2.1 Fractal dimension

Euclidian geometry describes regular objects such as points, curves, surfaces and cubes using integer dimensions 0, 1, 2 and 3, respectively. Associated with each dimension is a measure of the object such as the length of a line, area of a surface and volume of a cube. However, numerous objects found in nature, such as coastlines, rivers, lakes, porous media are disordered and irregular, which cannot be described by Euclidian geometry due to the scale-dependent measure of length, area, and volume. These objects are called fractals and their dimensions are non-integral and defined as fractal dimensions. A fractal object can be divided into parts, each of which is similar with the whole. However, self-similarity in a global sense is seldom observed in actual applications. Numerous objects found in nature do not exactly exhibit self-similarity, but statistical self-similarity, which implies that these objects exhibit the self-similarity in some average sense [15].

2.2 Modified fouling index (MFI) theory

MFI parameter gives an idea of the fouling potential of the feed. It is based on the cake filtration mechanism, as recently reported by Schippers et al. [13]:

The filtration occurs usually in three stages: (i) the first part is the blocking of the pores, (ii) the second part is the gradual formation of the cake, and (iii) the third part is the compression of the cake. When there is a formation of an incompressible cake, the relation between t/V and V is showed to be linear and the slope of the linear relation will give the indicator MFI which corresponds specifically to the fouling potential of the feed solution. The results of the test are thus a series of measurements of time and cumulated volumes of the permeate.

2.3 Resistance in series model

From Darcy's law, the flux is directly proportional to the transmembrane pressure, as can be written by Eq. (3):

2.4 Streaming-potential (SP) theory

According to the Helmholtz–Smoluchovsky equation, the streaming potential (denoted Δϕ/ΔP), is given by

3.1 Membranes and modules

The membrane used in this study is a flat sheet UF membrane of regenerated cellulose (denoted RC-UF) purchased from Millipore, (France) with a nominal molecular weight cut-off (NMWCO) of 100 kDa. The filtration cell is a dead-end cell (Model 8200, Amicon^®) (see Fig. 1), purchased from Millipore (France). Membranes tested are registered as N°K4SN9799 and purchased from Millipore (France). The permeate mass is determined using an electronic balance with an accuracy of 0.1 mg.

3.2 HA solution

Humic acid solution of 5 mg/L concentration was prepared by dissolving humic acid (supplied by Aldrich, France) in ultrapure water (milliQ water system, Millipore, France). The pH of the obtained solution was determined as 6.5. Humic acid particles have a size distribution around 250 nm and a zeta potential of −30 mV (determined with Zetasizer 4 apparatus, Malvern Inc., US) (see Fig. 2). All experiments were conducted at room temperature (20 °C).

3.3 FESEM analysis

FESEM apparatus is employed with a filed emission gun (JSM-6301F from JEOL, France). Images obtained are from secondary electrons under 3-keV beam energy with magnifications situated between 2000 and 10,000. RC membranes are dissected and glued to a carbon support. Finally, carbon of 2-nm thickness was deposited by evaporation under vacuum (BAL-TEC MED 020 Balzers Lichentstein apparatus).

3.4 Fractal dimension determination

3D-fractal dimensions (3D-FD) was determined using Image J software from the FESEM images plotting log N vs log ɛ, a straight line of slope 2D-FD, enabling the FD of the cake surface or of the membrane surface, to be determined.

3.5 Streaming potential measurements

Fig. 3 shows a photography of the newly designed SP apparatus to follow the zeta potential variations of the membrane before and after fouling with HA solution. To this system two Ag/AgCl electrodes are connected, which in turn are connected to a millivoltmeter (PHM250 from Radiometer Analytical, France) presenting a high enter impedance connected via an RS232 to a PC. The software (denoted proFluid 1.2) was developed in collaboration with NEOSENS (Toulouse, France). For each transmembrane pressure value a corresponding potential difference was indicated on the millivoltmeter, which is automatically transposed to a PC instantaneously. The same experiment is conducted under different pressures (from 0.5 to 3 bar, with a 0.5-bar increment). SP and the correlation coefficient R² are automatically generated. A mean average value of 1 mV/bar is attached to each SP measurement.

The sign of the SP directly yields the sign of the net charge of the membrane, i.e., the global charge behind the shear plane. We connected the positive potential to the feed and the negative to the permeate, then from the slope we obtained directly the sign of the membrane pore walls and consequently the charge density of the membrane pore walls [12,16].

3.6 Seawater experiments

A preliminary experiment was conducted by the ultrafiltration of a seawater sample from Biarritz (France) using the RC 100-kDa membrane during 2 h at a pressure of 3 bar using the pilot design described in Fig. 1. Hydraulic permeability and SP before and after the filtration has been estimated. The SDI of seawater was estimated to be 3.5. Then seawater was pre-filtered on coal, as previously described [17].

4.1 Resistance results

Ultrafiltration (UF) of humic acid solution (5 mg/L, pH 6.7) was carried out at a constant transmembrane pressure of 2 bar for 8000 s. Fig. 4 shows the variation of flux with time both for pure water and for humic acid. It is shown that the pure water flux remained constant (800 L m⁻² h⁻¹). For humic acid, the filtration was rapid during the first few minutes, then it became gradual and reached a quasi-steady state. At the end of the experiment, the decrease of the flux from the initial value was 90%. Humic acid particles were deposited and accumulated on the membrane surface, which gradually developed a cake layer, as illustrated in Fig. 5b and c. Resistance in series model helped to confirm the results about cake filtration formation. As indicated in Fig. 6 in the linear range of the curves, the membrane hydraulic permeability was 390 L m⁻² h⁻¹ bar⁻¹; permeability after adsorption was 380 L m⁻² h⁻¹ bar⁻¹ and the permeability with the cake was 122 L m² h⁻¹ bar⁻¹. The determined values are reported in Table 1. From these results we can understand that the cake formation is the major cause of fouling. Membrane resistance contributes to 46% of the total resistance. Adsorption resistance is only 2%. The cake resistance is the major factor, which is 52% of the total resistance.

The flux decline (loss of 90% of the initial value after 8000 s) is attributed to the formation of a cake, as illustrated on the SEM images (Fig. 5b and c).

Scanning electron micrographs (SEM) of the membrane before and after filtration (Fig. 5a and b) shows the clean membrane surface and the cake deposit on the membrane, respectively. The RC-UF membrane surface before and after filtration by humic acid had totally different morphologies.

Furthermore, during our SEM analysis we analysed a section of the cake (Fig. 5c) which in a magnified form (10,000×) revealed fractal structures (Fig. 7a). From the same image a threshold image is generated using image J software (see Fig. 7b) which permitted us to obtain the FD values. The thickness of the cake from Fig. 6b is estimated as 30 μm.

4.2 Fractal dimension results

Fractal dimension FD, is calculated using the well-known box counting method reported by Mandelbrot [15]. The FD values are reported both in Table 2 and in a double-logarithmic graph in Fig. 8. The slope of the double-logarithmic graph gave the fractal dimension of the image in three dimensions as 2.52. This value was found to be in good correlation with that of particle–cluster aggregation underlying diffusion-limited aggregation, as reported by Witten et al. [18]. The authors also described that particle–cluster aggregation has been shown to lead to flocs with a well-defined fractal dimensionality of 2.51 in three dimensions. Senesi et al. [19] reported that humic acid suspensions in aqueous medium are susceptible to exhibit fractal structures. The authors also found that the value of FD can also change according to different operating conditions, like humic acid solution concentration, pH and ionic strength.

In our study, the aggregates formed are having a complicated multi-branched structure. In these cases, diffusion of the species toward the surface (or heat away from it) can be the rate limiting process [18]. Meakin [20] reported that diffusion-limited deposition on fibres and surfaces also results in open dendrite structures with a “fractal” nature.

Recent results from Aimar et al. [21] show that FD decreases as the hydraulic permeability decreases. On the contrary Meng and Zhang [22] linked FD decrease to porosity increase.

In our case, the presence of the cake changes totally the FD of the initial membrane, FD values are 2.89 and 2.52 for the initial membrane and with the cake, respectively (see Table 2). But we cannot correlate FD with hydraulic permeability decrease because the cake has replaced the RC material by a new material which has its proper FD. More experiments have to be conducted to search correlations between FD values and the macroscopic parameters. We will study the effect of transmembrane pressure, nominal molecular weight cut-off of the membrane, pH and also HA concentration.

Thus, as a microscopic approach, FD can be used as an interesting parameter to describe cake formation and complete the classical flux decline macroscopic approach.

4.3 Fouling indice results

Firstly we have determined the classical SDI (silt density index) following the usual recommendations. The value obtained with the HA solution is 6.2 ± 0.3. SDI is not enough informative as it is dedicated to RO operations. Then a new index denoted as modified fouling index (MFI), which is a macroscopic parameter and a very good indicator of the fouling potential of the feed, is determined as reported by Schippers et al. [13]. The curve obtained (Fig. 9) has three distinct portions which indicate three different stages of filtration. The first part is the adsorption of the solute to the membrane surface, the second part is cake formation and the third part is cake compression. To get the MFI-UF value we determined the slope of the second portion of the curve and obtained 1650 s/L².

4.4 Streaming potential results

We determined the streaming potential (SP) of the membrane before and after filtration with humic acid under fixed pH conditions (pH = 6.5). Fig. 10 illustrates the variation of potential difference(mV) vs transmembrane pressure (bar) obtained using the SP measurements design described above. Both clean and fouled membranes were compared. The charge of the clean membrane was −27 mV/bar and that for the fouled membrane was shown to be −13 mV/bar. From these values, we can conclude that after the cake formation on the surface of the membrane, the charges carried by the membrane pore walls have drastically reduced. This modification of internal pore charge can be attributed to the penetration of lower-size humic acid fractions into the membrane pores which caused also fouling inside the membrane, as recently reported [2]. The same authors [2] characterized the molecular weight of humic acid fractions and found that humic acid fractions extracted from surface water were having molecular weights in the range of 1000–1500 Da, which is very low and can be explained by the SP results obtained in the present study. Further experiments have also demonstrated that NOM fractions are capable to penetrate inside NF membranes pores and can change their internal charges with a displacement of the iep of the membrane. As the size of the humic acid particles in our study is 250 nm and the average pore size of the membrane is 10 nm, it should be theoretically impossible to have fouling inside the pores. But from our SP results we checked that one portion of humic acid particles which are having particle sizes less than 10 nm (or low MW fractions) has entered into the membrane pores and changed the charge of the membrane pore walls.

Fig. 11 presents the pH dependence of zeta potentials (ζ) for a 10⁻³ M KCl solution. It appears to be sensitive to pH shifting as expected with surfaces for which the charging process involves dissociation of ionizable (acidic or basic) surface groups. The isoelectric point (iep), i.e., the particular pH for which the net charge on the membrane surface (and so, the streaming potential) is zero, is found to be close to 2.3 for the clean membrane (value in agreement with Pontie [12]) and for the fouled membrane ∼1.5. It was found that the zeta potential of HA particles that we used to form the cake is −30 mV (see Fig. 2). In principle, the global charge of the membrane in presence of the HA cake should be higher. Even so, the obtained results show that the membrane charge decreases with the HA cake formation. These results can be explained by the fact that conductivities employed to calculate the potential is that of the solution and not conductivities in the pores, which are much higher. In addition, the size of the membrane pores was decreased by deposition of particles on the pore walls.

Considering those results, we can hypothesise also that the membrane should be fouled inside the pores by positive or neutral fractions of the HA solution. Another hypothesis is that the role played by the cake should also be considered, which can also manage the membrane charges independently of the membrane itself. Further experiments have to be done to give a response to those interrogations.

Thus the new semi-automatic SP tool would help us in the future to assess the charge inside the pores caused by very low MW humic acid fractions. At the same time FESEM analysis should be engaged with pore analysis to complete such an approach.

4.5 Preliminary seawater results

As indicated in Fig. 12, in the linear range of the curves, the membrane hydraulic permeability was 757 L m⁻² h⁻¹ bar⁻¹; permeability after seawater filtration was 587 L m⁻² h⁻¹ bar⁻¹ and the permeability after rinsing with ultrapure water during half an hour was 651 L m² h⁻¹ bar⁻¹. At the same time, the SP measured, which was initially −24 mV/bar, decreased to −21 ± 1 mV/bar after fouling. The operation of rinsing had no effect. The attenuation of the charge (less negative) as deduced from the streaming potential measurements also indicates that foulants are also present in the membrane pores. This finding may indicate that fouling agents may correspond to neutral-type structures (i.e. polysaccharides) or possibly positively charged components (i.e. aminosugars) as recently reported [23].