3.2.1. Zeta Potential
Zeta potential data as a function of pH for the experiments performed are shown in
Figure 3 and
Figure 4 for both membranes. The DL membrane has an iso-electrical point (IEP) at pH = 4.1, and NF-99 has the same at pH = 4.7. For both membranes, the surface charge is positive in the lower pH range, passes through the IEP, and then becomes negative in the upper pH range.
The IEP for nanofiltration membranes is mostly found in the pH range of 3 to 6 [
16]. For the Filmtec NF245 (Dow Chemicals, Midland, MI, USA) membrane, an IEP close to 4 has been reported [
21]. In other studies, the IEP for the NF-99 membrane was measured at pH = 4.1–4.4 [
22] and that for DL was measured at pH = 2.7 [
16] and pH = 4.0 [
23]. However, it is very important that we know the electrolyte used, as the IEP can vary depending on the present ionic strength [
21].
Figure 3 shows that a constant value of zeta potential is already reached at pH = 8, while the zeta potential of the NF-99 membrane still slightly decreases above pH = 8. A comparison of the zeta potentials of both membranes shows a similar maximum zeta potential value at about −60 mV in both cases. However, the charge at acidic pH is more important for nanofiltration of FT. Both membranes have a positive zeta potential during nanofiltration of whey at pH = 3. After nanofiltration of FT, the zeta potential curve remains very similar to that of the unfouled membrane and practically overlaps with the zeta potential curve of the clean membranes in both cases.
The zeta potential of FT was determined between −2 and −3 mV, matching the imperceptible changes in the IEP of the two fouled membranes. The unchanged IEP after nanofiltration indicates that the fouling material is not charged or is only very slightly charged [
24], which was the case in the present FT study.
3.2.3. Membrane Fouling Studies and Modeling
The reversible and irreversible fouling of the two NF membranes was determined at 20 bar TMP using Equations (1) and (2). The results are presented in
Table 5.
It was found that irreversible and reversible fouling was lower when tested with DL. Thus, DL is superior to NF-99 due to its lower fouling rate; consequently, chemicals are saved and the environment is protected due to less pollution with less chemicals used for cleaning. In addition, the flux of FT is almost 2 times higher when a DL membrane is used.
Experiments were continued at 20 bar to determine the model of clogging. The curve
J−2 as a function of time was determined according to the result of Equations (3)–(6). R
2 was highest when the cake layer formation model was used (Equation (6)), so only this type of curve is shown (others not shown). In
Figure 7a, it can be seen that the slope
K was determined to be 0.56 and
R2 was 0.95 in the case of the DL membrane. In
Figure 7b, it can be seen that the slope
K for the NF-99 membrane was determined to be 0.015 and
R2 was 0.95. The fit to a linear plot was best when using Equation (6) for both membranes, indicating the formation of a cake layer.
The cake layer forms via the deposition of material on the membrane surface, rather than by penetration into the membrane pores [
17]. On the other hand, the same authors reported that pore blocking may form at the pore entrance, or the pore may be completely blocked. Since the
R2 values of the different types of pore blocking determined by Equations (3)–(5) in
Table 3 were lower, it can be concluded that these fouling mechanisms affect the membrane to a lesser extent. The results are consistent with the calculations of F
ir, which was much lower compared to reversible fouling; the latter is more easily removed from the membrane by back flushing.
In the next step, we fitted the experimental data to Equation (7) to investigate the relationship between time-dependent and time-independent resistance in membrane fouling. All three coefficients in Equation (7) were obtained by nonlinear fitting with experimental plots using GAMS. The values of
a,
b, and τ for both membranes are listed in
Table 6.
An analysis of the coefficient values showed that the membrane characteristics mainly influence the values of the model parameters. Despite the higher flux with the DL membrane, the fouling rate was slower and lower compared to that for NF-99. In the case of NF-99, the flux of FT was lower, and the time-dependent resistance b increased, leading to an earlier reaching of the critical point. When the coefficient a is much larger than b, it indicates membrane resistance [
25]. In our experiments with both membranes, the coefficient a was higher than b, but of the same order of magnitude, implying that fouling resistance is composed of membrane resistance and cake layer resistance. After a very short initial time, less than 1 min, a fouling layer formed. However, the fouling layer was loose and non-adhesive, as also reported in another study [
25]. The initial phase, when only membrane fouling accounts for a major part of the fouling resistance, is very short. Cake layer fouling accounts for a large fraction of resistance in both membranes from almost the beginning of nanofiltration.
In FT, large concentrations of Ca, K, and Fe ions are still present [
6], which contribute to inorganic fouling on the membrane surface. Fouling was alleviated more by the use of the DL membrane due to the intensification of inorganic fouling [
19]. The results in
Figure 5 and
Figure 6 show that the FT flux was lower for the NF-99 membrane, which is probably due to stronger interactions of the inorganic compounds with the NF-99 membrane compared to DL.
The results of nonlinear fitting with the experimental plots are shown in
Figure 8a,b for the DL and NF-99 membranes, respectively. It is evident from
Table 4 and
Figure 8 that there is a very high matching with the modified Tansel model. Hence, it can be concluded that the modified Tansel model is suitable for describing the resistance during whey FT nanofiltration.