Local rate of photon absorption

Figure 25 Illustration of the Monte Carlo algorithm presented in Section 4.1 for evaluation of the local rate of photon absorption A xc) at any location Xo within the culture volume left panel) the case of the one-dimensional Cartesian configuration shown in Fig. 6 and (right panel) the case of the DiCoFluV photobioreactor presented in Fig. 26.

An alternative approach, based on thermodynamic and biochemical considerations, consists of defining the specific local rate of photon absorption (LRPA), tj expressed in /tmoliu /kg-s represents the amount of photons in the PAR region absorbed per unit weight of biomass and per unit time (Comet et al., 1992 Pmvost and Comet, 2012). The LRPA depends on the mass spectral absorption cross-section of the species and on the spectral fluence rate in the PBR. It can be expressed as (Comet et al., 1992)... 

LVRPA local volumetric rate of photon absorption... 

It is rather atypical that a photochemical reaction will proceed in a single molecular pathway. Thus, several elementary steps are involved. Normally, the majority of them are dark (thermal) reactions while, ordinarily, one activation step is produced by radiation absorption by a reactant molecule or a catalyst. From the kinetics point of view, dark reactions do not require a different methodological approach than conventional thermal or thermal-catalytic reactions. Conversely, the activation step constitutes the main distinctive aspect between thermal and radiation activated reactions. The rate of the radiation activated step is proportional to the absorbed, useful energy through a property that has been defined as the local volumetric rate of photon absorption, LVRPA (Cassano et ak, 1995 Irazoqui et al., 1976) or the local superficial rate of photon absorption, LSRPA (Imoberdorf et al., 2005). The LVRPA represents the amount of photons that are absorbed per unit time and unit reaction volume and the LSRPA the amount of photons that are absorbed per unit time and unit reaction surface. The LVRPA is a property that must be used when radiation absorption strictly occurs in a well-defined three-dimensional (volumetrical) space. On the other hand, to... 

Three different but connected problems must be studied (i) the reaction kinetics model (ii) the development of the rate of electron-hole generation in a material particle of the solid suspension and (iii) the model for characterizing the radiation field to evaluate the local volumetric rate of photon absorption (LVRPA). Point (iii) has been already described in section 6.6.1 for quantum yield determinations. In the first part of this section, we will concentrate on problems (i) and (ii). 

In the earlier example, the local production rate was assumed to be known for the purposes of illustration. Nevertheless, as stated in Section 1 (and detailed in Section 5), is a function of the specific rate of photon absorption A. This is why photobioreactor studies require solution of the radiative transfer equation prior to estimation of the production... 

Determination of the local rate of energy (photons) absorption in pmolft kg s- ... 

Local volumetric rate of energy absorption (LVREA) is defined as the rate of the radiation-activated step in the photochemical reaction and depended on the photon distribution in the reaction space. 

The PC is actually the sum of two processes a fast component, which saturates only at extremely high irradiance levels and a slow component (69). The maximal amplitude amounts only to 10% of the fast component. The fast potential depends solely on the photoconversion rate of the photoreceptor and is the result of a localized calcium influx (67, 68). The late PC is driven by the transport of about 10 elementary charges across the membrane triggered by the absorption of approximately 10 photons. This means there is an amplification of about 10,000 (61). The amplification could be due to the activation of GTP in animal vision one excited rhodopsin can activate up to 500 G proteins, which in turn activate thousands of phosphodiesterase molecules. In Spermatozopsis evidence for the involvement of G-proteins in photoperception was presented (57, 58, 70). Light-dependent GTPase activity in isolated eyespot apparatuses was found with an action spectrum similar to that of rhodopsin absorption. 

Photon absorption rate by a material particle of the suspension. At this point we would like to know the LVRPA by the solid and to be able to isolate this value even if the liquid would also absorb radiation. To do this we need to model absorption by a material particle of the suspension. In the continuum mechanics sense, a material point in space is a volume for which every property can be well defined by a single value. For a catalytic suspension, it will be made of the liquid and the solid phases. Let us consider a small volume V of the suspension space representing this material particle. This volume is located at a point in space x (Figure 6.11). Any point inside V can be defined in terms of a local reference frame f. 

Initially, we will focus on the mesoscopic description associated with the radiative transfer equation. Then, we will introduce the single-scattering approximation and two macroscopic approximations the PI approximation and two-flux approximation. AH of these discussions are based on the configuration shown in Fig. 6. Collimated emission and Lambertian emission wiU also be considered in the discussion later they correspond to the direct component and the diffuse component of solar radiation, respectively. Throughout our study, the biomass concentration Cx is homogeneous in the reaction volume V (assumption of perfect mixing), and the emission phenomena in V are negligible. The concentration Cx is selected close to the optimum for the operation of the photobioreactor the local photon absorption rate. 4 at the rear of the photobioreactor is close to the compensation point A.C (see Section 5 and chapter Industrial Photobioreactors and Scale-up Concepts by Pruvost et al.). 

On the other hand, the specific local photon absorption rate (in [imolhi/ kg s ) (x) = fpyiKkinetic rates and radiant energy absorption rates can be easily formulated from the definition, as for any photo-reactive process (Cassano et al., 1995 Comet and Dussap, 2009 Comet et al., 2003 Pmvost and Comet, 2012), of the overall quantum yield as follows ... 

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