of foulants on membrane surface based on the ‘‘peeling’’ or ‘‘rolling’’ effects which would rise the leverage and separation distance (van Oss, 1997; Hong et al., 2014). As shown in Fig. 4, as compared with smooth membrane, rough membrane surfaces possess weaker interaction strength with foulant particle. This result indicates that, under the conditions of this study,
Table 1 Contact angle and zeta potential data for membrane and sludge foulant. Materials
PVDF membrane Sludge foulant
Contact angle (°)
Zeta potential (mV)
Water
Glycerol
Diiodomethane
59.59 (±1.34) 69.77 (±0.61)
52.30 (±1.74) 70.50 (±1.84)
22.00 (±1.07) 43.17 (±0.34)
31.30 (±1.10) 21.93 (±1.76)
251
H. Lin et al. / Bioresource Technology 171 (2014) 247–252 Table 2 Surface tensions, LW, AB and EL interaction energy per unit area (mJ m2) at contact for membrane and sludge foulant. Materials
cLW
c+
c
cAB
cTol
DGLW h0
DGAB h0
DGEL h0
PVDF membrane Sludge foulant
47.17 37.98
0.22 0.04
16.31 17.72
3.78 1.74
50.95 36.24
6.57
18.33
0.16
(a)
300 Total interaction
height
radius
Interaction energy (kT)
200
Fig. 2. AFM image of the rough surface membrane and illustration of an asperity.
(a)
Interaction energy (kT)
(b)
EL interaction
100
Energy barrier
Secondary energy minimum
0 -100
LW interaction AB interaction
-200 100 -300 0
2
4
50
6 8 10 12 14 16 Separation distance (nm) EL interaction
18
20
22
24
Total interaction Secondary energy minimum Energy barrier
0
-50
LW interaction AB interaction
(b)
Interaction energy (kT)
(c)
2500 -100 2000 0 1500
2
4
6
Total interaction
8 10 12 14 16 Separation distance (nm) EL interaction
18
20
22
24
1000 Energy barrier
500
Secondary energy minimum
0 -500 LW interaction
-1000 -1500
AB interaction
-2000 -2500 0
Fig. 3. Simulated rough membrane surface and distribution of local amplitude directly below the differential circular ring with different roughness.
existence of roughness on the membrane surface remarkably reduces interaction strength. Won et al. (2012) observed that the sludge cake formation on the rough membrane surface was significantly reduced compared to that on the smooth membrane surface. The calculation results based on the newly developed method in this study can serve as a theoretical explanation for this experimental observation. The interaction energy profiles for the two types of membrane surface morphologies are also significantly different (Fig. 4(a) and (b)), indicating that the surface morphology significantly affects the interaction energies. As indicated in this study, since membrane surface roughness and morphology significantly affected foulant adhesion process, it is possible to quantitatively design surface morphology for improving the antiadhesion ability of membrane. The combined method established in this study could serve for this purpose. A comprehensive study
2
4
6
8 10 12 14 16 Separation distance (nm)
18
20
22
24
Fig. 4. Profiles of interaction energies between (a) foulant particle and rough membrane with morphology 1, (b) foulant particle and rough membrane with morphology 2, and (c) foulant particle and smooth membrane (asperity height = 92 nm, asperity radius = 106 nm, particle radius = 10 lm, ionic strength = 0.01 mol/L NaCl, pH = 7.0).
regarding how to design membrane surface morphology is very desirable, and will be conducted in near future. 4. Conclusion This study proposed a novel approach which combined surface element integration (SEI) method and composite Simpson’s rule. This approach was successfully applied to quantitatively evaluate the physicochemical interactions between rough membrane surface and sludge foulant in a submerged membrane bioreactor. It was found that, the interaction energies were significantly affected by membrane surface roughness and morphology. This study demonstrated the feasibility of this approach. The newly developed approach had many potential uses in membrane fouling mitigation and membrane design, showing the fundamental significance of this approach for membrane fouling study.
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Acknowledgements Financial support of National Natural Science Foundation of China (No. 51108424), Zhejiang Provincial Project of Construction of Science and Technology Infrastructure (No. 2012F10019), and Zhejiang Provincial Environmental Protection Scientific Research Project (No. 2013A024) is highly appreciated.
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.2014.08. 074.
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