  This article examines the optimal design and ideal kinetic performances of
volumetrically-lightened photobioreactors (PBR). From knowledge models
developed for several years by the author, simple theoretical rules are
established at first to define the optimal functioning of solar and
artificially-lightened PBR. The constructal approach is then used accordingly,
what allows the emergence of the optimal design, or the best lighting
structures assembly, in Cartesian and curvilinear geometries, with a privileged
treatment for the practical case of the 2D-cylindrical geometry. The obtained
results confirm the considerable potential of this approach which is applied
here for the first time to the case of the radiant light transfer in
participating and reactive media. This enables to define clearly, from a
theoretical point of view, the concept of ideal PBR (both for solar or
artificial illuminations), which is demonstrated to correspond exactly in most
cases to volumetrically-lightened PBR, mainly for the solar DiCoFluV (Dilution
Contr\^ol\'ee du Flux en Volume) concept developed in this article. For this
last case, the results of the calculations allow to announce maximal biomass
productivities as thermodynamic limits, what can contribute to clarify a today
confused debate on this point. The work proposed in this article finally
establishes guidelines to conceive more efficient largescale PBR of any desired
geometry and criteria like volume (for artificial illumination) or surface (for
solar illumination) maximum productivities and internal or external
irradiation.
