## 4 Discussion  
### Effect of High CO\({}_{2}\) Supply  
According to the carbon mass balance analysis, the CO\({}_{2}\) supply was found to be higher than carbon assimilation by _Arthrospina_ in all conditions (Figure 5). Nonetheless, the strong pH buffer contained in alkaliophilic algal media allowed stable pH even with high CO\({}_{2}\) supply, and nearly 100% CO\({}_{2}\) recoveries were achieved for Runs 1 and 2 (Table 2). These results indicate the stability of the CO\({}_{2}\) recovery process using alkaliophilic algae culture. The highest CO\({}_{2}\) supply (Run 3) resulted in lower CO\({}_{2}\) recovery (63%) due to increased [CO\({}_{2}\)]. Absorption of CO\({}_{2}\) led to a reduction of pH and an increase in DIC, both resulting in increased [CO\({}_{2}\)]. When [CO\({}_{2}\)] reached a high level that equilibrated with gas CO\({}_{2}\) concentration, the CO\({}_{2}\) absorption terminated. Similar results were obtained in previous studies that tested CO\({}_{2}\) absorption with high-DIC medium [21; 22]. [PERSON] et al. [22] tested various concentrations of NaHCO\({}_{3}\) and Na\({}_{2}\)CO\({}_{3}\) for CO\({}_{2}\) recovery. Without the addition of alkaline agents, pH reduced from 10 to less than 7 in the first 2 min. On the other hand, >0.3 mol L\({}^{-1}\) of NaHCO\({}_{3}\) and Na\({}_{2}\)CO\({}_{3}\) sustained pH > 9.5 for more than 30 min, resulting in total carbon absorption of up to 2.0 g L\({}^{-1}\). Total absorptivity increased with increasing initial DIC. As such, estimation of the maximal CO\({}_{2}\) absorptivity of the target medium should be necessary for designing an efficient CO\({}_{2}\) recovery system. See Supplementary Material Sections S2 and S3 for the estimation of maximal CO\({}_{2}\) absorptivity of the current experiment.  
The effect of high CO\({}_{2}\) supply rates on _Arthrospira_ growth was minimized because of the separation of the CO\({}_{2}\) absorption column and the PBR, as suggested in previous studies [10; 21; 22]. While pH was reduced to less than 8.5 in the CO\({}_{2}\) absorption column of Runs 2 and 3, it was maintained at around 9.5 in PBRs (Figure 3). Since CO\({}_{2}\) absorption reached oversaturation in the absorption column of Run 3, further CO\({}_{2}\) absorption was prevented, which worked as a protection to avoid excess carbon supply for _Arthrospira_ growth. Since the optimum pH of _Arthrospira_ is 9.8, and its 20% growth reduction is estimated at pH < 9.2 [17], such protection worked effectively to prevent growth reduction.  
Figure 5: Carbon mass balance analysis of the experiments with CO\({}_{2}\) supply rate of Run 1 (16 mmol L-PBR d\({}^{-1}\)), Run 2 (33 mmol L-PBR d\({}^{-1}\)), and Run 3 (49 mmol L-PBR d\({}^{-1}\)). \(C_{in}\) represents a cumulative CO\({}_{2}\) supply. \(C_{out}\) mainly consisted of algal biomass (particulate organic carbon; POC), dissolved inorganic carbon (DIC) and dissolved organic carbon (DOC) in the medium. Remained CO\({}_{2}\) refers to the unabsorbed gas in the absorption columns.  
Carbon mass balance suggested a negligible escape of DIC from PBRs to the atmosphere as gaseous CO\({}_{2}\), although [CO\({}_{2}\)] was higher than air-equilibrium level (Figure 3a; cf. Section 3.1). This contradictory result could be explained by the prevention of air exchange between PBR headspace and atmosphere owing to the air-vent filters attached to the PBRs. In practical operations, _Arthospira_ cultures are majorly conducted in an outdoor pond or in an aerated PBR. To prevent DIC escapes in such conditions, CO\({}_{2}\) supply should be adjusted to maintain \(\Delta\)_DIC_ close to the air-equilibrium (in the current condition, \(\Delta\)_DIC_ \(<\) 0.02 mol L\({}^{-1}\)). Such \(\Delta\)_DIC_ level is also preferential for _Arthospira_ culture, since pH \(<\) 9.5 reportedly would increase the risk of contamination [2].