Light transfer in agar immobilized microalgae cell cultures

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Light transfer in agar immobilized microalgae cell

cultures

Razmig Kandilian, Bruno Jesus, Jack Legrand, Laurent Pilon, Jeremy Pruvost

To cite this version:

Razmig Kandilian, Bruno Jesus, Jack Legrand, Laurent Pilon, Jeremy Pruvost. Light transfer in agar

immobilized microalgae cell cultures. Journal of Quantitative Spectroscopy and Radiative Transfer,

Elsevier, 2017, 198, pp.81-92. �10.1016/j.jqsrt.2017.04.027�. �hal-01951137�

ContentslistsavailableatScienceDirect

Journal

of

Quantitative

Spectroscopy

&

Radiative

Transfer

journalhomepage:www.elsevier.com/locate/jqsrt

Light

transfer

in

agar

immobilized

microalgae

cell

cultures

Razmig

Kandilian

a ,c

_,

_Bruno

_Jesus

b

_,

_Jack

_Legrand

a

_,

_Laurent

_Pilon

c ,∗

_,

_Jérémy

_Pruvost

a ,∗

a Université de Nantes, GEPEA, UMR-CNRS 6144, Bd de l’Université, CRTT-BP 406, 44602, Saint-Nazaire Cedex, France b Laboratoire Mer Molécules Santé, EA2160, 2 rue de la Houssiniére, Université de Nantes, 44322 Nantes Cedex 3, France

c Mechanical and Aerospace Engineering Department, Henry Samueli School of Engineering and Applied Science, University of California, Los Angeles - Los

Angeles, CA 90095, USA

a

r

t

i

c

l

e

i

n

f

o

Article history: Received 8 December 2016 Revised 25 March 2017 Accepted 24 April 2017 Available online 25 April 2017

Keywords: Modeling Biofilm Radiation characteristics Immobilized microalgae Agar-entrapped Photobioreactors

a

b

s

t

r

a

c

t

Thispaperexperimentallyandtheoreticallyinvestigateslighttransferinagar-immobilizedcellcultures. Certainbiotechnologicalapplicationssuchas productionofmetabolitessecreted byphotosynthetic mi-croorganismsrequirecellsto beimmobilizedinbiopolymers tominimize contamination and to facil-itate metaboliterecovery.In suchapplications,lightabsorption bycells isone ofthe mostimportant parametersaffectingcellgrowthormetabolite productivity.Modelinglighttransferthereincanaid de-signandoptimizeimmobilized-cellreactors.Inthisstudy,Parachlorellakesslericellswitharealbiomass concentrationsrangingfrom0.36to16.9 g/m2 _{wereimmobilizedin2.6mmthickagargels.The}

aver-ageabsorptionandscattering cross-sectionsas wellasthescatteringphasefunctionofP.kesslericells weremeasured. Then,the absorptionand transport scatteringcoefficients ofthe agargelwere deter-minedusinganinversemethodbasedonthemodifiedtwo-fluxapproximation.Theforwardmodelwas usedtopredictthenormal-hemisphericaltransmittanceandreflectanceoftheimmobilized-cellfilms ac-countingforabsorptionandscatteringbybothmicroalgaeandtheagargel.Goodagreementwasfound betweenthemeasuredandpredictednormal-hemisphericaltransmittanceand reflectanceprovided ab-sorptionandscatteringbyagarweretakenintoaccount.Moreover,goodagreementwasfoundbetween experimentallymeasuredand predictedmeanrateofphotonabsorption.Finally,optimalarealbiomass concentrationwasdeterminedtoachievecompleteabsorptionoftheincidentradiation.

© 2017ElsevierLtd.Allrightsreserved.

1. Introduction

Photosynthetic microalgae, cyanobacteria, and diatoms have wide rangeofapplications inthenutraceutical[1] ,cosmetics [2] , pharmaceutical[3] ,biofuels[4] ,andfoodprocessingindustries[5] . Theyarealsousedintertiarywastewatertreatment[6] andanimal feedproduction[7] .Thesemicroorganismsare typically grownin openpondsorclosedphotobioreactors(PBRs)exposedtosolar ra-diation orartificialillumination. Then,the cellsare suspendedin nutrient media by mechanical mixingusing paddle wheelsor by air/CO2mixtureinjectionwithinthePBRsuspension[8] .However, forcertainbiotechnologicalapplications,suchaswastewater treat-ment[9,10] andsecretedmetabolite production[11,12] ,theuseof immobilized-cell reactors arepreferred. Then,metabolite produc-tion [11,12] or pollutant consumption [9,10] is favored instead of celldivision.

∗ _{Corresponding authors.}

E-mail addresses: pilon@seas.ucla.edu (L. Pilon), jeremy.pruvost@univ-nantes.fr

(J. Pruvost).

Fig. 1 showsaschematicofanimmobilized-cellPBRillustrating nutrientandmetabolite exchangebetweencellsimmobilizedina biopolymer andthenutrient medium flowing above.In this con-figuration,themetabolitesproducedby theimmobilized microor-ganisms diffuse out of the biopolymer into the growth medium whilethenutrientsconsumedbythemicroorganismsdiffuseinto the biopolymer. This allows maintaining biomass in the culture system while facilitating the recovery of metabolites exuded by thecells[9] .Immobilizationalsominimizesbiological contamina-tionoftheculturebycreatingaphysicalbarrierforpotential con-taminants[13] .Finally,itpreventsmetaboliteaccumulationinthe mediumwhichmayhavetoxicorinhibitoryeffectsonproductivity

[11] .Twoquintessentialmicroorganismsidealforimmobilized cul-tivationarethemicroalgaeBotryococcusbrauniiwhichsecretes liq-uidhydrocarbons usedforbiofuelproduction[14] andthediatom

Hasleaostreariawhichexudesabluepigmentusedinaquacultures andinthepharmaceuticalindustry[15] .

Lightabsorptionrateofthecellsandlightutilizationefficiency ofimmobilized-cellPBRsarearguablythemostimportant param-eters affecting cell and/or metabolite productivity [16–22] . Thus, carefullighttransferanalysismustbe conductedtooptimizelight

http://dx.doi.org/10.1016/j.jqsrt.2017.04.027

Fig. 1. Schematic of immobilized-cell PBR with nutrient medium flowing above im- mobilized cells suppling fresh nutrients and removing metabolites.

absorption rate by immobilized cells and to design and operate PBRsefficiently.Lighttransferin PBRscontainingcellssuspended in liquid media has been extensively studied [22–25] . Method-ologieshave been developedto measure the radiation character-istics and determine the optical properties of free-floating mi-croalgaeandcyanobacteria[23,25,26] .Moreover,modelsofvarious complexityhavebeendeveloped topredict the localfluence rate andthe rate of energyabsorption in open ponds, flat-plate, and cylindricalPBRs [24,27–31] and to predict transmittance and re-flectance[32,33] .However,tothebestofourknowledgenostudy hasinvestigatedlighttransferinimmobilized-cellfilms.Itremains unclear whether models and methodologies developed for con-ventional PBRs with free-floating microorganisms are applicable toimmobilized-cell PBRsgiven the presence ofthe immobilizing polymerandthelackofmixing.

Thisstudyaimstodevelopandexperimentallyvalidateamodel predictinglight transferin immobilized-cellPBRs. Validationwas performedwithParachlorellakesslericellsimmobilizedinagargel. Thisstudyalso reportsthespectral radiation characteristics,over the photosynthetically active radiation (PAR) region, of the two constituents of the immobilized-cell film, namely, the photosyn-theticcellsandtheagargel. Finally,theresultswere usedto de-finesimplerulesandstrategiesforoptimizingproductivityin light-limitedimmobilized-cellfilms.

2. Background

2.1.ModelinglighttransferinPBRs

The localandspectralspecificrateofphotonabsorption(RPA),

A_λ

(

r

)

(μmolhν/kg·s) represents the number of photons of wave-length

λ

absorbed per unit of dry biomass andper unit time at location r in the PBR [34] . It depends on the average mass ab-sorptioncross-sectionA¯_abs,λ(inm2_{/kg)ofthemicroorganismsand} onthelocalfluence rateG_λ(r) (inμmolhν/m2·s) atlocationrand wavelength

λ

,accordingto[34]

Aλ

(

r

)

=A¯abs,λGλ

(

r

)

. (1)

For absorbing and scattering media, such as microalgae suspen-sions,thelocalspectralfluencerateG_λ(r)canbeobtainedby solv-ing the radiative transfer equation [35] . Typically, the local PAR-averaged fluence rateGPAR(r) and PAR-averaged RPA APAR

(

r

)

are usedtomodelmicroalgaegrowthandproductivity[22] .The PAR-averagedfluencerateGPAR(r)canbeexpressedas[34]

GPAR

(

r

)

= 700



400

G_λ

(

r

)

d

λ

. (2)

Similarly,thelocalPAR-averagedrateofphotonabsorptionAPAR

(

r

)

canbedefinedas[34] APAR

(

r

)

= 700  400 Aλ

(

r

)

d

λ

. (3)

Finally,thevolume-averaged RPA orthemeanrateofphoton ab-sorption(MRPA)inaPBRofvolumeVcanbeestimatedaccording to[34]



APAR



= 1 V  V APAR

(

r

)

dV. (4) For flat-plate PBRs of thickness L with transparent front (z = 0 m) andback (z=L) windows containingstronglyforward scattering microalgae and exposed to normally incident spectral radiation flux q_in,λ, light transfer is one-dimensional and the lo-calfluence rateG_λ(z) canbepredictedatdepthz bythetwo-flux approximationas[27] G_λ

(

z

)

(

1−

ρ

1,λ

)

qin,λ = 2

(

1+

α

λ

)

eδλ( L−z)₋

₍

₁₋

_α

λ

)

e−δλ(L−z)

(

1+

α

λ

)

2eδλL₋

(

₁₋

α

λ

)

2e−δλL (5)

where the coefficients

α

_λ (unitless) and

δ

_λ (in m2_{/kg) are} ex-pressedas[27]

α

λ=



κ

λ

κ

λ+2bλ

σ

s,λ and

δ

λ=



κ

λ



κ

λ+2bλ

σ

s,λ



. (6)

Here,

κ

_λand

σ

_s,λarerespectivelytheaverageabsorptionand sin-glescatteringcoefficientsandb_λ istheaveragebackward scatter-ing fraction of the microalgae suspension [27] . In addition,

ρ

1,λ is the front surfacenormal-normal reflectivity given by Fresnel’s equations. For an optically smooth agar film/air interface under normallyincidentradiation

ρ

1,λcanbeexpressedas[36]

ρ

1,λ=

(

nm,λ− 1

)

2

(

nm,λ+1

)

2. (7)

where n_m,λ is thegrowth medium refractive index. The two-flux approximationhasbeenshowntogivegoodpredictionsofthe lo-calfluencerateG_λ(z)forflat-platePBRsandopenponds[27,30,34] . AnalternativewayofexpressingtheMRPAisbyperformingan energybalanceonthe incomingandoutgoingradiationina one-dimensionalPBRsuchthat[37]



APAR



= 1 XL



q” PAR

(

0

)

− q”PAR

(

L

)



=q ” PAR,in XL

(8) whereq"

PAR

(

0

)

andq"PAR

(

L

)

are the PAR-averagedradiation fluxat the front and back of the PBR, respectively. Similarly, q"

PAR,in is theincidentphotonfluxdensityaveragedoverthePAR region ex-pressed in μmolhν/m2·s. Moreover,

is the fraction of light ab-sorbedbythemicroalgaeoverthePARregionestimatedas

= 1

(

λ

max−

λ

min

)

 _λmax λmin



1− Tnh,λ− Rnh,λ



d

λ

. (9)

Here, Tnh,λ and Rnh,λ are respectively the normal-hemispherical spectral transmittance and reflectance of the immobilized-cell filmswhileintegrationisperformedoverthePARregionsuchthat

λ

min=400nmand

λ

max=700nm.

Finally,Cornetandco-workers[16,17,19,38,39] havedevelopeda kineticmodelthatcanpredictmicroalgaegrowthandproductivity basedonthelocalRPAAPAR

(

r

)

.Themodelpredictsboththelocal rateofoxygen productionandthelocalbiomassproductivity.The authorsreportedthat the maximumproductivityofa PBRoccurs whentheminimumPAR-averagedlocalRPAinthePBRisequalto theso-calledphotosynthesiscompensationpoint_Ac.Inaflat-plate PBR ofthicknessLilluminatedfromone side(z=0m), the min-imumRPA occurs attheback wall ofthe PBR, i.e., atz=L.Note that the photosynthesis compensation point Ac depends on the microorganismspecies.Forexample,itwasreportedtobearound 1500μmolhν/kg·sforChlorellavulgaris[39] .

2.2. Normal-hemisphericalreflectanceandtransmittance

Letusconsidera homogeneousabsorbing,scattering,but non-emitting slab of immobilized-cell film of thickness L exposed to collimated andnormallyincident radiationononeside.Radiation transferinthiscasecanbeassumedtobeone-dimensional[28,30] . The slab or film is assumed to be reflecting and refracting and subjectto internal reflection. Solving the radiationtransfer equa-tionbasedonthemodifiedtwo-fluxapproximationandthe trans-portapproximation leadstoananalyticalexpressionforthe spec-tral normal-hemispherical transmittance T_nh,λ,pred and reflectance

Rnh,λ,predgivenby[36]

Tnh,λ,pred=Tnh0,λ+D₂λ[

(

1+

ρ

1,λ

)

exp

(

−

τ

tr,λ,L

)

+Aλ/

ζ

λ] (10)

and Rnh,λ,pred=R0nh,λ+D₂λ

(

1+Bλ/

ζ

λ+Ctr,λ

)

(11)

where

τ

_tr,λ,L is thetransport optical thicknessdefinedas

τ

_tr,λ,L=

β

tr,λL where

β

tr,λ is the transport extinction coefficient of the immobilized-cell film. Here, T0

nh,λ and R0nh,λ are respectively the

spectralnormal-hemisphericaltransmittanceandreflectance ignor-ingmultiplescatteringandexpressedas[40]

R0 nh,λ=

ρ

1,λ+

(

1−

ρ

1,λ

)

2_C tr,λ 1−

ρ

1,λCtr,λ and T 0 nh,λ=

(

1−

ρ

1,λ

)

2 1−

ρ

1,λCtr,λe −τtr,λ,L (12)

TheparametersA_λ,B_λ,C_tr,λ,D_λ,and

ζ

_λ areintermediaryvariables definedinRefs.[33,36] .

Thetwo-fluxapproximationhasoftenbeenusedtopredict one-dimensional radiation transfer in plane-parallel absorbing, emit-ting,and/or isotropicallyscatteringslabs [40] .Ontheother hand, themodifiedtwo-fluxapproximationderivedbyDombrovskyetal.

[36] (i) takes intoaccount internal reflectionin the slab and(ii) uses thetransport approximation to accountfor anisotropic scat-tering. The modified two-flux approximation has been validated against predictions by the discrete ordinate method for strongly forward scattering media [36] and successfully applied to glass containingbubbles[36] andmicroalgaecultures[33] .

2.3. Determinationofradiationcharacteristics

The size-averaged spectral mass absorption and scattering cross-sections A¯abs,λ and ¯Ssca,λ offree-floating microalgaecan be experimentally measured according to a procedure reviewed by Pilon etal. [23,25] . In thismethod,the normal-normal T_nn,λ and normal-hemisphericalTnh,λtransmittanceofdilutemicroalgae sus-pensions of known concentrations are measured using a spec-trophotometer without and with an integrating sphere, respec-tively.Thepathlengthofthecuvetteand/orthemicroalgae concen-tration X mustbe chosen suchthat singlescatteringprevails,i.e., photons undergo at most one scattering event when they travel throughthesuspension.Inpractice,thecuvettepathlengthshould besmallerthanthephotonmean-freepathinordertoobtainthe average massabsorptionA¯_abs,λandscattering ¯S_sca,λcross-sections thatareindependentofconcentrationX.

The present study directly compares the measured normal-hemispherical transmittanceandreflectance offilmsconsistingof

P. kessleri cells immobilized in agar gel with predictions by the modifiedtwo-flux approximation previously discussed. It also re-ports direct measurements of the radiation characteristics of P. kessleriinsuspensionaswellastheabsorptionandtransport scat-tering coefficients of the agar gel alone retrieved from normal-hemispherical transmittance and reflectance measurements. Fi-nally,guidelinesforoptimizingimmobilized-cellPBRswithrespect totheincidentirradiancearepresented.

3. Materialsandmethods 3.1. Speciesandculturemedium

The microalgaeParachlorella kessleri(UTEX2229) wasobtained fromtheUniversityofTexasAustin(UTEX)collection.Itwas culti-vated ina modifiedBoldBasal medium withthe following com-position (in mM) NaNO3 8.02, Na2EDTA · 2H2O 0.122, MgSO4 · 7H2O0.83,K2HPO40.78,KH2PO4 0.88,CaCl2 · 2H2O0.155,FeSO4 · 7H2O0.046,ZnSO4· 7H2O7.72×10−4,CuSO44.95×10−4,MnCl2 · 4H2O9.15×10−3,H3BO34.63×10−2,Co(NO3)2· 6H2O1.51×10−4, Na2MoO41.06×10−3,andNaHCO31.5.Themediumwassterilized by autoclaving at 121 °C for25 min. The microalgae were culti-vated in a 1 l airlift PBR operated incontinuous mode and pre-viously describedin detail in Refs. [18,20] . The dilution rateand thephotonfluxdensityweresetto0.011/hand150μmolhν/m2·s, respectively.Theculture mediumpHwascontinuously monitored usinga pHsensor (Mettler ToledoSG3253) andwasmaintained at 8 by automatic injection of gaseous CO2 when the pH ex-ceeded 8. The culture under steady-state continuous operation achieveda drybiomass concentrationX of1.6g/l.Toobtain sam-pleswithlargerbiomassconcentrations,theharvestedculturewas centrifuged at 10,000g (ThermoScientific Sorvall RC 6 Plus, Mas-sachusetts,USA) for10 minat 4°C andsuspended inphosphate buffersaline(PBS)solution.

3.2.Biomassandpigmentconcentrations

Microorganism dry biomass concentration X (in kg/m3_{) was} measured gravimetricallyby filtering 5 mlof thecontinuous air-liftPBRculturethroughapre-driedandpre-weighed0.45μmpore sizeglass-microfiberfilter(WhatmanGF/F).Thefiltersweredried fora minimum of 24h in an oven at 105 °C andweighed after beingcooledinadesiccatorfor30min.Eachsamplewasanalyzed intriplicatesandthemeanvalueofthebiomassconcentrationwas reported.

Photosyntheticpigmentswere extractedinpure methanoland quantifiedspectrophotometrically. Avolumeof0.5mlofthe con-tinuous airlift PBR culture was first centrifuged at 13,400 rpm (12,100g) for 10 min. The medium was discarded and the cells were resuspended in 1.5 ml ofpure methanol andsonicated for 20s. The sampleswere left for1h in an ovenat 44°C andthe extractwasthencentrifuged.TheopticaldensityOD_λofthe super-natantwasmeasuredatwavelengths

λ

equalto750,665,652,and 480 nm using a UV–vis spectrophotometer (Jasco V-730 Easton, MD). All extractions were performedin triplicates. Chlorophyll a

andbconcentrations,respectivelydenotedbyCChla andCChlb,were estimatedaccordingtothecorrelations[41]

CChla[mg/l]=−8.0962

(

OD652− OD750

)

+16.5169

(

OD665− OD750

)

CChlb[mg/l]=27.4405

(

OD652− OD750

)

− 12.1688

(

OD665− OD750

)

.

(13)

Similarly, the total carotenoid concentration CPPC+PSC, account-ing for both photoprotective (PPC) and photosynthetic (PSC) carotenoids,wasestimatedaccordingto[42]

CPPC+PSC[mg/l]=4

(

OD480− OD750

)

. (14)

3.3.Microalgaeradiationcharacteristicsmeasurements

Thetotalscatteringphase function

_T,λ(



) ofthefree-floating microalgaewas measured at632.8 nm by a polarnephelometer describedinRef.[43] .Itwasassumedtobeindependentof wave-lengthoverthePARregion.Duetointerferenceoftheprobewith thelaser beam, the scatteringphase function could not be mea-suredbeyond160° withrespecttotheforwarddirection.Thishad

nosignificantimpactasthemicroalgaeweremuchlargerthanthe wavelengthand scattering was strongly in the forward direction

[25,26,32,43] .

The normal-normal transmittance T_nn,λ measurements were performed using a UV-vis-NIR spectrophotometer (Agilent Cary 5000, Santa Clara, CA). The normal-hemispherical transmittance

T_nh,λ measurements were performedusing the same spectropho-tometerwithanintegratingsphereattachment(AgilentCary DRA-2500, Santa Clara, CA). The microalgae suspensions were cen-trifugedat13,400rpm(12,100g)for10minandwashedwithPBS solutionandresuspendedinPBS to avoidabsorptionand scatter-ing by the growth medium. The measurements were performed in1 cm pathlength quartz cuvettes (110-10-40 HellmaAnalytics, Müllheim,Germany)inthewavelengthrangefrom350to750nm. Theaverage spectral absorptionA¯abs,λ andscattering ¯Ssca,λ cross-sectionsofmicroalgaesuspensionsweremeasuredforthree suffi-cientlydilutedbiomassconcentrationsX,namely0.041,0.048,and 0.061m2_{/kgtoensurethatsinglescatteringprevailedandthatthe} retrievedA¯abs,λ and ¯Ssca,λ wereindependent ofX [44] .The cross-sectionsreported correspond to themean of the three measure-mentsandtheerrorbarscorrespondto95%confidenceinterval.

3.4.Transmittanceandreflectanceofagar-immobilizedcells

3.4.1. Samplepreparation

First,a4%agarsolutionwaspreparedbymixing10gof bacte-riologicalagar(TypeABiokarA1010)with250mlofPBS.The so-lutionwasautoclavedat121°Cfor20mintomeltandsterilizethe agar.Themixturewasthenallowedtocoolto60°Cbeforeadding themicroalgaesuspensiontopreventcelldeath.Notethatagar so-lidifiesat35–40°C[45] andthemicroorganismschosenfor immo-bilizationmustbetoleranttotemporarythermalshocks.Chlorella

and Parachlorella, Dunaliella, Nannochloropsis, and Tetraselmis are examplesofspeciestoleranttothermalshocks[45] .Toimmobilize

P.kesslericellsinagar,25mlofthewarmagarsolutionwasmixed with15mlofmicroalgaesuspensioninPBS atroom temperature suchthatthefinalconcentrationofagarinthemixturewas3.2dry wt.%.Atotalvolumeof15mloftheagar/microalgaemixtureswere pouredintopolystyrenepetridishes,35mmindiameter, immedi-atelyaftermixing.Finally,theimmobilized-cellfilmswereallowed tocooltoroomtemperatureandformgelswitheffectivethickness

Lof2.6mm.Thebiomassconcentrationofthemicroalgae suspen-sionswaschosen such thatthe finalbiomass concentrationsX of theimmobilized-cellfilmswere0.0,0.139,0.281,0.559,0.975,4.35, and6.49kg/m3_{.These correspondedto arealbiomass} concentra-tionsXLof0.0,0.36,0.73,1.45,2.54,11.3,and16.9g/m2_.Thefilm correspondingtoXL₌0g/m2_{waspreparedinanidenticalmanner} tothoseused forimmobilizingthemicroalgaebutonlywithPBS insteadofthemicroalgaesuspension.Moreover,thesampleswere concentratedby centrifuging10–100 mlofculture,corresponding tothedesiredfinalconcentrationofthesample,andre-suspending themin15mlofPBS.Theywerenotpreparedbyconcentratingthe entirecultureandseriallydiluting ittoobtain thedesiredsample concentration.

3.4.2. Transmittanceandreflectancemeasurements

Acylindricaltemplatewithsharpedgeswasusedtocuta circu-lardiscof2cmindiameteroutoftheagar-immobilizedP.kessleri

samples (Fig. 2 a). The normal-hemispherical transmittance Tnh,λ andreflectanceRnh,λoftheimmobilized-cellfilmswere systemati-callymeasuredusingthepreviouslydescribedapparatus.The sam-ples were held in place usingthe solid sample holder accessory placedinfrontorbehindtheintegratingsphere.Notethatdespite therelatively large concentration ofagar inthe samples(3.2 dry wt.%),the cut outdiscs were fragileandhadto be handledwith caretopreventtearing.

3.5. Inversemethod

The inverse method, previously developed by Kandilianet al.

[33] , was used to simultaneously retrieve the absorption

κ

_a,λ andtransport scattering

σ

tr,a,λ=

(

1− ga,λ

)

σ

s,a,λ coefficientsofthe agar gel alone using the measured normal-hemispherical trans-mittance T_nh,λ and reflectance R_nh,λ betweenthe wavelengths of 350 and 750 nm. The objective was to find the values of

κ

a,λ and

σ

s,tr,a,λ that minimize the difference between the predicted

[Eqs. (10)–(12)] and the experimentallymeasured spectral normal-hemispherical transmittance and reflectance of the agar gel. For eachwavelength,theobjectivefunction



_λwasdefinedas,



λ=

Tnh,λ,pred− Tnh,λ Tnh,λ

2 +

Rnh,λ,pred− Rnh,λ Rnh,λ

2 . (15)

Here, the inverse method to retrieve

κ

_a,λ and

σ

_s,tr,a,λ was im-plemented in MicrosoftExcelusing thebuilt-in non-linear solver basedonthegeneralizedreducedgradient(GRG)algorithm[46] .

3.6. Dataanalysis

In order to predict the normal-hemispherical transmittance

Tnh,λ,pred andreflectanceRnh,λ,pred usingEqs. (10) –(12) ,one needs to know (i) the thickness L ofthe immobilized-cell film, (ii) the effectiverefractive indexofthe medium n_m,λ,(iii)the absorption coefficient

κ

_λ,and(iv)thetransportscatteringcoefficient

σ

s,tr,λ=

σ

s,λ

(

1− gλ

)

oftheimmobilized-cellfilm.Here,theindexof refrac-tionoftheagarmedium wasassumedtobe equaltothat ofPBS whose spectral refractive index can be expressed by the Cauchy dispersionrelation[47]

nm,λ=1.32711+0.0026

_λ

₂ +0.0

_λ

0₄005 (16)

wherethewavelength

λ

isexpressedinμmintherangefrom0.37 to1.610μm.Moreover,PBScanbesafelytreatedasnon-absorbing inthevisiblepartofthespectrum[47] .

Moreover, absorption andscattering by the agar matrix must beaccountedforwhenpredictingnormal-hemispherical transmit-tance Tnh,λ and reflectance Rnh,λ of the immobilized-cell films. Here, the absorption

κ

_λ and scattering

σ

s,λ coefficients (in 1/m) of the immobilized-cell films were expressed as the sum of the respectivecontributions oftheagarmatrixandofthemicroalgae cellsofconcentrationXsothat

κ

λ=

κ

μ,λ+

κ

a,λ=A¯abs,λX+

κ

a,λ and

σ

s,λ=

σ

s,μ,λ+

σ

s,a,λ=¯Ssca,λX+

σ

s,a,λ (17)

where

κ

_μ,λ=A¯_abs,λX and

σ

_s,μ,λ= ¯S_sca,λX arerespectivelythe aver-ageabsorption andsinglescatteringcoefficients ofrandomly ori-ented microalgae in PBS while A¯abs,λ and ¯Ssca,λ are the average spectral massabsorptionandscatteringcross-sections(inm2_/kg). Similarly, the transport scattering coefficient ofthe immobilized-cellfilmswasexpressedas

σ

s,tr,λ=¯Ssca,λX

(

1− gμ,λ

)

+

σ

s,a,λ

(

1− ga,λ

)

(18)

where g_μ,λ and g_a,λ are the asymmetry factors of themicroalgae andoftheagargel,respectively.

Finally, the two-flux approximation for predicting the fluence rateG_λ(z) in flat-plate PBRs [Eqs. (5) and (6) ] can be applied to immobilized-cellfilmsbyexpressingthebackwardscattering coef-ficientb_λ

σ

s,λofthefilmas

b_λ

σ

s,λ=bμ,λ

σ

s,μ,λ+ba,λ

σ

s,a,λ. (19)

Here, backward scatteringcan be neglected in Eq. (6) compared withabsorption,(i.e.,

κ

_λ>>2b_λ

σ

_s,λ)leadingto

α

_λ=1and

δ

_λ=

κ

λ,

Fig. 2. (a) Color photographs of seven immobilized P. kessleri samples with areal biomass concentration XL ranging from 0 to 16.9 g/m 2 and (b) micrographs of the immobilized-cell films with biomass concentration X equal to 0.559 and 4.35 kg/m 3 .

4. Resultsanddiscussion

4.1. Biomassandpigmentconcentrationofimmobilized-cellfilms

Fig. 2 apresentsaphotographofsevenagar-immobilizedP. kess-leri samples withareal biomass concentration XL ranging from0 to 16.9 g/m2_{. Moreover, Fig. 2 b shows micrographs of the} im-mobilized cells for biomass concentrations of 0.559 kg/m3 _and 4.35 kg/m3_{.It showsrelatively loosepacking ofthe cellsinboth} lowandhighconcentrationsamples.Infact,Souliésetal.[48] re-ported that thevolume fraction ofChlorella vulgaris, a green mi-croalgaesimilarinsizetoParachlorellakessleri,was1.6%whenthe biomassconcentrationXoftheculturewasequalto4kg/m3_.

The concentrations ofChl a, Chl b, andtotal carotenoids ofP. kessleri grownin thecontinuousairlift PBR were measured spec-trophotometricallyandfoundtobe CChla =46.8± 1.41mg/l,CChlb = 13.0 ± 0.62 mg/l, CPPC+PSC = 12.0 ± 0.29 mg/l. These corre-spondedtomassfractionsofwChla=4.81± 0.15wt.%,wChlb=1.33 ± 0.06wt.%,andwPPC+PSC=1.24± 0.03wt.%.

4.2. Radiationcharacteristicsofmicroalgaecells

Fig. 3 a plots the experimentally measured scattering phase functionofP.kessleriat632.8nm.Asexpected,themicroalgaecells scattered light strongly in the forward direction with asymme-tryfactorgμ,633andback-scatteredfractionbμ,633correspondingto 0.974 and0.0042,respectively. Moreover,Figs. 3 band3 cplotthe average massabsorptionA¯abs,λandscattering ¯Ssca,λcross-sections (inm2_{/kg)themicroalgaesuspendedinPBSsolutionmeasured} be-tween 350 and750 nm. Fig. 3 b features absorption peaks corre-spondingtoChlaat435,630,and676nm.Similarly,theshoulder from455to485nmwasduetothesuperpositionofChlb absorp-tionpeakat475nmandthatofPPCaround462and490nm[49] . Asecond absorptionpeakofChlb appearedalsoaround650nm. Inaddition,Figs. 3 band3 cindicatethatthemicroalgaescattering cross-section ¯Ssca,λ was significantly larger than their absorption

cross-sectionA¯abs,λ.However,Fig. 3 dshowsthattransport scatter-ing cross-section ¯Ssca,tr,λ= ¯Ssca,λ

(

1− gμ,λ

)

wasmuchsmallerthan

the absorption cross-section ofthe microalgaeatall wavelengths consideredsincegμ,λapproachedunity.Theseresultswerein qual-itativeandquantitative agreementwiththe radiation characteris-tics of microalgae with similar size and pigment concentrations

[26,32] . Note that the reported absorption A¯abs,λ and scattering

¯S_sca,λcross-sectionswerethemathematicalmeanofsampleswith three different biomass concentrations andthe error bars corre-spondedto95%confidenceintervals.Theseerrorbarswere signif-icantly smaller than the magnitudes ofA¯_abs,λ or ¯S_sca,λ indicating that absorption and scattering coefficients were directly propor-tionalto the biomass concentration. This satisfiedvan de Hulst’s simpleand conclusivetest forthe absence ofmultiple scattering

[44] .

4.3.Transmittanceandreflectanceofimmobilized-cellfilms

Figs. 4 a and 4 b plot the experimentally measured normal-hemisphericaltransmittanceT_nh,λ andreflectanceR_nh,λ of2.6mm thick immobilized-cell films as functionsof wavelength between 350 and750 nm for P. kessleri biomass concentration X ranging from0to16.9g/m2_{.First,thenormal-hemisphericaltransmittance}

T_nh,λ of agargel withPBS (XL=0 g/m2_{) increased monotonously} with increasing wavelength between 350 and 750 nm. By con-trast,thecorrespondingnormal-hemisphericalreflectanceR_nh,λ de-creased from 9.7% at 350 nm to 1.9% at 750 nm. Moreover, the normal-hemispherical transmittance Tnh,λ decreased as the areal biomassconcentration increaseddueto absorptionby the immo-bilizedmicroalgae.Similarly,thenormal-hemisphericalreflectance

Rnh,λ of the film decreased with increasing concentration in the PARregion(400≤

λ

≤ 700nm).However,Rnh,λincreasedwith in-creasingvaluesofXLforwavelengthslargerthan700nm.Thiswas dueto backscatteringbythemicroalgaecellsandtothefactthat agarandmicroalgaeare weakly ornon-absorbingatthese wave-lengths.

4.4.Remoteimmobilized-cellfilmPBRmonitoring

Fig. 5 plotsthenormal-hemisphericalreflectanceRnh,750 ofthe immobilized-cellfilms at750 nm as a function of arealbiomass concentrationXL.Thewavelength

λ

_{= 750} nmwaschosen onthe basis that green microalgaeand cyanobacteria are non-absorbing atthiswavelengthandmeasurementsofnormal-hemispherical re-flectanceRnh,750are notsensitiveto variationinpigment concen-tration.Fig. 5 establishes that Rnh,750 waslinearlyproportional to

XLleadingtoaleastsquarefitof

Rnh,750

(

XL

)

=Rnh,a,750+



XL (20) wherethecoefficientofproportionality



wasequalto 5.5×10−3 ± 3.1×10−4 _m2_{/kg while R}

Fig. 3. (a) Experimentally measured scattering phase function of P. kessleri at 632.8 nm and average spectral mass (b) absorption ¯A abs,λ, (c) scattering ¯S sca,λ, and (d) transport

scattering ¯S sca,tr,λcross-sections of P. kessleri suspensions between 350 and 750 nm. Note that error bars were smaller than the symbols or lines.

Fig. 4. Experimentally measured normal-hemispherical (a) transmittance T nh,λand (b) reflectance R nh,λbetween 350 and 750 nm for P. kessleri cells immobilized in agar gel

Fig. 5. Experimentally measured normal-hemispherical reflectance R nh,750 of the immobilized-cell films at 750 nm as a function of areal biomass concentration XL between 0 and 16.9 g/m 2 along with linear curve fit.

reflectance of agarfilm alone(i.e., XL=0g/m2_{) equal to0.018 ±} 0.0024.Thelatterwasingoodagreementwiththenormal-normal reflectance

ρ

1,750of0.02attheair/agarinterfaceestimatedbyEq.

(7) usingnm,750ofPBS. Theresultssuggestthat measurementsof normal-hemispherical reflectance R_nh,750 can be usedto remotely andnon-invasivelyestimatethearealbiomassconcentration XLof immobilized-cellfilms in realtime.Note,however, thatthe pres-enceofexcessivenumberofdeadcellsand/orcontaminantsinthe culturemayleadtoinaccurateestimatesofthearealbiomass con-centrationXL.

4.5. Agarfilmradiationcharacteristics

Figs. 6 a and 6 b show the spectral absorption

κ

a,λ and trans-portscattering

σ

_s,tr,a,λcoefficientoftheagargelretrievedfromthe normal-hemisphericaltransmittanceTnh,λandreflectanceRnh,λ be-tween350and750nm.Itindicatesthattheabsorptioncoefficient

κ

a,λ oftheagargelwasrelativelyconstantaround30–40m−1 for the wavelengthrangeofinterest. Absorptioncanbe attributedto thefact that bacteriologicalgradeAagar,usedinthisstudy, typ-ically has an ash content of approximately 5–6 wt.% [50] in the formofimpuritiescomposedofmetalssuchasCu, Mn,Fe,Al,Cr, Cd,Ni,Zn,andSnandsaltsfoundinseawatercontainingelements suchasNa,Cl,Ca,P,S,K,andN[51] .

On the other hand, thetransport scatteringcoefficient

σ

_s,tr,a,λ increasedexponentiallywithdecreasingwavelengthfrom approxi-mately6.7m−1 at750nmto reach179m−1 at350nm. The cor-responding least-square fit yielded

σ

_s,tr,a,λ=2660e−0.008λ _with

_λ

expressed in nm andR2 _{= 0.99. In fact,agar gelshavea porous} microstructure with a broad pore size distribution ranging from 100 to600 nm[52] resultingin stronglight scattering.Notealso that mean agarpore size decreases and its size distribution nar-rowswithincreasingdryagarconcentrationinthegel[52,53] .This couldreduce scatteringbutwouldalsoincreaseabsorption.In ad-dition,increasingdryagarconcentrationincreasesthegel mechan-icalstrength[10] .However,italsoincreasesitsliquidstate viscos-itymakingmixingwiththemicroalgaecellsandcastingthe mix-tureintoafilmdifficult.

Overall, these results establish that agar is an absorbing and scatteringmediumanditseffectsshouldbeaccountedforin mod-eling radiation transfer in immobilized-cell films. Note however, that absorptionandscatteringbyimmobilizedmicroalgaeat

con-Fig. 6. Retrieved spectral (a) absorption κa,λand (b) transport scattering σs,tr,a,λ=

(1 − g a,λ)σs,a,λcoefficients of the 2.6 mm thick agar gel used for immobilizing the

microalgae and containing 3.2 dry wt.% of agar.

centrationXlargerthan 0.5kg/m3 _{still dominateoverthe} contri-butionofagargelbetween350and700nm.

4.6.Predictedtransmittanceandreflectance

Figs. 7 a to 7 l compare the measured and predicted normal-hemisphericaltransmittanceT_nh,λandreflectanceR_nh,λof immobi-lizedP. kessleri films withareal biomass concentrations XL equal to (a,b) 0.36, (c,d) 0.73, (e,f) 1.45, (g,h) 2.54, (i,j) 11.3, and (k,l) 16.9g/m2_{.PredictionsofthetransmittanceT}

nh,pred,λandreflectance

R_nh,pred,λwerebasedonthemodifiedtwo-fluxapproximationgiven byEqs. (10) –(12) basedontheeffectiveabsorption

κ

_λ and trans-portscattering

σ

s,tr,λcoefficientsoftheimmobilized-cellfilms esti-matedaccordingtoEqs. (17) and(18) using(i)theaveragespectral absorptionA¯abs,λandscattering ¯Ssca,λcross-sectionsandthe asym-metryfactorgμ,633measuredforthemicroalgaesuspendedinPBS (Figs. 3 ato3 d)and(ii)theretrievedabsorption

κ

_a,λandtransport scattering

σ

s,tr,a,λ coefficientsof the agar film with XL=0 g/m2 (Figs. 6 aand6 b). Good overallagreement wasobservedbetween measurementsandpredictionsofT_nh,λandR_nh,λ.

The modified two-flux approximation tended to underpredict theexperimentally measured transmittanceTnh,λ and to overpre-dict the experimentally measured reflectance Rnh,λ, particularly forlarge areal biomass concentrationsXL. This can be attributed to (a) the assumption of constant microalgae asymmetry factor

Fig. 7. Comparison of measured and predicted normal-hemispherical transmittance T nh,λand reflectance R nh,λof agar immobilized P. kessleri with areal biomass concentration XL of (a, b) 0.36, (c, d) 0.73, (e, f) 1.45, (g, h) 2.54, (i, j) 11.3, and (k, l) 16.9 g/m 2 .

Fig. 8. Dimensionless mean rate of photon absorption = APAR XL/q ”in as a func- tion of areal biomass concentration XL estimated by (i) Eqs. (1) –(6) or (ii) by Eq. (9) using either the measured or (iii) the predicted normal-hemispherical transmit- tance T nh,λ,pred and reflectance R nh,λ,pred .

g_μ,λ over the PAR region andmoreimportantly (b)to the use of the transport approximation instead of a more accurate scatter-ingphasefunction.Indeed,thetransportapproximationexpresses the scatteringphase function ofthe microorganismsasa sumof an isotropic componentandaforward scatteringpeakat



=0o_. By contrast the measured microalgae scattering phase function (Fig. 3 a)featuressmallvaluesinthebackwarddirections(



_{≥ 90}o₎ that are overestimated by the isotropic component of the trans-port approximation leadingto the overprediction ofthe normal-hemispherical reflectanceR_nh,λ particularlyfor

λ

_{≥ 700} nmwhen thefilmisweaklyabsorbing.

4.7. Meanrateofphotonabsorption

Fig. 8 comparesthedimensionlessmeanrateofphoton absorp-tion

₌



_APAR



XL/qPAR” ,in, asa functionofthearealbiomass con-centration XL estimated either (i) using the PAR-averaged mean rate of photon absorption estimated by Eqs. (1) –(6) or(ii) using

Eq. – (9) basedonthemeasuredor(iii)onthepredicted transmit-tanceTnh,λ,predandreflectanceRnh,λ,pred.

First, predictions of the PAR-averaged absorbance

given by

Eq. (9) using the experimentally measured or predicted normal-hemispherical transmittanceT_nh,λ andreflectanceR_nh,λ fell within 10% ofeach otherforarealbiomassconcentrationXLgreaterthan 1g/m2_{.However,their relativedifferenceincreasedupto30% for}

XL smaller than 1 g/m2 _{due to the fact that the modified} two-flux approximation underpredicted the experimentally measured normal-hemisphericaltransmittanceTnh,λ.Thedifferencebetween thetwoapproacheswasnotassignificantatlargerXL,asT_nh,λand

Rnh,λtendedtozero.

Moreover, Fig. 8 indicates that predictions of



_APAR



XL/q”PAR,in using Eqs. (1) –(6) were systematically smaller than those esti-mated usingEq (9) .This wasduetothe fact that Eq. (9) implic-itly accountedforabsorption andscatteringbyboth the microal-gaeandtheagargel(seeSupplementalMaterial).Bycontrast,Eqs. (1) –(6) considerabsorption andscatteringby microalgaeandagar

when predicting the local fluence rate G_λ(z) but only take into accountabsorption by microalgaewhen predictingthemeanrate of photon absorption



APAR



. In other words, Eq. (9) predict the meanrateofphoton absorptionofthe ensembleofagarand mi-croalgaewhileEqs. (1) –(6) estimate onlythat ofthe microorgan-isms.Thelatteristheparameterthatshouldbe usedwhen mod-eling the kinetics of microalgae since only photons absorbed by microalgaecanparticipateinthebiochemicalreactionswithinthe cell.Herealso,thedifferencebetweenthetwoapproacheswas ap-parentandmostsignificantatverylow microalgaeconcentrations

XL<<1g/m2 _whentheMRPA

_

_A

PAR



convergestozero.Therefore, theMRPA



APAR



inimmobilized-cellfilmsshouldbepredicted us-ingEqs. (1) –(6) .

4.8.Optimalarealbiomassconcentration

As previously discussed, in order to maximize secondary metabolite productivityof immobilized-cellfilm PBRsexposed to normally incident solar radiation on the front face, the biomass concentration Xandthe filmthicknessLshould be selectedsuch that the local rate of photon absorption APAR

(

L

)

on the film backside is equal to the photosynthetic compensation point Ac

[16,17,38,39] .

Figs. 9 a and 9 b show (a) the optimum PAR-averaged fluence rateGPAR(z)estimatedbyEqs. (5) and(6) and(b)the correspond-ingoptimum RPA_APAR

(

z

)

predictedby Eq. (3) forimmobilizedP.

kesslerifilmexposedtoanintermediatevalueofPAR-averaged inci-dentsolarirradianceq"

PAR,in=200μmolhν/m2·s.Here,theoptimum areal biomass concentration (XL)opt was 15.2 g/m2 (5.85 kg/m3) andsuchthatAPAR

(

L

)

=Ac=1,500μmolhν/kg·s.Notethatthe lat-ter correspondedto the photosynthetic compensationpoint of C. vulgaris but it was used in this study due to a lack of data for

P.kessleriandbecauseboth specieswere greenmicroalgaeofthe samefamilyandsize.

Furthermore,Figs. 9 cand9 dshowthe(c)optimalbiomassXopt and(d) optimal areal biomass (XL)opt concentrations of immobi-lizedP. kesslerifilms asfunctionsof incidentphoton flux density

q"

PAR,in ranging from 50 to 1,500 μmolhν/m2·s and for three dif-ferent values of film thickness L of 2.6, 5, and 10 mm. Fig. 9 c alsoshowsthe fittingcurvesof theformof Xopt=c1ln

(

q"PAR,in

)

+

c2 where c1 and c2 are constants estimated by the least square methodforeach filmthicknessconsidered. First,Fig. 9 cindicates that the optimum biomass concentration Xopt decreased with in-creasingfilm thickness Lforthe same incident photon flux den-sity q"

PAR,in. However, Fig. 9 establishes that the optimum values ofXLwereindependentofthefilmthicknessL.Instead,the prod-uctXL,representingthefilmopticalthickness,determinedthePBR performance.Thiswasalsoobservedforconventional PBRs(open ponds,flat-plate,andtubular)inbothbatchandcontinuousmodes

[30] .

Fig. 9 dalsoillustratesthattheoptimumarealbiomass concen-tration (XL)opt increasedwith increasing q"_PAR,in. IncreasingXL be-yond(XL)optwouldresultinthepresenceofaso-called“darkzone” wheretherespirationrateofthemicroorganismsislargerthanthe photosynthesis rate. This would result in loss of biomass and/or metaboliteproductivity.Ontheotherhand,XL<(XL)optwouldlead toalargerthanoptimumAPAR

(

z

)

causingexcessivedissipationof the absorbedenergy by the microorganisms in the form of heat andfluorescencethusloweringmetaboliteproductivityandPBR ef-ficiency[54] .

Moreover, the relationship between (XL)opt andq"_PAR,in can be fittedas

(

XL

)

opt=6.44ln



q" PAR,in



− 18.51 (21)

withcoefficientofdeterminationR2_{=0.99.Themathematicalform} ofthis correlation can be derived from Eqs. (1) –(6) assuming (i)

Fig. 9. Optimum local PAR-averaged (a) fluence rate G PAR ( z ) and (b) rate of photon absorption APAR(z) in immobilized P. kessleri film with areal biomass concentration XL equal to 15.2 g/m 2 exposed to incident irradiance q "

PAR,in = 200 μmol hν/m 2 ·s. Optimal (c) biomass X opt and (d) areal biomass ( XL ) opt concentration as a function of incident photon flux density q " PAR,in for film thickness L of 2.6 mm, 5 mm, and 10 mm.

monochromaticincidentphotonfluxdensityorgreyfilmPBRand (ii)negligiblysmallbackwardscatteringratio(b_λ=0).Itis impor-tant to note that this design ruleis valid forP. kessleri with the radiationcharacteristicsreportedinFig. 3 foranyfilmthicknessL. Finally, we assumed that the culture is only light-limited with no mineral limitation or oxygen inhibition. While this can be achieved in properly operated open-ponds and closed PBRs containing suspended microalgae, it must be validated for immobilized-cellfilm PBRs asthe presence of agar gel may also leadto nutrient limitations.However, thisfallsoutside thescope ofthepresentstudy.

5. Conclusion

This paper developed and experimentally validated a model based on the modified two-flux approximation to predict light transferinimmobilized-cellPBRs.Thiswasdemonstrated success-fullyusingParachlorellakesslericellsimmobilizedinagargelwith

areal biomass concentration XL ranging from 0.36 to 16.9 g/m2 (X between 0.145 and 6.49 kg/m3_{). The absorption and} trans-port scattering coefficients of the microalgae cells and the agar gelwere measured independently.Then, theabsorptionand scat-tering coefficients of the immobilized-cell films were expressed as the sum of the respective contributions of their constituents. Predictions of the normal-hemispherical transmittance and re-flectance of the immobilized-cell films by the two-flux approxi-mation agreed well withthe experimental measurements for all biomass concentrations considered. The results also suggest that normal-hemispherical reflectance at 750 nm could be used for real-timeremotemonitoringofthearealbiomassconcentrationof immobilized-cellfilms.Finally,theoptimumarealbiomass concen-tration (XL)opt wasestimatedas a function ofincident irradiance

q"

PAR,inandwasfoundto(i)beindependentoffilmthicknessLand (ii)increase logarithmicallywithincreasing q"

PAR,in inlight-limited cultures.

Acknowledgments

ThisstudywassupportedbytheregionPaysdelaLoire,France through the project Atlantique Microalgae (AMI). L.P. thanks the RégionPaysdelaLoirefortheResearchChairforInternational Ju-niorScientists.

Supplementarymaterial

Supplementary material associated with this article can be found,intheonlineversion,at10.1016/j.jqsrt.2017.04.027

References

[1] Saha S , McHugh E , Murray P , Walsh D . Microalgae as a source of nutraceuti- cals. In: Phycotoxins: chemistry and biochemistry; 2016. p. 255–91 .

[2] Wang H-M D, Chen C-C, Huynh P, Chang J-S. Exploring the poten- tial of using algae in cosmetics. Biores Technol 2015;184:355–62. doi: 10.1016/j.biortech.2014.12.001 . http://www.sciencedirect.com/science/ article/pii/S0960852414017350 .

[3] Yan N , Fan C , Chen Y , Hu Z . The potential for microalgae as bioreactors to produce pharmaceuticals. Int J Mol Sci 2016;17(6):962 .

[4] Quinn J, Davis R. The potentials and challenges of algae based biofuels: a review of the techno-economic, life cycle, and resource assessment model- ing. Biores Technol 2015;184:4 4 4–52. doi: 10.1016/j.biortech.2014.10.075 . http: //www.sciencedirect.com/science/article/pii/S0960852414014977 .

[5] Griffiths M, Harrison S, Smit M, Maharajh D. Major commercial products from micro- and macroalgae. In: Bux F, Chisti Y, editors. Algae biotechnology: prod- ucts and processes. Berlin, Germany: Springer; 2016. p. 269–300. ISBN 978-3- 319-12334-9. doi: 10.1007/978- 3- 319- 12334- 9 _ 14 .

[6] Caporgno M, Taleb A, Olkiewicz M, Font J, Pruvost J, Legrand J, et al. Microal- gae cultivation in urban wastewater: nutrient removal and biomass production for biodiesel and methane. Algal Res 2015;10:232–9. doi: 10.1016/j.algal.2015. 05.011 . http://www.sciencedirect.com/science/article/pii/S2211926415001319 . [7] Vigani M, Parisi C, guez Cerezo ER, Barbosa M, Sijtsma L, Ploeg M, et al. Food

and feed products from microalgae: market opportunities and challenges for the EU. Trends Food Sci Technol 2015;42(1):81–92. doi: 10.1016/j.tifs.2014.12. 004 . http://www.sciencedirect.com/science/article/pii/S0924224414002787 . [8] Chisti Y. Large-scale production of algal biomass: raceway ponds. In:

Bux F, Chisti Y, editors. Algae biotechnology: products and processes. Berlin, Germany: Springer; 2016. p. 21–40. ISBN 978-3-319-12334-9. doi: 10.1007/ 978- 3- 319- 12334- 9 _ 2 .

[9] Travieso L, Benitez F, Dupeiron R. Sewage treatment using immobi- lized microalgae. Biores Technol 1992;40(2):183–7. doi: 10.1016/0960-8524(92) 90207-E . http://www.sciencedirect.com/science/article/pii/096085249290207E . [10] de Bashan L, Bashan Y. Immobilized microalgae for removing pollutants: review of practical aspects. Biores Technol 2010;101(6):1611–27. doi: 10. 1016/j.biortech.2009.09.043 . http://www.sciencedirect.com/science/article/pii/ S0960852409012498 .

[11] Lebeau T, Moan R, Turpin V, Robert J-M. Alginate-entrapped Haslea ostrearia as inoculum for the greening of oysters. Biotechnol Tech 1998;12(11):847–50. doi: 10.1023/A:1008885222634 .

[12] Lebeau T, Junter G-A, Jouenne T, Robert J-M. Marennine production by agar-entrapped Haslea ostrearia Simonsen. Biores Technol 1999;67(1):13–17. doi: 10.1016/S0960-8524(99)0 0 096-6 . http://www.sciencedirect.com/science/ article/pii/S09608524990 0 0966 .

[13] Covarrubias S, de Bashan L, Moreno M, Bashan Y. Alginate beads provide a beneficial physical barrier against native microorganisms in wastewater treated with immobilized bacteria and microalgae. Appl Microbiol Biotechnol 2012;93(6):2669–80. doi: 10.10 07/s0 0253- 011- 3585- 8 .

[14] Jin J, Dupré C, Yoneda K, Watanabe MM, Legrand J, Grizeau D. Charac- teristics of extracellular hydrocarbon-rich microalga Botryococcus braunii for biofuels production: recent advances and opportunities. Process Biochem 2015;51:1866–75. doi: 10.1016/j.procbio.2015.11.026 . http://www.sciencedirect. com/science/article/pii/S1359511315301392 .

[15] Gastineau R, Turcotte F, Pouvreau J-B, Moranais M, Fleurence J, Windarto E, et al. Marennine, promising blue pigments from a widespread Haslea diatom species complex. Mar Drugs 2014;12(6):3161–89. doi: 10.3390/md12063161 . http://www.mdpi.com/1660-3397/12/6/3161 .

[16] Takache H , Christophe G , Cornet J-F , Pruvost J . Experimental and theoreti- cal assessment of maximum productivities for the microalgae Chlamydomonas reinhardtii in two different geometries of photobioreactors. Biotechnol Prog 2010;26(2):431–40 .

[17] Takache H , Pruvost J , Cornet J-F . Kinetic modeling of the photosynthetic growth of Chlamydomonas reinhardtii in a photobioreactor. Biotechnol Prog 2012;28(3):681–92 .

[18] Pruvost J , Vooren GV , Cogne G , Legrand J . Investigation of biomass and lipids production with Neochloris oleoabundans in photobioreactor. Biores Technol 20 09;10 0(23):5988–95 .

[19] Pruvost J , Cornet J . Knowledge models for the engineering and optimization of photobioreactors. In: Posten C, Walter C, editors. Microalgal biotechnology: potential and production. Berlin, Germany: De Gruyter; 2012. p. 181–224 .

[20] Kandilian R , Pruvost J , Legrand J , Pilon L . Influence of light absorption rate by Nannochloropsis oculata on triglyceride production during nitrogen starvation. Biores Technol 2014;163:308–19 .

[21] Kandilian R , Tsao T-C , Pilon L . Control of incident irradiance on a batch oper- ated flat-plate photobioreactor. Chem Eng Sci 2014;119:99–108 .

[22] Pruvost J, Cornet J-F, Pilon L. Large-scale production of algal biomass: pho- tobioreactors. In: Bux F, Chisti Y, editors. Algae biotechnology: products and processes. Netherlands: Springer; 2016. p. 41–66. ISBN 978-3-319-12334-9. doi: 10.1007/978- 3- 319- 12334- 9 _ 3 .

[23] Pilon L , Berbero ˘glu H , Kandilian R . Radiation transfer in photobiological carbon dioxide fixation and fuel production by microalgae. J Quant Spectrosc Radiat Transfer 2011;112(17):2639–60 .

[24] Dauchet J, Blanco S, Cornet J-F, Fournier R. Calculation of the radiative prop- erties of photosynthetic microorganisms. J Quant Spectrosc Radiat Trans- fer 2015;161:60–84. doi: 10.1016/j.jqsrt.2015.03.025 . http://www.sciencedirect. com/science/article/pii/S0 0224073150 01272 .

[25] Pilon L , Kandilian R . Interaction between light and photosynthetic microorgan- isms. In: Legrand J, editor. Photobioreaction engineering, 48. Cambridge, MA: Academic Press; 2016. p. 107–49 .

[26] Kandilian R , Lee E , Pilon L . Radiation and optical properties of Nannochlorop- sis oculata grown under different irradiances and spectra. Biores Technol 2013;137:63–73 .

[27] Pottier L , Pruvost J , Deremetz J , Cornet J-F , Legrand J , Dussap C . A fully predic- tive model for one-dimensional light attenuation by C hlamydomonas reinhardtii in a torous photobioreactor. Biotechnol Bioeng 2005;91:569–82 .

[28] Berbero ˘glu H , Yin J , Pilon L . Light transfer in bubble sparged photo- bioreactors for H 2 production and CO 2 mitigation. Int J Hydrogen Energy 2007;32(13):2273–85 .

[29] Berbero ˘glu H , Pilon L . Maximizing solar to H 2 energy conversion efficiency of outdoor photobioreactors using mixed cultures. Int J Hydrogen Energy 2010;35:500–10 .

[30] Lee E , Pruvost J , He X , Ramakanth R , Pilon L . Design tool and guidelines for outdoor photobioreactors. Chem Eng Sci 2014;106:18–29 .

[31] Kong B, Vigil RD. Simulation of photosynthetically active radiation distri- bution in algal photobioreactors using a multidimensional spectral radia- tion model. Biores Technol 2014;158:141–8. doi: 10.1016/j.biortech.2014.01.052 . http://www.sciencedirect.com/science/article/pii/S09608524140 0 0777 . [32] Kandilian R , Pruvost J , Artu A , Lemasson C , Legrand J , Pilon L . Comparison of

experimentally and theoretically determined radiation characteristics of photo- synthetic microorganisms. J Quant Spectrosc Radiat Transfer 2016;175:30–45 .

[33] Kandilian R , Soulies A , Pruvost J , Rousseau B , Legrand J , Pilon L . Simple method for measuring the spectral absorption cross-section of microalgae. Chem Eng Sci 2016;146:357–68 .

[34] Cornet J-F , Dussap C , Dubertret G . A structured model for simulation of cul- tures of the cyanobacterium Spirulina platensis in photobioreactors: I. Coupling between light transfer and growth kinetics. Biotechnol Bioeng 1992;40:817–25 .

[35] Jonasz M , Fournier G . Light scattering by particles in water: theoretical and experimental foundations. San Diego, CA: Academic Press; 2007. ISBN 9780123887511 .

[36] Dombrovsky L , Randrianalisoa J , Baillis D , Pilon L . Use of Mie theory to analyze experimental data to identify infrared properties of fused quartz containing bubbles. Appl Opt 2005;44(33):7021–31 .

[37] Pruvost J , Cornet J-F , Legrand J . Hydrodynamics influence on light conver- sion in photobioreactors: an energetically consistent analysis. Chem Eng Sci 2008;63:3679–94 .

[38] Cornet J , Dussap C . A simple and reliable formula for assessment of maximum volumetric productivities in photobioreactors. Biotechnol Prog 2009;25:424–35 .

[39] Soulies A, Legrand J, Marec H, Pruvost J, Castelain C, Burghelea T, et al. In- vestigation and modeling of the effects of light spectrum and incident an- gle on the growth of Chlorella vulgaris in photobioreactors. Biotechnol Prog 2016;32(2):247–61. doi: 10.1002/btpr.2244 .

[40] Modest M . Radiative heat transfer. third. Oxford, UK: Elsevier; 2013 .

[41] Ritchie R . Consistent sets of spectrophotometric chlorophyll equations for ace- tone, methanol and ethanol solvents. Photosynth Res 2006;89(1):27–41 .

[42] Strickland J , Parsons T . A practical handbook of seawater analysis: pigment analysis. Bulletin of fisheries research board of canada. Fisheries Research Board of Canada; 1968 .

[43] Berbero ˘glu H , Pilon L , Melis A . Radiation characteristics of Chlamydomonas reinhardtii CC125 and its truncated chlorophyll antenna transformants tla1, tlaX , and tla1-CW+ . Int J Hydrogen Energy 2008;33(22):6467–83 .

[44] Hulst HVD . Light scattering by small particles. New York, NY: Wiley; 1957 .

[45] Moreno-Garrido I. Microalgae immobilization: current techniques and uses. Biores Technol 2008;99(10):3949–64. doi: 10.1016/j.biortech.2007.05.040 . http: //www.sciencedirect.com/science/article/pii/S0960852407004567 .

[46] Press W , Teukolsky SA , Vetterling WT , Flannery BP . Numerical recipes: the Art of scientific computing. New York, NY: Cambridge University Press; 2007 .

[47] Zhernovaya O , Sydoruk O , Tuchin V , Douplik A . The refractive index of human hemoglobin in the visible range. Phys Med Biol 2011;56(13):4013–21 .

[48] Souliés A, Pruvost J, Legrand J, Castelain C, Burghelea T. Rheological proper- ties of suspensions of the green microalga Chlorella vulgari s at various volume fractions. Rheol Acta 2013;52(6):589–605. doi: 10.10 07/s0 0397- 013- 0700- z .

[49] Bidigare RR , Ondrusek MEE , Morrow JHH , Kiefer DAA . In-vivo absorption prop- erties of algal pigments. Proceedings of the SPIE 1990;1302:290–302 .

[50] Agar product information sheet. http://www.sigmaaldrich.com/content/dam/ sigma-aldrich/docs/Sigma/Product _ Information _ Sheet/a4550pis.pdf .

[51] Scholten H , Pierik R . Agar as a gelling agent: chemical and physical analysis. Plant Cell Rep 1998;17(3):230–5 .

[52] Pernodet N, Maaloum M, Tinland B. Pore size of agarose gels by atomic force microscopy. Electrophoresis 1997;18(1):55–8. doi: 10.1002/elps.1150180111 .

[53] Narayanan J, Xiong J-Y, Liu X-Y. Determination of agarose gel pore size: ab- sorbance measurements vis a vis other techniques. J Phys 2006;28(1):83–6 . http://stacks.iop.org/1742-6596/28/i=1/a=017

[54] Pruvost J, Gouic BL, Lepine O, Legrand J, Borgne FL. Microalgae culture in building-integrated photobioreactors: biomass production modelling and en- ergetic analysis. Chem Eng J 2016;284:850–61. doi: 10.1016/j.cej.2015.08.118 . http://www.sciencedirect.com/science/article/pii/S1385894715012012 .