Kinetics and Energetics of Photosynthetic Micro-Organisms in Photobioreactors
175
Light energy dissipation inside a liquid medium considered as non-emitting
and non-fluorescing depends on two independent phenomena: absorption by
pigments and scattering by whole cells. The scattering of radiant light energy
makes the mathematical description of light transfer extremely complex, since
the available energy at any point of the reactor derives both from the main light
source and from all directions as light scattered by the suspension.
The radiative transfer theory [36, 37] provides analytical tools to calculate
local intensity or local energy flux in such complex media. As the specific radiant
light intensity for wavelength ~, Ix, depends on the observation direction (Fig. 3),
variables integrated over all space directions may be used in mathematical
modeling. The radiant energy flux F~ and mean specific intensity J~ for
the wavelength X are defined by the following integrals over the solid angle co
(Fig. 3):
F~ = ~ I~ cos 0 dco
(39)
4 n
J~ = ~ n ~ Ixdo
(40)
Fig. 3. Definitions of specific intensity I, radiant energy flux vector F and available radiant energy
4nJ for radiative transfer theory