Supplemental Information pH Data The modified M8-a media, which was made according to the recipe reported by Klipuis et al. (2010), is essentially unbuffered. Consequently, in the absence of (or at very low concentrations of) algae the solution pH is determined primarily by the CO2 gas-liquid equilibrium and is largely independent of any adjustments to the initial pH. Consequently, by following the protocol used by Kliphuis et al. (2010) and adjusting the initial value of the solution pH to 6.7 immediately prior to inoculating the reactor the solution pH was found to almost instantly decrease from the inoculation value of 6.7 to approximately ~ 6.3 before rapidly increasing over the first day of the experiment to a steady value of 7.4-7.5 as shown in Figure S1 for two typical experiments. Consequently, the solution pH during most of the duration of each experiment was approximately 7.0 – 7.5. Nutrient Depletion in Batch Growth Experiments Figure S2 shows optical density as a function of time for a typical long-duration batch growth experiment for Chlorella vulgaris using M8-a growth media in a Taylor vortex reactor operated at 800 rpm and a cylinder gap width of 2.5 cm. The feed gas consisted of 5 mole percent carbon dioxide and 95 percent nitrogen flowing at 0.1 vvm. The incident light intensity was 250 mol/m2-s. After rapid initial growth followed by a linear regime, growth is arrested at long times (~120-150 hours). Subsequent to reaching this plateau, approximately 40 ml of concentrated stock solution (equivalent to the starting nutrient concentrations) of the M8-a media was added to the culture at the times indicated by the two arrows in Figure S2 and it is evident that the addition of fresh nutrients causes growth to resume. Consequently, it can be concluded that nutrient depletion is a major (and perhaps the primary) cause for cessation of growth at the high biomass concentrations obtained in the batch experiments. Estimation of Light Penetration In order to estimate the reactor dark volume as a function of algal biomass concentration, several light measurement experiments were carried out in the Taylor vortex reactor using a submersible spherical micro quantum sensor (Walz US-SQS/L), and these data were fitted to an exponential function (Beer-Lambert law). Specifically, the photon flux (mol/m2-s) was measured at three radial locations (probe touching the inside surface of the outer cylinder, probe at the middle of the annular gap, and probe touching the outer wall of the inner cylinder) and approximately at the middle of the reactor length. At each measurement radius, readings were taken at three azimuthal locations separated by 120 degrees, and these three readings were used to obtain an average value for each radial position. The resulting data are plotted in Figure S3 for biomass dry weight loadings of 0.84, 1.51, 2.45, and 4.31 g/liter. Subsequently, the pre-factors and exponents for exponential fits of the experimental data were plotted as a function of biomass concentration, and these in turn were fit to lines as shown in Figure S4. Lastly, the linear functions for the preexponential fits and the exponents were used to construct a general equation for the radiant flux as a function of radial position and biomass concentration given by: (S1) where I is the radiant photon flux in mol/m2-s, C is the dry biomass concentration in g/liter, and r is the radial distance (cm) measured from the inside surface of the outer cylinder that forms the annular reaction space. Plots of the resulting radial photon flux distributions for each of the dry biomass concentrations for which data were collected are plotted as solid lines in Figure S3. For a given dry biomass concentration, Eq. (S1) can be used to predict the radial position at which the radiant flux falls below the dark threshold (80 mol/m2-s) and consequently the reactor dark volume fraction can be easily computed. 1