## 2 Materials and Methods
### Sequential Batch Photobioreactor Experimentation  
The sequential batch culture system consisted of a photobioreactor (PBR-1) containing duckweed connected in series to a second photobioreactor (PBR-2) with a microcalga, either _Chlorella_ sp. MC18 or _Scenedesmus_ sp. MJ23-R. The chosen RW to distilled water (DW) proportions (10, 20, and 30%, \(v/v\)) and initial population surface density of duckweed (5.00 g dm\({}^{-2}\)) from results provided by Section 2.3 were used in this experimentation. The hydraulic residence time in each PBR was 0.268 \(\pm\) 0.039 h. At the start of the experiment, PBR-2 containing 3.8 L of RW medium was inoculated with 0.2 L of exponentially growing cells (5% \(v/v\)) of one of the two microalgae as reported earlier [13], where 5.00 g dm\({}^{-2}\) of duckweed biomass was added in PBR-1 containing culture medium based on RW to DW proportions (10%, 20%, and 30%, \(v/v\)). The experiment was run for 96 days, equivalent to 3 cycles, under the conditions described in Section 2.1, a sufficient number of cycles to ensure acclimation of duckweed and microalgae to the cultivation system. The bath culture times in PBR-1 and PBR-2 were 6 and 7 days, respectively, equivalent to hydraulic residence times of 0.280 \(\pm\) 0.041 h and 0.236 \(\pm\) 0.036 h, respectively. Upon completion of each experimental cycle in PBR-1, 3.8 L of treated cheese raw whey (TRW) were transferred to PBR-2 for further treatment, while an equal volume was removed from PBR-2. Only the last cycle was monitored. Thus, at the start and at the end of this last experimental cycle, the chlorophyll concentration in _Lemma minor_ was measured in PBR-1, while cell counting of the culture was also measured in PBR-2 for the estimation of microalgal growth. Both PBR-1 and PBR-2 were identical to those used in a previous study [13]. Inspired by innovative indoor duckweed farming techniques [11], our PBR system utilizes multi-tiered cultivation systems and low-cost LED strip lighting commonly used in horticulture. Commercially available stacking flow-through systems hold promise for large-scale microalgae cultivation, particularly for optimizing duckweed cultivation within horizontally stacked photobioreactors. Recent reports also highlight the integration of stacked horizontal planar waveguide modules for attached cultivation photobioreactors [21]. Briefly, PBRs were flat-panel structures, each comprising a 4 L parallelepiped-shaped glass container (17 cm wide, 35 cm long, 10 cm high). To ensure uniform light exposure and mitigate self-shading, the top-illuminated PBRs maintained a shallow culture depth of 8.5 cm, allowing for potential stacking in scale-up scenarios. Culture medium circulation relied on a submerged centrifugal pump positioned near one PBR wall. Air sparging, at a rate of 2 L min\({}^{-1}\) (0.125 vvmin) for duckweed and 8 L min\({}^{-1}\) (i.e., 0.5 vvmin) for microalgae, utilized compressed air filtered from a compressor. A 12 mm nozzle sparer near the pump outlet facilitated efficient air bubble dispersion, while regularly spaced baffles along the axial axis enhanced culture mixing. Employing a 12 h/12 h light/dark (L/D) cycle, the culture temperature was controlled at 25 \(\pm\) 2 \({}^{\circ}\)C. PBR sterilization and cleaning procedures, detailed elsewhere [13], were executed before use. The initial pH was set at 7.2 and allowed to fluctuate naturally. COD, NO\({}_{3}\)\({}^{-}\), PO\({}_{4}\)\({}^{3-}\), and SO\({}_{4}\)\({}^{2-}\) in the supernatants were monitored regularly. After attaining the stationary phase in PBR-2 within 7 days, the microalgal brodths underwent centrifugation at 23,478 RCF-max for 10 min at 4 \({}^{\circ}\)C. The resulting pellets were delicately rinsed with distilled water. Subsequently, it underwent two additional pelleting cycles, with careful decantation of the supernatants each time.