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.
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