*3.2. Copper Loading Capacity of HB-PEI, PE-PEI, and MOD-PEI Using Fly Ash Extract*

Besides the qualitative characterization of the metal binding behavior of the PEIs, Cu loading capacity was also determined. During the stepwise addition of Cu(II) nitrate trihydrate to the feed solution of the PEIs in fly ash extract from KEBAG Zuchwil, each of the three feed solutions became deeper blue. The Cu loading was visible due to the formation of blue tetraamminecopper(II) complexes formed by dissolved Cu(II) and the amino groups of the polymers. As illustrated in Figure 3, HB-PEI shows the highest loading capacity for Cu(II) closely followed by PE-PEI and with a much higher distance MOD-PEI.

**Figure 3.** Cu(II) loading capacity for HB-PEI (4.6 g L<sup>−</sup>1), PE-PEI (4.7 g L−1), and MOD-PEI (3.7 g L−1) using fly ash extract (KEBAG Zuchwil).

The determined Cu(II) loading capacities of HB-PEI and PE-PEI are in the same range as stated in [20]. However, the experiments described in this study were not carried out with real wastewater, but with a synthetic solution containing only copper sulfate. As a remarkable result, the very high concentration of interfering ions in real fly ash extract did not have any influence on the Cu(II) loading capacity of polyethyleneimines. The Cu loading capacity of PE-PEI is slightly lower compared to HB-PEI, because the amino groups are partially ethoxylated and therefore not available for Cu(II) binding. MOD-PEI is even more modified, which leads to an additional reduction of the Cu loading capacity: Even though MOD-PEI showed the highest selectivity for Cu(II) (see Section 3.1), its low Cu loading capacity restricts the applicability for Cu enrichment.

### *3.3. Viscosity of PEI Solutions*

The viscosity of pretreated aqueous MOD-PEI, HB-PEI, and PE-PEI solutions was investigated. The membrane-permeant size fraction of the polymers was removed before measurement according to Section 2.2.3. Polymer concentrations up to 75 g L−<sup>1</sup> were considered at a temperature of 30 ◦C.

The obtained data are given in Table 3. The viscosity of the aqueous solutions rose with increasing polymer concentration. Solutions of HB-PEI (Mw ≈ 25 kDa) showed higher viscosity than solutions of PE-PEI (Mw <sup>≈</sup> 70 kDa), but both remained fluid even at 75 g L−<sup>1</sup> polymer. MOD-PEI (Mw <sup>≈</sup> 2000 kDa) showed far higher viscosity, with gel being formed at >20 g L−<sup>1</sup> polymer.

**Table 3.** Dynamic viscosity of aqueous PEI solutions (30 ◦C). Membrane-permeant size fraction was removed before measurement. Gel was formed with >20 g L−<sup>1</sup> MOD-PEI.


Solutions of HB-PEI and PE-PEI provide a viscosity that is low enough for efficient treatment in tangential flow ultrafiltration, although if very high polymer concentrations in PAUF are desired, the use of PE-PEI may be advantageous [21]. Application of very-high-molecular-weight polymers in PAUF, such as MOD-PEI, is disadvantageous. Even at moderate polymer concentrations, the aqueous solutions cannot be treated properly in tangential flow ultrafiltration.

### *3.4. Operating Data of PAUF Pilot Plant Using HB-PEI*

Operating data of the PAUF pilot plant were investigated by treating a fly ash extract from MVA Ingolstadt containing different concentrations of HB-PEI by tangential flow ultrafiltration. The pilot plant was operated at a transmembrane pressure (TMP) of 5 bar, and the temperature in the filtration circuit was 40 ◦C. The water-soluble polymer was trapped inside the filtration circuit and the polymer-free permeate was led back into the feed reservoir of the pilot plant.

The influence of polymer concentration and tangential velocity on the permeate flux and specific power uptake of the pilot plant are summarized in Figure 4. Power uptake included the power consumption of the pressure and the tangential flow pump. Performance of the tangential flow filtration clearly increased with increasing tangential velocity and decreased with increasing polymer concentration in the filtration circuit.

**Figure 4.** Influence of tangential velocity and polymer concentration on (**a**) permeate flux and (**b**) specific power consumption (pressure and cross-flow pump) of the pilot plant. HB-PEI diluted in fly ash extract. Transmembrane pressure (TMP) = 5 bar, T = 40 ◦C.

PAUF is influenced by gel layer formation [21–23], which occurs in the boundary layer on the membrane surface due to the retention of the water-soluble polymer. This results in additional flow resistance, decreasing the achievable permeate flux and increasing the specific power uptake of the process [35]. Gel layer formation is reduced by increased tangential velocity in tangential flow filtration, as turbulent flow conditions on the membrane surface reduce the thickness of the boundary layer [36]. Consequently, the permeate flux of the pilot plant increased with increasing tangential velocity.

The transition from laminar to turbulent flow regime in the channels of the tubular ceramic membranes appeared at tangential velocities between 0.3 and 0.8 m s−<sup>1</sup> and was observable in a strong decrease of specific power uptake. Depending on the HB-PEI concentration, a minimum specific power uptake was observed at a tangential velocity of about 0.8 m s−<sup>1</sup> (1–10 g L−<sup>1</sup> HB-PEI) and 1.0 m s−<sup>1</sup> (20 and 30 g L−<sup>1</sup> HB-PEI). With further increase of tangential velocity, the specific power uptake rose moderately. This results from the logarithmic rise of the permeate flux, but a disproportional rise of pressure loss in the filtration circuit with increasing tangential velocity occurs.

The permeate flux achieved by the pilot plant is comparable to other work [15,21–23] but rather low. Reasons for this are the very high salt content of the treated fly ash extract, the high water-soluble polymer concentration used in the filtration circuit, and a progressive fouling of the ceramic tubular membranes that were used for the treatment of PEI containing fly ash extract. Irreversible fouling (i.e., by irreversible pore blocking), which cannot be reversed by counter-flushing of the membranes, was significant, but remained in a steady state. So, the pilot plant data given in this work represent realistic conditions using ceramic tubular membranes.
