Appropriate mixing is the basis for sufficient mass transfer in bioprocesses and simultaneously prevents cell sedimentation. On the reactor scale, homogenous con­ditions in terms of equal supply with all nutrients and CO2 is mainly determined by convection while on a cellular scale, mainly turbulent dispersion and diffusion influence mass transfer. Turbulences in the liquid phase reduce diffusion barriers around gas bubbles and therewith enhance not only carbon dioxide supply for pho­tosynthetically active cells but also oxygen removal [23, 34]. Stoichiometric CO2 demand of microalgae is strain-dependent and influenced by the physiological state as well as product formation (e. g., lipid accumulation) but can be considered to be in the range of 1.65 g/g biomass up to 3 g/g biomass for oil rich algae [26]. Low volumetric productivities of phototrophic cultures together with their related CO2 demand imply that the intensity of mass transfer is generally less problematic than in heterotrophic bacterial cultures (up to two magnitudes smaller). Nevertheless, significant gradients along the way of gas bubbles through the reactor can occur. This is mainly caused by the fact that the light path length and therewith depth of a reactor is limited (see above). Consequently, scale-up is restricted to extension in the two other dimensions. Reactor geometries are not inherently comparable between different conceptual design approaches. The occurrence of CO2 and O2 gradients is particularly significant for reactors with long distances between several aeration and degassing points like in tubular reactors [39].

Therefore, hydrodynamics have to be carefully considered to make sure that high local oxygen concentrations, and thus a shift towards photorespiration, are avoided. For some species, oxygen concentrations higher than 120% air saturation can already cause inhibition. High oxygen concentrations can also cause [30] photooxidative damage when algae cultures are exposed to intense sunlight at the same time [10].

Similarly, a balanced distribution of CO2 shall ensure that the local CO2 partial pres­sure does not drop below 0.1-0.2 kPa in any region of the photobioreactor (Fig. 5) [54].

Fig. 5 CFD simulation of a plate bioreactor (height 1 m, width 0.5 m, thickness 0.1 m). The red lines indicate trajectories of volume elements, representing the axial dispersion

If partial pressure drops below that level growth kinetics can be limited [15, 49]. Gradients of CO2 are also related to gradients of pH in the reactor since pH and CO2 concentration are interconnected by the chemical equilibrium of carbon dioxide, hydrogen carbonate, and carbonate [39]. These coherences are shown in Fig. 2 by the intersection of the key areas, “hydrodynamics” and “reaction.”

Mixing times of 100 s (at superficial gas velocities usually below 0.05 m/s) are not unusual for bubble column reactors. Upward liquid movement is induced by aeration; downward movement occurs close to the reactor wall. Axial dispersion coefficients are influenced by the superficial gas velocity and are typically in the range of 0.01-0.02 m2/s. Radial dispersion coefficients, however, are one to two orders of magnitudes lower than axial dispersion coefficients, yet gain special importance in photobioreactors [8]. With regard to the superimposed light field and considering the fact that photosynthesis occurs especially close to the reactor wall, where enough light is available, an equalized gas distribution at the edge of the col­umn is desirable. In addition, radial dispersion fundamentally determines the resi­dence time of cells in dark and illuminated volume elements. Radial dispersion coefficients (especially in volume elements close to the edge of the reactor) can be increased with higher superficial gas velocities, yet shear stress imposed on the cells and high costs of increased auxiliary energy input considerably limit aeration rates.

The interdependency between “hydrodynamics” and “light distribution” (Fig. 2) is further addressed in the following section.