The chlorophyll content of the samples of D. salina culture taken each day was determined by measuring the optical density at wavelengths of 645 nm and 663 nm using the method described by Zimmerman et al. [12]. The overall specific growth rate were obtained at the end of the culture growth period as described by Scragg [13], which was estimated from the slope of a semilog plot of ln(C_t/C₀) versus t.

The CO₂ concentration dissolved in the medium was calculated from the current pH using Equation (2), of which the detailed derivation is shown in Appendix A.

Each day, the difference between the concentration of dissolved CO₂ before and after dosing, calculated based on the pH, indicates the amount of CO₂ that has been transferred into the medium (dosed CO₂). The reading taken the following day before dosing indicates the decrease in the dissolved CO₂ and gives the amount of CO₂ uptake by D. salina.

Figure 3 gives the plot of chlorophyll content versus culture time for ALB cultures and flask cultures. Generally, the D. salina cells cultured in ALB, either with or without fluidic oscillator engaged, were growing faster compared with the flask culture. As can be seen in Figure 3, for the flask culture, without daily gas supply the microalgae were growing relatively slowly, with the chlorophyll content increasing from about 0.15 mg·L⁻¹ to eventually 4.30 mg·L⁻¹ through 18 days. In contrast, the algal chlorophyll content in all ALB cultures increased from the similar initial concentration to an even higher point (4.73 - 7.24 mg·L⁻¹) within only 6 days. For these ALB cultures, the active growth phase started from the third day and lasted about 13 days, with the peak varying from 26.43 to 32.65 mg·L⁻¹ (depending on flow rate and dosing method). Entry into stationary phase was observed after about 15 days. In general, about 6 - 8 times higher chlorophyll content was achieved in ALB cultures

than in the flask cultures for the same culture period. It is easily understood that the ALB engaged with microbubble/fine-bubble dosing enables a high mass transfer of CO₂ dissolution and O₂ removal, which makes the culture both CO₂ sufficient and O₂ stripped, therefore, algae grew better in such “well served” circumstances. Zimmerman et al. [12] demonstrated a pilot scale microalgal culture using a similar design of ALB as in this study, the results also showed that such ALB culture was neither CO₂ limited nor O₂ inhibited, which led to a high algal growth rate.

Apart from the relatively higher CO₂ mass transfer and an appreciable O₂ stripping by “micro/fine-bubbling”, a better pH control is also one of the reasons that explain why ALB cultures exceeded the flask cultures in productivity. Commonly, pH in the culture medium increases as the algae grows, and when the pH increases beyond the optimum range, the culture may be adversely affected. As algae grow, the photosynthetic uptake of CO₂ leads to the increase in pH, but as a consequence of increasing pH, increases while and CO₂ decrease, which inhibits the photosynthetic reaction and improves the rate of algal respiration [14]. Therefore, for many algal cultures, either buffer solutions (e.g. HEPES) are usually included in culture medium or acid is added when pH increases over a suitable level via an auto-controlled system. However, in this study, neither buffer solution nor acid is added, because it was expected that the increasing pH could be neutralized by daily CO₂ supply via microbubble dosing technique, and indeed the results strongly supported this hypothesis.

Figure 4 shows the daily pH changes in ALB cultures (either with or without fluidic oscillator) and in control experiment (flask cultures). For control experiment, because of the absence of CO₂ supply and the accumulation of O₂, D. salina grew relatively slowly in the first 9 days, with its chlorophyll content increased from 0.15 mg·L⁻¹ to only 3.04 mg·L⁻¹ (Figure 3). Correspondingly, its pH also increased slowly, rising from 7.9 to 9.1 through the first 9 days (Figure 4). However, after 9 days the pH barely increased and was maintained at 9.1 - 9.5, whilst the algae almost stopped growing as well, with its chlorophyll content maintained at 3.04 - 3.33 mg·L⁻¹. One of the reasons is that, after pH went above 9 the culture was inhibited, because for most microalgae the suitable pH ranges from 6 to 9 [15], and over this range inhibition of

growth occurs. In terms of ALB cultures (FO engaged or not), chlorophyll increased dramatically (from around 0.05 - 0.15 mg·L⁻¹ to 26.43 - 32.65 mg·L⁻¹) until the growth entered steady phase (the last 3 days). Correspondingly, pH was supposed to rise even faster than control culture, however, due to daily micro-bubble (300 μm) or fine-bubble (600 μm) dosing, the culture pH was maintained in a suitable range of 6.5 - 8.5 (Figure 4). As can be seen, for each day, after 30 min of 5% CO₂ dosing, pH was reduced to around 7, but because of the desirable culture condition (CO₂ unlimited and O₂ free), pH increased back to about 9 within only one day. The next day, another 30 min of dosing dragged it back to around 7 again. Such a virtuous cycle kept pH within a desirable range, making the culture also not limited by pH.

One thing needs to be clarified that for all ALB cultures in this study, the pH value seems to be similar despite the different dosing flow rates or dosing methods. But theoretically, for various dosing conditions with different mass transfer capabilities, the dissolved CO₂ in the culture medium differs, correspondingly, the pH value indicating the amount of dissolved CO₂ differs as well. Such a ‘contradiction’ can be explained by Table 2. As can be seen, one magnitude of difference in the concentration (mol/L) of dissolved CO₂ only changes the pH by one unit, while the difference in the total CO₂ mass transfers (daily) for this study are in the range of 10⁻⁴ to 10⁻³ mol/L, for different dosing conditions. Therefore, the difference in the pH value was barely affected by the different mass transfer capabilities. This also supports the hypothesis that the pH was scientifically controlled in the study, and it can be considered as a controlled parameter when comparing the impact of mass transfer on the algal growth (see 3.2).

Figure 3 shows the comparison between the ALB cultures with fluidic oscillator engaged and normal ALB

Table 2. The corresponding dissolved CO₂ for different pH values. The amount of CO₂ was calculated based on Equation (2) and on the particulate NaHCO₃ concentration in medium.

culture. Generally, for each dosing flow rate D. salina grew better in FO engaged ALBs (microbubble dosing) than in normal ALBs (fine-bubble dosing). The peak chlorophyll content reached 27.03 - 32.65 mg·L⁻¹ when FO was applied, while only 23.13 - 26.47 mg·L⁻¹ was achieved without FO. To quantify the comparison of D. salina growth under different dosing conditions, the overall specific growth rate was estimated from the slope of a semilog plot of ln(C_t/C₀) versus time. Hence the specific growth rate under each ALB dosing condition was obtained, which was plotted in Figure 5. Generally, fluidic oscillator engaged ALB cultures presented a higher algal specific growth rate (μ), showing an approximately 20% - 40% enhancement compared with conventional ALB cultures. The highest specific growth rate (near 0.13 d⁻¹) for normal ALB culture was achieved at a dosing flow rate of 1.1 L·min⁻¹, while the similar specific growth rate for ALB culture (with FO) was achieved at only 0.1 L·min⁻¹, which shows a considerable energy saving potential.

Generally, the specific growth rate (μ) was found to increase along with dosing flow rate, either with or without FO engaged. The maximum μ of 0.13 d⁻¹ and 0.17 d⁻¹ was achieved at flow rate of 0.9 L·min⁻¹ (without FO) and at 1.1 L·min⁻¹ (with FO), respectively. This overall trend was found similar to gas-liquid mass transfer study [10] (see Figures S1(a) and (b) in Supplementary information). Considering both algal specific growth rate

(Figure 5) and mass transfer coefficient (Figures S1(a) and (b)) under different dosing flow rates, the algal growth appears to be correlated to mass transfer via following hypothesis.

For the ALB cultures with fine-bubble dosing (NoFO), within the flow rate range of 0.3 - 1.1 L·min⁻¹, mass transfer coefficient K_la (either for CO₂ dissolution or for O₂ removal) increased with flow rate, and consequently CO₂ dissolution and O₂ stripping efficiency were enhanced. The culture therefore had more dissolved CO₂ available for algal uptake and less O₂ inhibition. Thus, specific growth rate increased as the flow rate went up. The same scenario was observed for the novel ALB cultures (microbubble dosing) under the flow rate of 0.3 - 0.7 L·min⁻¹. However, the specific growth rate did not significantly increase by further increasing the flow rate when it exceeded 0.7 L·min⁻¹. This can be explained by assuming that for 0.3 - 1.1 L·min⁻¹ of dosing (ALB cultures, NoFO) and 0.3 - 0.7 L·min⁻¹ of dosing (ALB cultures, FO), the daily total amount of CO₂ mass transfer (average CO₂ mass transfer rate × dosing time) did not reach or exceed the saturation concentration, therefore higher mass transfer led to a greater amount of available CO₂, which consequently resulted in a higher growth rate. For the flow rate of 0.9 - 1.1 L·min⁻¹ with mcirobubble dosing, the total CO₂ mass transfer is likely to be excessive (average CO₂ mass transfer rate × dosing time > CO₂ saturation). The extra CO₂ was therefore released to the atmosphere and did not contribute to the algal growth. Thus increasing the flow rate over a valid range may not effectively improve the growth. Based on the above discussion, 30 min·d⁻¹ of dosing under 0.7 L·min⁻¹, close enough to reach CO₂ saturation, turns out to be the optimal dosing condition for the 3L-ALB culture (with microbubble dosing).