## 3 Results and Discussion  
### Effect of Different Carbon Sources on Microalgal Growth, Pigments, and Nutrient Removal  
As an essential nutrient, carbon sources significantly affect the growth rate, biomass accumulation, physiological metabolism, and target product synthesis in microalgae. Carbon sources serve as fundamental components for photosynthesis and the cellular metabolism, where appropriate carbon supplementation ensures a sufficient carbon availability to enhance the microalgal proliferation and biomass production [35]. Under mixotrophic cultivation, microalgae perform photosynthesis while simultaneously utilizing both CO\({}_{2}\) and organic carbon sources for biomass synthesis. This cultivation mode enables microalgae to integrate phototrophic and heterotrophic metabolic pathways. In other words, they assimilate organic compounds alongside CO\({}_{2}\) during heterotrophic phases, while respired CO\({}_{2}\) is subsequently captured and reutilized through photosynthetic activity [36]. Mixotrophic cultivation faces two key limitations: extreme light levels (low/high) or an insufficient organic carbon supply, both of which restrict cell growth. Many algal species exhibit metabolic flexibility, utilizing both autotrophic and heterotrophic pathways for biomass synthesis. The capacity of mixotrophs to assimilate organic substrates demonstrates that cellular proliferation is not exclusively reliant on photosynthesis, thereby reducing the absolute dependence on light energy as a growth-limiting factor [37]. Representative species with mixotrophic capabilities include the cyanobacterium _Limnospira platensis_ (formerly _Spirulina platensis_) and the green microalga _Chlamydomonas reinhardtii_. Notably, glucose supplementation during both light and dark phases directly affects cell growth [27]. Accordingly, mixotrophic cultivation in wastewater with carbon supplementation seems to be an effective way to boost the algal biomass, achieving dual benefits: an efficient nutrient removal and a simultaneous production of high-value products, such as lipids. Studies have shown that the type and concentration of carbon sources can modulate cellular metabolic pathways, probably altering the energy allocation and carbon flux within microalgal cells [38]. The supplementation of either inorganic or organic carbon sources can improve the microalgae growth and shortens the cultivation time. Typically, microalgae require CO2 to maintain stable pH levels in their growth medium. Recent research has studied how CO2 impacts the algae biomass, lipid and hydrocarbon production, and fatty acid composition [39]. Microalgae can also use soluble carbonate (CO3\({}^{2-}\)) for growth by either directly absorbing it or converting it to CO2 through the enzyme carbonic anhydrase [40]. Hence, to determine the optimal carbon source for biomass production, FACHB-8 was cultivated in ADSW supplemented with six different inorganic/organic carbon sources: sodium carbonate (Na2 CO3), sodium bicarbonate (NaHCO3), sodium acetate (CH3 COONa), glucose, sucrose, and glycerol (10 g/L each). The biomass growth profiles of FACHB-8 under these carbon sources are shown in Figure 2. Table 2 summarizes the biomass production, biomass productivity, maximum biomass productivity, specific growth rate, and maximum specific growth rate of FACHB-8 cultivated in ADSW supplemented with different carbon sources. Figure 2 illustrates that the algal cells in all six carbon-supplemented groups and the control group (CK) exhibited a lag phase during days 0-2. From days 2-6, cells cultured in glucose- or sodium acetate-supplemented ADSW rapidly transitioned to the logarithmic phase, whereas other groups remained in the lag phase (Figure 2). This indicates that the optimal carbon source supplementation shortens the lag phase, accelerates entry into the exponential growth phase, and enhances biomass accumulation. By day 8, growth rates in glucose and sodium acetate groups began to decline as cells entered the stationary phase.