# _Arthrospira platensis_ Cultivation in a Bench-Scale Helical Tubular Photobioreactor
## 3 Results and Discussion
This finding demonstrates that an increase in PPFD, under non-photoinhibiting conditions, results in an increased dissipation of energy, which is not utilized for photosynthesis. [PERSON] et al. [53] observed a slightly lower PE in a similar horizontally arranged helical reactor (PE = 9.4%) but at a higher PPFD (125 \(\upmu\)mol photons m\({}^{-2}\) s\({}^{-1}\)); however, the photoinhibition threshold was substantially lower (PPFD = 166 \(\upmu\)mol photons m\({}^{-2}\) s\({}^{-1}\)). A comparison with literature data shows that the helical configuration under consideration was able to guarantee a cell concentration substantially higher than those reported for open ponds (\(X_{\rm m}\) = 0.84-1.21 g\({}_{\rm DW}\) L\({}^{-1}\)) [22] and two-plane tubular reactors (\(X_{\rm m}\) = 4.2 g\({}_{\rm DW}\) L\({}^{-1}\)) [54]. In addition, although [PERSON] et al. [55] obtained the best growth parameters for _Arthrospina_ sp. LEB 18 cultures in a tubular photobioreactor with a maximum biomass concentration about 63% higher (1.22 g\({}_{\rm DW}\) L\({}^{-1}\)) than in a raceway pond (0.72 g\({}_{\rm DW}\) L\({}^{-1}\)), these values were lower than those found in the present study. From the results of \(\mu_{\rm X}\) listed in Table 1, one can propose the following empirical second-degree polynomial equation relating this kinetic parameter to PPFD:  
\[\mu_{\rm X}=0.011\ {\rm PPFD}-5.0\ \times 10^{-5}\ {\rm PPFD}^{2}\ ({\rm R}^{2}=0.8498) \tag{5}\]  
which, together with Equation (4), may be usefully employed to optimize this process on an industrial scale. Equations (4) and (5) allowed for estimating two different PPFD ranges (100-120 and 155-170 \(\upmu\)mol photons m\({}^{-2}\) s\({}^{-1}\)) within which cell productivity and specific growth rate reached maximum values of 0.527-0.528 g\({}_{\rm DW}\) L\({}^{-1}\) day\({}^{-1}\) and 0.600-0.605 day\({}^{-1}\), respectively. A flow analysis was finally done to check the suitability of mixing in the photobioreactor because _A. platensis_ suspensions behave as Newtonian and non-Newtonian (pseudoplastic) fluids at low (<2 g L\({}^{-1}\)) and high (>4 g L\({}^{-1}\)) biomass concentrations [56], respectively. For this purpose, to investigate all the mixing conditions possibly occurring in the photobioreactor, the Reynolds number (\(N_{\rm Re}\)) was estimated, according to that study, at culture flowrates in the range of the selected airlift system (0.33-1.4 L min\({}^{-1}\)) using two biomass concentrations (0.05 and 10 g\({}_{\rm DW}\) L\({}^{-1}\)) representative of poor and excellent growth conditions, which were below and over the above threshold values, respectively. As can be seen in Figure 4, the \(N_{\rm Re}\) would range from about 100 and 600 under the former growth conditions and about 600 and 2500 under the latter, with respective values of about 400 and 1900 at the recycling flowrate selected for this study (1.0 L min\({}^{-1}\)), corresponding to a residence time of 4 min and a culture speed of about 6.0 m min\({}^{-1}\). Even  
\begin{table}
\begin{tabular}{c c c c c} \hline
**PPFD 1** & \(X_{\rm m}\) 2 & \(P_{\rm X}\) 3 & \(\mu_{\rm X}\) 4 & **PE 5** \\
**(\(\upmu\)mol photons m\({}^{-2}\) s\({}^{-1}\))** & **(g\({}_{\rm DW}\) L\({}^{-1}\))**  
though the higher value (1900) is about 5% lower than that (2100) required to ensure a turbulence regime [56], which is often considered preferable for satisfactory mixing, it is worth reminding that the mechanical stress under these conditions could lead to the damage of cyanobacterial thricomes [57].