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Simple method for measuring the spectral absorption cross-section of microalgae Razmig Kandilian, Antoine Soulies, Jeremy Pruvost, Benoit Rousseau, Jack Legrand, Laurent Pilon

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Razmig Kandilian, Antoine Soulies, Jeremy Pruvost, Benoit Rousseau, Jack Legrand, et al.. Simple method for measuring the spectral absorption cross-section of microalgae. Chemical Engineering Science, Elsevier, 2016, 146, pp.357-368. 10.1016/j.ces.2016.02.039. hal-01949492

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Chemical Engineering Science

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Simple method for measuring the spectral absorption cross-section of microalgae

Razmig Kandilian a,b, Antoine Soulies b, Jeremy Pruvost b, Benoit Rousseau c, Jack Legrand b, Laurent Pilon a,n a Mechanical and Aerospace Engineering Department, Henry Samueli School of Engineering and Applied Science, University of California, 420 Westwood Plaza, Eng. IV 37-132, Los Angeles, CA 90095, USA b Université de Nantes, GEPEA CNRS, UMR 6144, Bd de l'Université, CRTT - BP 406, 44602 Saint-Nazaire Cedex, France c Laboratoire de Thermocinétique de Nantes, Université de Nantes, UMR CNRS 6607, Nantes, France

HIGHLIGHTS

A simple procedure for measuring microalgae spectral absorption cross-section is proposed. It is based on normal–hemispherical transmittance and reﬂectance measurements. It was validated against direct measurements of the radiation characteristics of C. vulgaris. It can be used for other suspensions of absorbing and scattering particles. It can be used to predict and control light transfer and biomass productivity in PBRs. article info abstract

Article history: The spectral absorption cross-section of microalgae is an essential parameter in modeling the microalgae Received 15 October 2015 metabolism and growth kinetics as well as in estimating the productivity and efficiency of photo- Received in revised form bioreactors. This paper presents a simple experimental procedure for retrieving the average spectral 16 February 2016 absorption cross-section of concentrated microalgal suspensions. The method combines experimental Accepted 23 February 2016 measurements of the normal–hemispherical transmittance and reflectance of the suspensions in con- Available online 3 March 2016 ventional cuvettes with an inverse method and analytical expressions obtained from the modified two- Keywords: flux approximation accounting for absorption and multiple scattering. The method was validated with Light transfer direct measurements of the scattering phase function and of the absorption and scattering cross-sections Photobioreactors of freshwater microalgae Chlorella vulgaris. It was able to retrieve the absorption cross-section with Light absorption acceptable accuracy. The latter was then used to estimate successfully the fluence rate using a simplified Microalgae fl Growth modeling light transfer model, the local rate of photon absorption, and the biomass productivity in at plate PBRs. & 2016 Elsevier Ltd. All rights reserved.

1. Introduction photosynthetic microorganisms (Cornet et al., 1998; Pilon et al., 2011). Illumination conditions within the culture can vary strongly with time Cultivation of photosynthetic microorganisms has received sig- depending on the season, on the local weather, and on the photo- niﬁcant interest in recent years as a way to produce a broad range of adaptation of the microorganisms which reduces or increases their chemical compounds including food supplements, fertilizers, hydro- pigment concentrations under excessive illumination or light limiting gen gas, and lipids for biodiesel production (Richmond, 2004). A wide conditions, respectively. Physical modeling coupling light transfer to variety of microalgae and cyanobacteria species can be cultivated in growth kinetics and metabolic activities can facilitate the optimum design, operation, and control of photobioreactors (Cornet et al., 1992, fresh or brackish waters as well as in seawater. Cultivation typically 1992, 1995; Cornet and Dussap, 2009; Murphy and Berberoğlu, 2011; takes place in outdoor raceway ponds or photobioreactors. Light Pilon et al., 2011; Takache et al., 2010, 2012; Pruvost et al., 2012; transfer in such systems is arguably one of the most important Wheaton and Krishnamoorthy, 2012; Kandilian et al., 2014; Kong and parameters affecting both the growth rate and metabolism of the Vigil, 2014). To do so, knowing the radiation characteristics of microalgae and the amount of light they absorb to drive the photo- n Corresponding author. Tel.: þ1 310 206 5598; fax: þ1 310 206 2302. synthesis is essential. In fact, the radiation characteristics of micro- E-mail address: [email protected] (L. Pilon). organisms vary signiﬁcantly among species (Berberoğlu and Pilon, http://dx.doi.org/10.1016/j.ces.2016.02.039 0009-2509/& 2016 Elsevier Ltd. All rights reserved. 358 R. Kandilian et al. / Chemical Engineering Science 146 (2016) 357–368

ğ μ μ ¼ μμ0 þ 2007; Berbero lu et al., 2008; Heng et al., 2014) or during the culti- geometrical consideration, 0 can be expressed as 0 = = vation process. This is particularly true during nitrogen starvation ð1μ2Þ1 2ð1μ02Þ1 2 (Modest, 2013). used to trigger lipid accumulation (Kandilian et al., 2013; Heng et al., In cases when scatterers are much larger than the radiation 2014; Heng and Pilon, 2014; Kandilian et al., 2014). wavelength, scattering is mainly forward and the scattering phase The goal of the present study is to develop a simple yet accu- function can be estimated based on the transport approximation ðμ Þ¼ þ δð μ Þ rate experimental method for determining the spectral absorption as pλ 0 1 gλ 2gλ 1 0 (McKellar and Box, 1981). Here, cross-section of microalgae over the photosynthetically active δðμÞ is the Dirac delta function and gλ is the asymmetry factor at radiation (PAR) region, corresponding to wavelength between 400 wavelength λ defined as and 700 nm. This method does not require the knowledge of the Z 1 scattering phase function of the microorganisms or the use of a ¼ 1 ðμ Þμ μ : ð Þ gλ pλ 0 0 d 0 3 nephelometer, which can be costly and difficult to operate. 2 1 Moreover, it only requires an integrating sphere spectro- Then, the RTE can be expressed as photometer. It also aims to demonstrate that the use of the Z fi ∂ σ 1 absorption cross-section alone with a simpli ed light transfer μ Iλ ¼ðκ þσ Þ þ s;tr;λ ðμ0; Þ μ0 ð Þ fi ∂ λ s;tr;λ Iλ Iλ z d 4 model is suf cient to predict light transfer, growth kinetics, and z 2 1 biomass productivity of PBRs. The unicellular microalgae Chlorella σ ¼ð Þσ fi vulgaris was used to illustrate the new method because of the where s;tr;λ 1 gλ s;λ is the transport scattering coef cient. interest in the wide range of compounds it can produce. In the context of light transfer in photobioreactors, the absorption and scattering coefficients are linearly proportional to 3 the number density NT of the microalgae cells (in #/m ) and 2. Background expressed as κ ¼ σ ¼ ð Þ λ C abs;λNT and s;λ C sca;λNT 5 2.1. Chlorella vulgaris 2 where C abs;λ and C sca;λ (in m ) are the average spectral absorption Chlorella vulgaris is a unicellular microalgae with spherical and scattering cross-sections of a cell, respectively. Alternatively, shape and 1–6 μm in diameter (Safi et al., 2014). This particular the biomass concentration of the microalgal suspension X, species of green microalgae has garnered special attention for its expressed in mass of dry weight per unit volume (g/L or kg/m3), is large areal biomass productivity and its relatively short cell dou- κ σ often measured instead of NT. Then, one can express λ and s;λ as bling time (Griffiths and Harrison, 2009). In addition, it has been κ ¼ σ ¼ ð Þ identified as a potential source of protein for human and animal λ Aabs;λX and s;λ Ssca;λX 6 feed (Tokuşoglu and Ünal, 2003). It is also an important source for the commercial production of carotenoids and various bio- where Aabs;λ and Ssca;λ are the average spectral mass absorption 2 pharmaceuticals (Mendes et al., 2003). It can also produce lipids to and scattering cross-sections expressed in m /kg dry weight. be converted into biodiesel (Brennan and Owende, 2003). Finally, Typically, the biomass concentration X in conventional PBR vary 3 this freshwater species can be cultivated in wastewater for from 0.1 to 2.0 kg/m (Takache et al., 2010). simultaneous wastewater treatment and production of value- added products (Feng et al., 2011). 2.3. Fluence rate

2.2. One-dimensional radiative transfer equation The local spectral fluence rate GλðzÞ in a PBR is defined as the irradiance incident at location z from all directions. It is expressed 2 2 Fig. 1 shows a schematic of a microalgae suspension of thick- in W/m μmorμmolhν=m s μm and defined, in 1D radiation ness ℓ illuminated with collimated, unpolarized, and normally transfer, as incident light along with the associated coordinate system. Light Z 1 transfer through such absorbing, anisotropically scattering, and GλðzÞ¼2π Iλðz; μÞ dμ: ð7Þ non-emitting suspension can be treated as one-dimensional (1D) 1 along the z-direction taken as the direction of the incident light. It Cornet and co-workers solved the above 1D RTE using the is governed by the 1D radiation transfer equation (RTE) expressed Schuster–Schwarzschild two-flux approximation to predict the in terms of the local spectral light intensity Iλðμ; zÞ (in W/ local fluence rate GλðzÞ in flat plate PBR illuminated on one side m2 sr μm) at location z, in direction θ, and at wavelength λ as with a black (Cornet et al., 1992) or diffusely reflecting (Pottier et (Modest, 2013), Z al., 2005) wall on the other. Their solution accounted for multiple ∂ σ 1 fl ð Þ μ Iλ ¼ðκ þσ Þ þ s;λ ðμ0; μÞ ðμ0; Þ μ0 ð Þ and anisotropic scattering. For example, the local uence rate Gλ z ∂ λ s;λ Iλ pλ Iλ z d 1 z 2 1 in a flat plate PBR with a transparent front window and a diffusely μ ¼ θ κ σ reflecting back wall of reflectance ρλ exposed to collimated spec- where cos is the direction cosine, λ and s;λ are respec- ″ 0 tral irradiance q normally incident onto the photobioreactor as tively the absorption and scattering coefficients while pλðμ ; μÞ is in;λ the azimuthally symmetric scattering phase function. The latter (Pottier et al., 2005), 0 represents the probability that photons coming from direction μ δλL δλL δλz δλL δλL δλz 0 ″ ½ρλð1þαλÞe ð1αλÞe e þ½ð1þαλÞe ρλð1αλÞe e GλðzÞ¼2q ;λ ¼ cos θ be scattered in direction μ ¼ cos θ. It is normalized such in 2 δ L 2 δ L 2 δ L 2 δ L ð1þαλÞ e λ ð1αλÞ e λ ρλð1αλÞe λ þρλð1αλÞe λ that ð Þ Z 8 1 1 0 0 pλðμ ; μÞ dμ ¼ 1: ð2Þ where α and δ are expressed as (Pottier et al., 2005) 2 λ λ 1 vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 0 u qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi For the azimuthally symmetric problem, pλðμ ; μÞ depends only on u t Aabs;λ αλ ¼ and δλ ¼ X A ;λðA ;λ þ2bλS ;λÞ: μ ¼ cos θ0 where θ0 is the angle between the radiation incident abs abs sca 0 0 A ;λ þ2bλS ;λ on the scatterer along direction μ0 ¼ cos θ and the intensity abs sca μ ¼ θ ðμ0; μÞ¼ ðμ Þ ð9Þ scattered in direction cos , i.e., pλ pλ 0 . From R. Kandilian et al. / Chemical Engineering Science 146 (2016) 357–368 359

fi μ = Here, bλ is the backward scattering fraction de ned as photosynthesis, and K and Kr (in molhν kgX s) are, respectively, Z π 1 the half-saturation constant for photosynthesis and the saturation bλ ¼ pλð0; θÞ sin θ dθ: ð10Þ constant describing the inhibition of respiration in light. Note that 2 π=2 the first term on the right hand side of Eq. (15) represents oxygen Microalgae suspensions in PBRs scatter visible light strongly in production due to photosynthesis while the second term repre- the forward direction. Then, bλ tends to zero, αλ approaches unity, sents oxygen consumption due to respiration. Similarly, J and NADH2 δ ¼ ¼ κ ð Þ ν fi fi and λ Aabs;λX λ. Thus, the above expression for Gλ z can be NADH2 O2 are the speci c rate and stoichiometric coef cient of simplified to (Lee et al., 2014) cofactor regeneration on the respiratory chain. The kinetic model

″ ″ ð Þ presented by Eqs. (14) and (15) was developed and experimentally G ðzÞ¼q e Aabs;λXz þρ q e Aabs;λX 2L z : ð11Þ λ in;λ λ in;λ validated for the green microalgae C. reinhardtii by Takache et al. The first term represents the remainder of the incident irradiance (2012). Recently, Pruvost and co-workers (Pruvost et al., 2016; after it has traveled a distance z in the microalgae suspension Soulies et al., 2016) adjusted the model parameter values to adapt while the second term accounts for the incident irradiance that the model to C. vulgaris by fitting the model to experimentally has traveled once through the suspension, got reflected by the measured biomass productivity at various culture dilution rates back wall, and continued traveling a distance ðLzÞ in the sus- and incident irradiances. Detailed description of the kinetic model pension. Note that reflectance ρλ¼0 for PBRs with a transparent parameters as well as how they were estimated can be found in back wall. This simplified expression has been validated against Cornet and Dussap (2009); Takache et al. (2012); Soulies et al. predictions by Eq. (8) and by the numerical solutions of the 3D RTE (2016). Table 1 summarizes the kinetic model parameters and using the discontinuous Galerkin method combined with the their corresponding values for C. vulgaris (Soulies et al., 2016). discrete-ordinate method for outdoor open ponds and flat plate Finally, the LRPA AðzÞ can be expressed as (Cornet et al., 1992; PBRs (Lee et al., 2014). Note that Eq. (11) differs from Beer-Lam- Cornet and Dussap, 2009) Z bert's law in that (i) it depends only on the absorption coefficient 700 κ ¼ fi β ¼ð þ Að Þ¼ ð Þ λ: ð Þ λ Aabs;λX and not on the extinction coef cient λ Aabs;λ Ssca;λ z Aabs;λGλ z d 16 ÞX and (ii) it accounts for reflection within the PBR. More impor- 400 tantly, the simplified expression for the fluence rate GλðzÞ given by Similarly, the mean rate of photon absorption (MRPA) 〈A〉 can be Eq. (11) depends only on the average spectral mass absorption obtained by integrating the LRPA over the volume of the flat-plate cross-section Aabs;λ of the suspension. PBR as Z 1 L 2.4. Growth kinetics and productivity 〈A〉 ¼ AðzÞ dz: ð17Þ L 0 The time rate of change of the microorganism mass con- Here, it is interesting to note that, for strongly forward scattering 〈A〉 ð Þ centration X(t) in continuous cultures satisfies the mass balance media, the MRPA depends only on Gλ, Aabs;λ,andL where Gλ z is equation (Pires, 2015) dX ¼ 〈μ〉X DX ð12Þ dt where D (in h1) is the dilution rate of the culture and 〈μ〉 (in h1) corresponds to the volume-average specific growth rate of the microorganisms. In addition, the volumetric biomass productivity

〈rX 〉 is defined as 〈rX 〉 ¼ 〈μ〉X. For PBRs operated in continuous dX ¼ mode, steady-state conditions are achieved when dt 0. This condition is satisfied when 〈μ〉 ¼ D (Pires, 2015). Several models have been developed to predict the average specific growth rate 〈μ〉 as a function of the illumination conditions in the PBR over the PAR region. The most general approach is to define the average specific growth rate 〈μ〉 over the entire flat- plate PBR depth L from the local growth rate μðzÞ at location z according to (Fouchard et al., 2009) Z 1 L Fig. 1. Schematic of one-dimensional light transfer in a refracting, absorbing, and 〈μ〉 ¼ μðzÞ dz: ð13Þ scattering microalgae suspension illuminated with collimated and normally L 0 incident light. The local growth rate μðzÞ is related to the local oxygen production rate J ðzÞ (in mol =kg s) by Takache et al. (2012) O2 O2 X Table 1 J ðzÞMx μðzÞ¼ O2 : ð14Þ Kinetic model parameters used for predicting biomass productivity of C. vulgaris ν O2 X (Soulies et al., 2016).

Here, M (in kg/mol) is the molar mass of the biomass and ν x O2 X Parameter Value Units the stoichiometric coefﬁcient of the oxygen production. Then, the local oxygen production rate J ðzÞ can be expressed as a function Mx 0.024 kg/mol O2 J : 3 mol =kg s of the local rate of photon absorption (LRPA) AðzÞ according to NADH2 1 80 10 NADH2 ν 1.13 mol =mol (Takache et al., 2012) O2 X O2 X ρM 0.8 0 7 K 0 JNADH Kr ϕ : molO =μmol ν ð Þ¼ρ ϕ Að Þ 2 ð Þ O2 1 10 10 2 h JO z M O z 15 2 þAð Þ 2 ν þAð Þ ν 2 mol =mol K z NADH2 O2 Kr z NADH2 O2 NADH2 O2 4 μ = 0 K 4:0 10 molhν kg s where ρM is the maximum energy yield for photon conversion, ϕ O2 K 500 μmol ν=kg s =μ r h is the quantum yield of O2 (in molO2 molhν) for the Z-scheme of 360 R. Kandilian et al. / Chemical Engineering Science 146 (2016) 357–368

μ = 2 given by Eq. (11). This emphasizes the importance of determining the Pottier et al. (2005). The PBR was illuminated with 200 molhν m spectral mass absorption cross-section Aabs;λ over the PAR region. s white LEDs incident on one side. It was operated in continuous mode by injection of fresh medium at the dilution rate D of 2.5. Microalgae radiation characteristics 0.06 h 1 using a peristaltic pump. The microalgae were grown in modiﬁed Sueoka medium with the following composition (in grams

The radiation characteristics of microalgae can be directly per liter of MilliQ water): NH4Cl 1.45, MgSO4–7H2O 0.28, CaCl2 0.05, measured experimentally (Berberoğlu and Pilon, 2007; Berberoğlu KH2PO4 0.61, NaHCO3 1.68, ZnSO4–7H2O0.022,H3BO3 0.0114, et al., 2008; Pilon et al., 2011) or predicted theoretically (Pottier MnCl2–4H2O 0.00506, CoCl2–6H2O 0.00161, CuSO4–5H2O 0.00157, et al., 2005; Berberoğlu et al., 2007; Dauchet et al., 2015). Direct FeSO4–7H2O 0.00499, (NH4)6Mo7O24–4H2O0.0011,KOH0.05, experimental measurements can be performed on microorganisms Na2EDTA 0.02. The culture temperature was maintained at 22 °C of any size and shape. However, they require expensive equipment thanks to a liquid cooled heat exchanger attached to the stainless and can be time consuming, and need to be repeated for different steel PBR back wall. The culture medium pH was continuously growth conditions, such as different pH, temperature, and/or monitored using a pH sensor (Mettler Toledo SG 3253) and was photon flux density change, as these parameters can alter the maintained at 7.5 by automatically injecting CO2 gas when it radiation characteristics of the microalgae (Berberoğlu et al., 2008; exceeded 7.5. Agitation of the culture was achieved by mechanically Pilon et al., 2011). Recently, Bellini et al. (2014) developed an mixing the culture using a marine propeller attached to an electric experimental method to determine the absorption Aabs;λ and the motor. The culture under steady-state continuous operation had dry ð Þ transport scattering 1 gλ Ssca;λ cross-sections of microalgae. The biomass concentration X of 0.33 g/L. To obtain samples with larger authors measured the total reflectance (diffuse plus specular biomass concentrations, a small volume of culture was harvested reflectance) and the normal–hemispherical transmittance of and centrifuged at 10,000 g (ThermoScientific Sorvall RC 6 Plus, microalgae suspensions using a double integrating sphere spec- Massachusetts, USA) for 5 min at 4 °C and suspended in 3 ml of ð Þ trophotometer and retrieved Aabs;λ and 1 g Ssca;λ using the phosphate buffer saline (PBS) solution. The volume of culture inverse-adding-doubling (IAD) method (Prahl et al., 1993). The sampled was chosen based on the biomass concentration desired microalgae suspensions featured a concentration between for optical measurements and ranged from 0.035 to 111 g/L. Note 1.1 1013 and 2.4 1013 cells/m3. This method was not able to that the biomass concentration of only the most concentrated estimate the absorption and the transport scattering cross-section sample was measured, i.e., 11175 g/L and the biomass concentra- accurately especially for samples with low absorption coefficient. tions of the remaining samples, namely, 55.672.5, 11.170.5, Indeed, the authors stated that “in samples with low absorption 5.5670.25, 1.1170.05, 0.55670.025, and 0.11170.0125 g/L, were and high scattering coefficients, the unwanted light losses may be estimated based on the dilution performed. interpreted by the IAD algorithm as absorption phenomena inside the sample rather than losses in the outside world, leading to an 3.2. Culture characterization overestimation of the absorption coefficient” (Bellini et al., 2014). They recommended for this method to be only used for qualitative The cell size distribution of C. vulgaris was measured using 165 analysis of microalgae cultures. Alternatively, the radiation char- microscope images captured using a digital camera (AxioCam MRc) acteristics of microalgae can be estimated theoretically using mounted on an optical microscope (Zeiss Axio Scope A1). The dia- electromagnetic wave theory and solutions of Maxwell's equations meters of 2873 cells were measured manually using an image pro- such as the Lorenz–Mie theory. However, such theoretical pre- cessing software (Axio Vision Routine) and their volume equivalent dictions rely on several simplifying assumptions such as treating sphere radius was reported for the sake of completeness. These the cells as homogeneous and spherical with some effective results were not used in either experimental approaches investigated. spectral complex index of refraction predicted based on simplified The culture dry biomass concentration X (in g/L) was determined models (Pottier et al., 2005; Berberoğlu et al., 2007; Dauchet et al., gravimetrically by filtering 5 mL of culture through a pre-dried and 2015). For example, fractal colonies and aggregates of microalgae pre-weighed 0.45 μm pore size glass-fiber filter (Whatman GF/F). The (Kandilian et al., 2015) and filamentous cyanobacteria such as filters were dried overnight in an oven at 105 °Candweighed,inan Nostoc pondiforme and Anabaena iyengari (Lee and Pilon, 2013), or analytical balance (Mettler Toledo XA204, Columbus, OH) with a the dumbbell shaped cyanobacteria Synechocystis sp. (Heng et al., sensitivity of 0.1 mg, after being cooled in a desiccator for 10 min. The 2015) cannot be treated as spherical. By contrast, a simple samples were analyzed in triplicates and the reported biomass con- experimental method that is able to determine the absorption centration corresponded to the mean value. In addition, the cell 3 cross-section of microorganisms with any arbitrary shapes and density NT (in #/m )wascountedusinga200μm deep Malassez optical properties could be valuable. counting chamber.

This paper presents a simple method for measuring the spectral The volume fraction of water in the cells xw was estimated absorption cross-section C abs;λ or Aabs;λ from simple and rapid mea- using the relation derived by Pottier et al. (2005) and given by surements of normal–hemispherical transmittance and reflectance of X 1 relatively concentrated suspensions in conventional cuvettes. In fact, x ¼ 1 ð18Þ w N V ρ we have argued that the absorption cross-section is sufficient to T 32 dm predict the local fluence rate GλðzÞ,theMRPA⟨Α⟩,andtheaverage where ρdm corresponds to the density of dry biomass and was 3 growth rate ⟨μ⟩. taken as 1350 kg/m (Dauchet, 2012) while V32 is the cell volume corresponding to the Sauter mean diameter of the microorganisms. The latter is defined as the diameter of a sphere that has the 3. Materials and methods same volume to surface area ratio as the original cell. The concentration of photosynthetic pigments in C. vulgaris 3.1. Microalgae cultivation and sample preparation grown under the above mentioned conditions were estimated spectrometrically in terms of mass of pigments per unit volume of The microalgae C. vulgaris CCAP 211/19 were obtained from the suspension (mg/m3). A volume of 0.5 mL of culture was first cen- culture collection of algae and protozoa (CCAP, Scotland, UK). trifuged at 13,400 rpm (12,100 g) for 10 min. The medium was dis- The microorganisms were cultivated in a 4 cm thick, 1.4 L torus carded and the cells were resuspended in 1.25 mL pure methanol PBR constructed with transparent PMMA described in detail in and sonicated for 10 s. Pigments were extracted for 1 h at 45oCand R. Kandilian et al. / Chemical Engineering Science 146 (2016) 357–368 361

the extract was centrifuged. The optical density ODλ of the super- reference medium (e.g., PBS) denoted by Tnn;λ;ref . Then, the apparent n natant was measured at wavelengths 750, 665, 652, and 480 nm extinction coefficient βλ was defined as (Davies-Colley et al., 1986) using a UV-VIS-NIR spectrophotometer (Agilent Cary 5000, Santa ! n 1 Tnn;λ Clara, CA). All extractions were performed in triplicates. Chlorophyll a βλ ¼ ln : ð22Þ ℓ T ;λ; and b concentrations, respectively denoted by CChla and CChlb (in mg/ nn ref L), were estimated according to the correlations (Ritchie, 2006) In addition, microalgae are relatively large compared with the ¼½ : ð Þþ : ð CChla 8 0962 OD652 OD750 16 5169 OD665 wavelength of light and thus scatter strongly in the forward direction. Þ ℓ 1 1 ð Þ ϵ OD750 V 2 V 1 19 Afraction n of the light that is scattered in the forward direction reaches the detector due to its finite acceptance angle. This fraction ¼ ½ : ð Þ and CChlb 27 4405 OD652 OD750 can be expressed as a function of the scattering phase function pλðθÞ : ð Þ ℓ 1 1 ð Þ 12 1688 OD665 OD750 V 2 V 1 20 previously measured (Agrawal and Mengüç, 1991; Privoznik et al., 1978) where V1 and V2 are the volumes of the culture and of the solvent Z Θ (methanol), respectively while ℓ is the thickness of the cuvette used 1 a ϵn ¼ pλðθÞ sin θ dθ ð23Þ to measure the optical density. Similarly, the total photoprotective 2 0 (PPC) and photosynthetic (PSC) carotenoid concentration CPPC þ PSC (in Θ mg/L) was estimated according to (Strickland and Parsons, 1968) where a is the half acceptance angle of the detector. Then, the apparent extinction coefficient can be related to the actual absorption ¼ ð Þ ℓ 1 1: ð Þ CPPC þ PSC 4 OD480 OD750 V 2 V 1 21 and scattering coefficients by (Davies-Colley et al., 1986), The corresponding mass fraction of pigment “i” per dry weight of n n βλ ϵnκλ βλ ¼ κλ þσ ;λ ϵ σ ;λ so that βλ ¼ : ð24Þ biomass can be estimated as wi ¼ Ci=X. s n s 1ϵn fi κ – 3.3. Direct radiation characteristics measurements The absorption coef cient λ was obtained from normal hemispherical transmittance Tnh;λ measurements. Then, the fi κn 3.3.1. Experiments apparent absorption coef cient λ can be expressed as ! ðμ Þ First, the total scattering phase function p 0 of the microalgae n 1 Tnh;λ suspension was measured at 632.8 nm using a polar nephelometer κλ ¼ ln : ð25Þ ℓ T ;λ; equipped with He–Ne laser. The experimental setup and data nh ref analysis were previously reported in detail by Berberoğlu et al. Due to imperfect reflections at the inner surface of the integrating (2008) and need not be repeated. Due to probe interference with sphere and to the geometry of the experimental setup, the detector the incident laser beam, it was only possible to collect measure- was unable to capture all the scattered light. To account for these ments for scattering angles θ up to 160°. Then, the asymmetry n 0 phenomena, the apparent absorption coefficient κλ can be related to factor g633 and the back-scattered fraction b633 at 632.8 nm were the absorption and scattering coefficients by (Pilon et al., 2011) estimated according to Eqs. (3) and (10), respectively. κn ¼ κ þð ϵ Þσ ð Þ Second, the normal–normal transmittance of dilute suspen- λ λ 1 h s;λ 26 sions of C. vulgaris in a cuvette, denoted by T ;λ, was measured nn where ϵh represents the fraction of scattered light not collected by using a UV-VIS-NIR spectrophotometer equipped with a detector the integrating sphere or not measured by the detector. It accounts ° Θ with a 8 half acceptance angle a (Agilent Cary 5000, Santa Clara, for backward scattered light that does not enter the integrating – CA). The normal hemispherical transmittances Tnh;λ of the same sphere and for forward scattered light that does not reach the suspensions were measured using an integrating sphere attach- detector because of imperfect reflection, for example. This correction ment (Agilent Cary DRA-2500, Santa Clara, CA) to the spectro- factor is assumed to be constant over the PAR region. Davies-Colley photometer. Due to masking by the cuvette holder, the cuvette et al. (1986) assumed that the microalgae did not absorb radiation at area exposed to the normally incident beam was 20 8 mm and wavelength λ .Forexample,λ ¼750 nm for Chlamydomonas rein- o o the cuvette holder was positioned directly in front of the 19 hardtii (Berberoğlu et al., 2008) and Chlorella sp. (Berberoğlu et al., 17 mm opening of the integrating sphere. The size of the incident 2009). At this wavelength, the absorption coefficient vanishes, i.e., beam was 9 5 mm. These measurements were performed with 1 κλ ¼ 0m ,andϵh can be estimated from Eq. (26) as (Pilon et al., 1 cm pathlength quartz cuvettes (11010-40 Hellma Analytics, 2011)

Mülheim, Germany) in the wavelength range from 350 to 750 nm n κλ with 1 nm spectral resolution. To avoid absorption and scattering ϵ ¼ o ð Þ h 1 σ 27 by the growth medium, the microalgae were centrifuged at s;λo 13,400 rpm for 10 min and washed twice with PBS solution and Combining Eqs. (24)–(27) yields the expression for the actual suspended in PBS. Two biomass concentrations were considered, absorption coefficient κλ given, in terms of measurable quantities, by namely 0.035 and 0.049 dry mass g/L. Such dilute suspensions (Pilon et al., 2011) ensure that single scattering prevails so that measurements of ! βn κn Tnn;λ and Tnh;λ can be used in the direct measurements of the n n λ λ κλ ¼ κλ κλ n ð28Þ radiation cross-sections of C. vulgaris. Note that the samples were o n βλ κλ manually shaken prior to each of the transmission measurements o o – fi β so as to prevent sedimentation. The sample normal normal Tnn;λ Finally, the actual extinction coef cient λ can be obtained by sub- – κ fi and normal hemispherical Tnh;λ transmittances were measured stituting λ into Eq. (24).Then,thescatteringcoefcient can be fi σ ¼ β κ three times and the results were averaged for each concentration. computed using the de nition s;λ λ λ. fi κ σ The absorption and scattering coef cients λ and s;λ were 3.3.2. Data analysis divided by the sample dry biomass concentration X to obtain the The extinction coefficient of the microalgae suspension βλ was average spectral mass absorption and scattering cross-sections obtained from normal–normal transmittance measurements. In order Aabs;λ and Ssca;λ according to Eq. (6). The spectral cross-sections fl to correct for the effects of re ection and refraction by the cuvette, the Aabs;λ and Ssca;λ for different cell densities/concentrations should measurements were calibrated using the transmittance of the collapse onto a single line if single and independent scattering 362 R. Kandilian et al. / Chemical Engineering Science 146 (2016) 357–368

ð Þ Fig. 2. Block diagram of the procedure used to retrieve the average mass absorption and transport scattering cross-sections Aabs;λ and 1 gλ S sca;λ of concentrated suspensions at a given wavelength λ from spectral normal–hemispherical transmittance and reﬂectance measurements. We used P¼120 individuals per generation for a maximum of 50 generations. prevailed (Van De Hulst, 1957). This provided further validation of the experimental procedure and data analysis. Finally, the direct measurement method with the previously described apparatus and data analysis were successfully validated by comparing the measurements with predictions by Lorenz–Mie theory for monodisperse spherical latex particles 1.9870.01 or 4.51870.158 μm in diameter (Polysciences Inc., Warrington, PA).

4. Inverse method

4.1. Experiments

– fl The normal hemispherical transmittance Tnh;λ and re ectance Rnh;λ of C. vulgaris suspensions, with mass concentration ranging from 0.111 g/L to 111 g/L, were systematically measured using the above described spectrophotometer/integrating sphere assembly. Measurements for the different concentrations were performed within less than 1 h in order to minimize changes in cell biomass, composition, and pigment concentrations and thus their radiation characteristics during the successive measurements. For the relatively large concentrations considered, multiple scattering prevailed and the direct measurement method, previously described in Section 3.3 and valid for single scattering, could not be used. Fig. 3. Experimentally measured size distribution of C. vulgaris with mean radius Instead, experimentally measured values of T λ and R ;λ were nh; nh r ¼ 1:98 μm. used as input parameters in the inverse method to retrieve the average spectral mass absorption Aabs;λ and scattering Ssca;λ cross- assumed to be one-dimensional (Pilon et al., 2011; Pottier et al., 2005; sections of C. vulgaris. Lee et al., 2014; Dauchet et al., 2015; Stramski and Piskozub, 2003). We further assumed that the scattering phase function was given by 4.2. Forward problem formulation the transport approximation. Then, the spectral normal–hemispherical transmittance and reflectance of the suspension, after Let us consider one-dimensional radiation transfer in microalgal accounting for internal reflection, can be expressed as (Dombrovsky suspension exposed to normally incident, collimated, monochro- et al., 2005) matic, and randomly polarized light as illustrated in Fig. 1. The sus- 0 Dλ pension was assumed to be well-mixed and the microorganisms T ;λ; ¼ T ;λ þ ½ð1þρ ;λÞ exp ðτ ;λ;ℓÞþAλ=ζλð29Þ nh pred nh 2 1 tr were randomly oriented and azimuthally symmetric. Under these conditions and due to strong forward scattering by microalgae sus- 0 Dλ and R ;λ; ¼ R λ þ ð1þBλ=ζλ þC ;λÞð30Þ pensions and the relatively thin cuvettes, light transfer can be nh pred nh; 2 tr R. Kandilian et al. / Chemical Engineering Science 146 (2016) 357–368 363 λ

Fig. 4. Experimentally measured phase function of C. vulgaris at 632.8 nm along with the associated Henyey–Greenstein phase function for asymmetry factor g633¼0.974.

τ ﬁ τ ¼ where tr;λ;ℓ is the transport optical thickness de ned as tr;λ;ℓ

β ℓ ¼½ þð Þ ℓ 0 0 λ tr;λ Aabs;λ 1 gλ Ssca;λ X . Here, Rnh;λ and Tnh;λ are the spectral normal–hemispherical reﬂectance and transmittance of the suspension ignoring multiple scattering expressed as (Dombrovsky et al., 2005; Modest, 2013)

ρ þð1ρ Þ2C ð1ρ Þ2 0 ¼ 1;λ 1;λ tr;λ 0 ¼ 1;λ ðτ Þ Rnh;λ ρ and Tnh;λ ρ exp tr;λ;ℓ 1 1;λCtr;λ 1 1;λCtr;λ ð31Þ ρ – ﬂ where 1;λ is the normal normal re ectivity of the quartz/air inter- face given by Fresnel's equations. For an optically smooth surface with normally incident radiation and assuming that the absorption index kλ of the quartz was negligible compared with its refractive index nλ so that ð Þ2 ρ ¼ nλ 1 ð Þ 1;λ 2 32 ðnλ þ1Þ

ﬁ Fig. 5. Directly measured average spectral mass absorption Aabs;λ and scattering The parameters Aλ, Bλ, Ctr;λ,andDλ are de ned as (Dombrovsky et al., Ssca;λ cross-sections of C. vulgaris suspensions between 350 and 750 nm for biomass 2005) concentrations X of 0.035 and 0.049 g/L. ðγ γ ρ Þðφ þ Þ ðτ Þðγ γ Þ 1;λ 2;λ 1;λ λsλ cλ exp tr;λ;L 2;λ 1;λCtr;λ Aλ ¼ ð33Þ ρ 2 ω ;λ 1 ;λ 2 4 1ω ;λ ð1þφλÞsλ þ2φλcλ χ ¼ tr 1 ; φ ¼ γ =ζ ; ζ ¼ tr ; λ λ 2 λ λ λ 2 1ω ;λ 1ρ C ;λ ð þμ Þ 1ω ;λμ tr 1;λ tr 1 c;λ tr c;λ ðγ γ ρ Þ ðτ Þðγ γ Þðφ þ Þ 1;λ 2;λ 1;λ exp tr;L 2;λ 1;λCtr;λ λsλ cλ Bλ ¼ ð34Þ 2 sλ ¼ sinh ðζλτ ;λ;ℓÞ; and cλ ¼ cosh ðζλτ ;λ;ℓÞð37Þ ð1þφλÞsλ þ2φλcλ tr tr

where μ λ is the director cosine of the critical angle θ beyond which ¼ ρ ð τ ÞðÞ c; c Ctr;λ 1;λexp 2 tr;λ;ℓ 35 totalinternalreflection occurs while the transport single scattering fi ω ¼ σ =β albedo is de ned as tr;λ tr;s;λ tr;λ. In order to predict the nor- γ ð μ2 Þχ ζ2 – fl λ 1 c;λ λ λ mal hemispherical transmittance and re ectance Tnh;λ and Rnh;λ Dλ ¼ ð36Þ 2 – ℓ ζλ 1 using Eqs. (29) (37), one needs to know (i) the thickness of the suspension, (ii) the index of refraction of the quartz cuvette nλ, (iii) γ μ γ γ γ φ ζ Here, the parameters λ, c;λ, λ, 1;λ, 2;λ, λ, λ, sλ,andcλ are given the absorption coefficient of the suspension κλ, and (iv) the transport by Dombrovsky et al. (2005) fi σ ¼ σ ð Þ ℓ scattering coef cient s;tr;λ s;λ 1 gλ . Here, the thickness of the = 1ρ ðn2 1Þ1 2 cuvette was 10 mm. The spectral refraction index nλ of quartz was γ ¼ 1;λ; μ ¼ λ ; λ þρ c;λ given by the dispersion relation (Heraeus, 2015) 1 1;λ nλ γ λ2 λ2 λ2 λ 2 B1 B2 B3 γλ ¼ ; γ ;λ ¼ 12γ λ; γ ;λ ¼ 1þ2γ λ; n −1 ¼ þ þ ð38Þ þμ 1 2 λ 2 2 2 1 c;λ λ −C1 λ −C2 λ −C3 364 R. Kandilian et al. / Chemical Engineering Science 146 (2016) 357–368 where the wavelength λ is expressed in μm and ranges from 0.2 to evident that C. vulgaris scattered visible light strongly in the for-

2.5 μm. The constants B1, B2, B3, C1, C2,andC3 are respectively ward direction, as expected for such large scatterers with mean 1 1 1 equal to 4.73115591 10 ,6.31038719 10 , 9.06404498 10 , size parameter χ ¼ 2πr s=λ ranging from 16 to 36 over the PAR. In 2 µ 2 3 µ 2 1.29957170 10 m , 4.12809220 10 m , and 9.87685322 fact, the asymmetry factor g633 and back-scattered fraction b633 101 µm2 (Heraeus, 2015). On the other hand, in the visible part of the were 0.974 and 0.0042, respectively. Fig. 4 also plots the corre- spectrum, quartz can be treated as non-absorbing, i.e., kλ 0(Her- sponding Henyey–Greenstein approximate phase function. In μ aeus, 2015). This corresponded to c around 0.73 or to a critical angle addition, the fraction ϵn of light scattered in the forward direction θ fl ° fl ρ c, for total internal re ection, of about 43 while the re ectivity 1;λ reaching the detector was estimated to be ϵn ¼ 0:71. This value was about 3.5%. was used in the direct measurements of the extinction cross- section [Eq. (24)]. 4.3. Inverse method optimization Fig. 5a and b respectively plot the average mass absorption 2 Aabs;λ and scattering Ssca;λ cross-sections (in m /kg) as functions of Fig. 2 shows a block diagram of the procedure used to simul- wavelength between 350 and 750 nm measured directly for small taneously retrieve the spectral mass absorption Aabs;λ and trans- biomass concentrations of 0.035 and 0.049 g/L. First, the cross- ð Þ – port scattering 1 gλ Ssca;λ cross-sections from the normal sections measured for both concentrations collapse on the same fl hemispherical transmittance Tnh;λ and re ectance Rnh;λ measure- curve confirming that single scattering conditions prevailed ments over the PAR region. The objective is to find the values of ð Þ Aabs;λ and 1 gλ Ssca;λ that minimize the difference between the a predicted and experimentally measured normal–hemispherical 35 transmittance and reflectance of the microalgal suspension in the X=0.111X = 0.1113 g/L g/L least-square sense. Various optimization algorithms can be used to X=0.556X = 0.5565 g/L g/L

(%) 30 minimize, for each wavelength, the objective function δλ deﬁned X=1.11X =1.113 g/L g/L as, nh, X=5.56X = 5.565 g/L g/L X=11.1X = 11.13 g/L g/L 2 2 25 Tnh;λ;pred Tnh;λ Rnh;λ;pred Rnh;λ X=55.6g/LX = 55.65 g/L δλ ¼ þ : ð39Þ Tnh;λ Rnh;λ X=111X = 111.3 g/L g/L ð Þ 20 Here, the inverse method to retrieve Aabs;λ and 1 gλ Ssca;λ was implemented in Microsoft Excel using the built in non-linear optimization solver based on the generalized reduced gradient (GRG) algo- 15 rithm. A simple Excel ﬁle with instruction is available in digital form online (Pilon, 2015) or directly from the corresponding author upon request. For the sake of comparison, the inverse method was also 10 implemented based on genetic algorithm using the general purpose function optimization code PIKAIA (Charbonneau and Knapp, 1995; 5

Charbonneau, 2002, 2002). Here, the spectral mass absorption and Normal-hemispherical reflectance, R ð Þ transport scattering cross-sections Aabs;λ and 1 gλ Ssca;λ were retrievedandassumedtorangefrom0to1000m2/kg based on past 0 experience and on the literature (Pilon et al., 2011). The genetic 350 450 550 650 750 algorithm used a maximum of 50 generations with a population Wavelength, (nm) consisting of P¼120 individuals. The convergence criteria was set as 4 δλ o10 . Note that both retrieval methods gave identical results. b 100

90 5. Results and discussion (%)

nh, 80 5.1. Chlorella vulgaris characterization 70 Fig. 3 shows the measured size distribution of C. vulgaris obtained with 2873 cells. The cells featured a mean radius rs of 60 1.98 μm with a standard deviation of 0.41 μm. Moreover, the mean ratio of minimum and maximum axis of each cell ﬁtted to an 50 ellipse was 0.81. The cell number density NT was related to the dry 14 40 biomass concentration X by NT ¼ 1:17 10 X. Thus, the mass ¼ fraction of water in the microorganisms was estimated as xw 82 30 wt.% based on Eq. (18). The pigment concentrations were measured spectrophotometrically according to the procedure 20 described earlier. The concentrations of Chl a, Chl b, and total ¼ : 7 : = ; ¼ : carotenoids were such that CChla 25 95 0 82 mg L CChlb 4 81 10 Normal-hemispherical transmittance, T 70:36 mg=L; CPPC þ PSC ¼ 6:14 70:29 mg=L. These results corresponded to the weight percentage w ¼ 4:4170:14 wt:%; w 0 Chla Chlb 350 450 550 650 750 ¼ 0:8270:05 wt:%, and wPPC þ PSC ¼ 1:0470:06 wt:%. Wavelength, (nm)

5.2. Direct measurements – ﬂ Fig. 6. Experimentally measured normal hemispherical (a) re ectance Rnh;λ and (b) transmittance Tnh;λ between 350 and 750 nm for C. vulgaris suspensions in Fig. 4 shows the azimuthally symmetric scattering phase quartz cuvettes with a path length of 1 cm with different values of biomass con- function of C. vulgaris measured experimentally at 632.8 nm. It is centrations X ranging from 0.111 to 111 g/L. R. Kandilian et al. / Chemical Engineering Science 146 (2016) 357–368 365

(Van De Hulst, 1957). Fig. 5 also indicates that the scattering cross- as the mass concentration increased. In fact, for concentration larger section Ssca;λ was much larger than the absorption cross-section or equal to 5.56 g/L, the transmittance, over the PAR region, fell below Aabs;λ. Note, however, that the transport scattering cross-section the detection limit of the spectrophotometer. On the other hand, the ð Þ Ssca;λ 1 gλ was smaller than the absorption cross-section since gλ reflectance remained relatively constant around 4%. Interestingly, it approached unity. The absorption peaks of Chl a were apparent at increased with increasing concentration beyond 700 nm due to the 435, 630, and 676 nm, based on the absorption peaks of in vivo fact that the suspension absorption coefficient vanished and scatter- photosynthetic pigments reported by Bidigare et al. (1990). The ing, including back-scattering, increased. Overall, only normal–hemi- shoulder from 455 to 485 nm can be attributed to superposition of spherical transmittance and reflectance measurements for cell con- the absorption peaks of Chl b at 475 nm and of PPC around 462 centrations 0.111, 0.556, and 1.11 g/L had a large enough signal to and 490 nm (Bidigare et al., 1990). Another absorption peak of Chl noise ratio to be used in the inverse method. Data for larger con- b can be observed around 650 nm. These absorption and scattering centrations led to very noisy and unrealistic retrieved values of both ð Þ cross-sections obtained from direct measurements will be treated Aabs;λ and Ssca;λ 1 gλ . as references in evaluating the performance of the inverse method. 5.3.2. Model validation fl 5.3. Results from inverse method The measured transmittance Tnh;λ and re ectance Rnh;λ of C. vulgaris suspensions of biomass concentration X equal to 0.111, 0.556, 5.3.1. Normal–hemispherical transmittance and reflectance and 1.11 g/L over the PAR region were in reasonably good agreement Fig. 6a and b respectively show the normal–hemispherical with predictions by the modified two-flux approximation (Eqs. (29)– fl re ectance Rnh;λ and transmittance Tnh;λ as a function of wavelength (37)) using the average absorption Aabs;λ and scattering Ssca;λ cross- between 350 and 750 nm for C. vulgaris concentration ranging from sections and the asymmetry factor g measured directly with dilute 0.111 to 111 g/L. It indicates that the transmittance decreased sharply suspensions (see Supplementary Material). This establishes that a b 700 60 /kg) 2 600 (m 50 /kg) 2 sca, )S (m 500

abs, 40

400 30 300

20 200

10 Absorption cross-section, A 100 Transport scattering cross-section, (1-g cross-section, scattering Transport 0 0 400 450 500 550 600 650 700 750 400 450 500 550 600 650 700 750 Wavelength, (nm) Wavelength, (nm) c 800 /kg) 2 700 (m

600 tr,ext, Direct measurement Inverse method (X=0.111 g/L) 500 Inverse method (X=0.556 g/L) Inverse method (X=1.11 g/L) 400

300

200

100 Transport extinction cross-section, E 0 400 450 500 550 600 650 700 750 Wavelength, (nm)

Fig. 7. Retrieved average spectral mass (a) absorption Aabs;λ, (b) transport scattering ð1gλÞS sca;λ, and (c) transport extinction E tr;ext;λ cross-sections of C. vulgaris suspensions between 400 and 750 nm for biomass concentrations X of 0.111, 0.556, and 1.11 g/L. 366 R. Kandilian et al. / Chemical Engineering Science 146 (2016) 357–368

(1) the radiation transfer in cuvettes containing microalgae cultures 5.3.3. Retrieved cross-sections can be treated as one-dimensional and (2) the modified two-flux Fig. 7 compares the average mass (a) absorption Aabs;λ,(b)transport ð Þ ¼ þð approximation is an adequate model for predicting the associated scattering 1 gλ Ssca;λ, and (c) transport extinction Etr;ext;λ Aabs;λ Þ normal–hemispherical transmittance and reflectance. Note that the 1 gλ Ssca;λ cross-sections as functions of wavelength between 400 transmittance was underpredicted and reflectance was overpredicted and 750 nm either measured directly or retrieved by the inverse at wavelengths between 500 nm and 600 nm. This may be due to the method from measurements of Tnh;λ and Rnh;λ for three different concentrations. First, the retrieved spectral average mass absorption fact that the asymmetry factor gλ was assumed to be constant over cross-section A ;λ was similar for each biomass concentration, as the PAR region. In fact, the spectral asymmetry factor gλ of C. vulgaris abs fi can vary by as much as 80% over the PAR region relative to its value at expected from its de nition (Eq. (6)). In addition, the values of Aabs;λ retrieved by the inverse method were in relatively good agreement 633 nm (Dauchet, 2012). Moreover, the use of transport approxima- with those obtained from direct measurements except above 700 nm tion may have also contributed to the inaccuracy in the predicted where it should vanish. Note that the inverse method retrieved A ;λ transmittance and reflectance, particularly at higher cell concentra- abs for each wavelength independently. Yet, the retrieved spectral tions. Indeed, Dombrovsky et al. (2005) state that “the error of the absorption cross-section Aabs;λ was a continuous and smooth function transport approximation increases with optical thickness but it is of wavelength. On the other hand, the retrieved transport scattering insignificant in the range of weak extinction”.

ν ν ν ν

Fig. 9. Comparison of biomass productivity 〈rX 〉 of C. vulgaris grown in a 1 cm thick fl ð Þ= ″ fl μ = 2 Fig. 8. Comparison of (a) uence rate ratio GPAR z qin and (b) local rate of photon at-plate PBRs exposed to 200 or 500 molhν m s incident white LED light, pre- absorption (LRPA) AðzÞ as a function of depth in a 1 cm thick flat plate PBR predicted using Eqs. (12)–(16) as a function of either (a) the steady-state biomass dicted by Eqs. (8) and (16), respectively. The predictions used the radiation char- concentration X or (b) the dilution rate D. The predictions used the radiation acteristics obtained from either direct measurements or retrieved by the inverse characteristics obtained from either direct measurements or retrieved by the method for concentrations 0.111, 0.556, and 1.11 g/L. inverse method. R. Kandilian et al. / Chemical Engineering Science 146 (2016) 357–368 367

ð Þ cross-section 1 gλ Ssca;λ depended on the concentration considered section retrieved by the inverse method was very similar to pro- and featured non-physical fluctuations as a function of wavelength. It ductivity predictions using the fluencerateestimatedbythetwo-flux was also significantly smaller than the values obtained from direct approximation and the directly measured radiation characteristics. measurements. Finally, excellent agreement was found between all Indeed, the relative difference between these two methods was less three retrieved transport extinction cross-sections Etr;ext;λ and the than 10% for all dilution rates D investigated and for both realistic experimentally measured one. Note that the inverse method over- incident irradiances considered. estimated the value of Aabs;λ and compensated for it by under- ð Þ predicting the transport scattering cross-section 1 gλ Ssca;λ of the microorganisms. This was due to the fact that normal–hemispherical 6. Conclusion fl transmittance Tnh;λ and re ectance Rnh;λ measurements of microalgae were not very sensitive to the cells' transport scattering cross-section This paper presented a method to easily measure the spectral as microalgae scattered light mainly in the forward direction. In absorption cross-section of randomly oriented microalgae of any addition, the forward scattered light was collected by the integrating shape from conventional normal–hemispherical transmittance sphere used in the measurements of Tnh;λ. In fact, the absorption and reflectance measurements of well-mixed suspensions in cross-section dominated over the transport scattering cross-section conventional cuvettes. It was successfully demonstrated with ⪢ð Þ (i.e., Aabs;λ 1 gλ Ssca;λ)sothatsmallerrorsinAabs;λ had strong suspension of C. vulgaris with relatively large biomass concentra- effects on the shape and magnitude of the transport scattering cross- tions such that multiple scattering prevailed. Even though the ð Þ fi section 1 gλ Ssca;λ.Thiswasconrmed by the fact that good method was unable to properly retrieve the transport scattering agreement was observed between the direct and inverse methods for cross-section, the retrieval of the absorption cross-section com- the transport extinction cross-section Etr;ext;λ. bined with the simplified two-flux approximation was sufficient to Moreover, the same inverse procedure and algorithm was used predict accurately the local fluence rate, the local rate of photon to retrieve the three parameters Aabs;λ, Ssca;λ, and gλ independently. absorption, and the biomass productivity of flat plate PBRs. This This resulted in strongly oscillating values of Ssca;λ and gλ. How- new method can also be applied to other absorbing and scattering ð Þ ever, the same values of Aabs;λ and 1 gλ Ssca;λ as those shown in particles of various shapes with large enough size parameter to Fig. 7 were obtained. This can be attributed to the facts that (i) the ensure strong forward scattering and therefore a small transport solution of the ill-posed inverse problem was not unique and (ii) scattering cross-section compared with the absorption cross- the modified two-flux approximation for the expressions of section.

Tnh;λ;pred and Rnh;λ;pred depended on the transport scattering coef- fi σ σ cient s;tr;λ and not on s;λ and gλ separately. As argued earlier, the average mass absorption cross-section Acknowledgement Aabs;λ is the most important radiation characteristic in analyzing, predicting, and controlling coupled light transfer and growth This work was supported by the French National Research kinetics in PBRs. In fact, Fig. 8a shows the fluence rate ratio Agency project DIESALG (ANR-12-BIME-0001-02) for biodiesel ð Þ= ″ fl GPAR z qin in a 1 cm thick at plate PBR illuminated normally on production based on solar production of microalgae, and is part of one side with a front transparent window and a back reflectivity the French “BIOSOLIS” research program on developing photo- ρλ ¼ 0:02. The fluence rate ratio was predicted by using either bioreactor technologies for mass-scale solar production (http:// (i) the two-flux approximation given by Eq. (8) based on the www.biosolis.org/). Additional support was provided by the CNRS directly measured radiation characteristics Aabs;λ and Ssca;λ with bλ program Cellule énergie. R.K. is grateful to the Embassy of France ¼ 0:0042 or (ii) the simplified two-flux approximation given by Eq. in the United States, Office for Science and Technology for the (11) based on the retrieved values of Aabs;λ for concentrations 0.111, Chateaubriand Fellowship. L.P. thanks the Région Pays de la Loire 0.556, and 1.11 g/L. for the Research Chair for International Junior Scientists. Fig. 8b compares the local rate of photon absorption (LRPA) A ðzÞ as a function of flat plate PBR thickness predicted by Eq. (16) using the fluence rate shown in Fig. 8a and the associated Appendix A. Supplementary data absorption and scattering cross-sections. Here, the light source was assumed to be collimated white LEDs delivering a total inci- Supplementary data associated with this paper can be found in fl μ = 2 dent ux of 200 molhν m s as previously used experimentally the online version at http://dx.doi.org/10.1016/j.ces.2016.02.039. (Soulies et al., 2016). Fig. 8 indicates that the absorption cross- section retrieved by the inverse method combined with the sim- fi fl pli ed two- ux approximation (Eq. (11)) led to acceptable pre- References dictions of the fluence rate GPAR(z) and of the LRPA AðzÞ. This was achieved while requiring fewer experimental measurements and Agrawal, B.M., Mengüç, M.P., 1991. Forward and inverse analysis of single and only an integrating sphere spectrophotometer. multiple scattering of collimated radiation in an axisymmetric system. Int. J. Finally, Fig. 9a and b shows the volume averaged steady-state Heat Mass Transf. 34, 633–647. biomass productivity 〈r 〉 of C. vulgaris as a function of steady-state Bellini, S., Bendoula, R., Latrille, E., Roger, J.-M., 2014. Potential of a spectroscopic X measurement method using adding-doubling to retrieve the bulk optical biomass concentration X and dilution rate D, respectively. Productivity properties of dense microalgal media. Appl. Spectrosc. 68 (October (10)), was predicted using Eqs. (12)–(16) combined with either (i) the two- 1154–1167. ğ flux approximation given by Eq. (8) and the directly measured Berbero lu, H., Pilon, L., 2007. Experimental measurement of the radiation characteristics of Anabaena variabilis ATCC 29413-U and Rhodobacter sphaeroides ¼ : radiation characteristics Aabs;λ, Ssca;λ with bλ 0 0042 or (ii) the ATCC 49419. Int. J. Hydrog. Energy 32, 4772–4785. simplified two-flux approximation given by Eq. (11) and the retrieved Berberoğlu, H., Yin, J., Pilon, L., 2007. Light transfer in bubble sparged photobioreactors for H production and CO mitigation. Int. J. Hydrog. Energy 32, values of A ;λ.Atorustype4cmthickflat-plate PBR in continuous 2 2 abs 2273–2285. μ = 2 mode was simulated exposed to 200 or 500 molhν m s of colli- Berberoğlu, H., Melis, A., Pilon, L., 2008. Radiation characteristics of Chlamydomonas mated white LEDs and the dilution rate D varied from 0.02 to 0.1 h 1 reinhardtii CC125 and its truncated chlorophyll antenna transformants tla1, þ as previously used experimentally (Soulies et al., 2016). Fig. 9 illus- tlaX, and tla1-CW . Int. J. Hydrog. Energy 33, 6467–6483. Berberoğlu, H., Gomez, P.S., Pilon, L., 2009. Radiation characteristics of Botryococcus trates that the productivity predicted using the fluencerateestimated braunii, Chlorococcum littorale, and Chlorella sp used for CO2 fixation and biofuel with the simplified two-flux approximation and the absorption cross- production. J. Quant. Spectrosc. Radiat. Transf. 110, 1879–1893. 368 R. Kandilian et al. / Chemical Engineering Science 146 (2016) 357–368

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