Bioresource Technology 162 (2014) 123–128

Contents lists available at ScienceDirect

Bioresource Technology

journal homepage: www.elsevier .com/locate /bior tech

First steps towards a constructal Microbial Fuel Cell

http://dx.doi.org/10.1016/j.biortech.2014.03.1390960-8524/� 2014 Elsevier Ltd. All rights reserved.

⇑ Corresponding author. Tel.: +33 4 79 75 86 26; fax: +33 4 79 75 86 42.E-mail address: gerard.perrier@univ-savoie.fr (G. Perrier).

1 Present address: Naturamole, ZA du Villaret, 38350 Susville, France.

Guillaume Lepage 1, Gérard Perrier ⇑, Julien Ramousse, Gérard MerlinLaboratoire Optimisation de la Conception et Ingénierie de l’Environnement, CNRS UMR 5271, Université de Savoie, Polytech Annecy-Chambéry, 73376 Le Bourget du Lac, France

h i g h l i g h t s

� A constructal-inspired approach istested in a 2D double chamber MFCprototype.� Regular and singular pressure drops

are considered for the entropygeneration.� The determination of entropy

generation allowed the fluiddistribution optimization.� Stability and robustness of the

bioelectrochemical system are shownup to 10 weeks.� The potential of the constructal

approach in MFC is shown.

g r a p h i c a l a b s t r a c t

a r t i c l e i n f o

Article history:Received 10 January 2014Received in revised form 24 March 2014Accepted 25 March 2014Available online 2 April 2014

Keywords:Microbial Fuel CellBioelectrochemical systemEntropy generationConstructal design

a b s t r a c t

In order to reach real operating conditions with consequent organic charge flow, a multi-channel reactorfor Microbial Fuel Cells is designed. The feed-through double chamber reactor is a two-dimensionalsystem with four parallel channels and Reticulated Vitreous Carbon as electrodes. Based on thermody-namical calculations, the constructal-inspired distributor is optimized with the aim to reduce entropygeneration along the distributing path. In the case of negligible singular pressure drops, the Hess–Murraylaw links the lengths and the hydraulic diameters of the successive reducing ducts leading to one givenworking channel. The determination of generated entropy in the channels of our constructal MFC is basedon the global hydraulic resistance caused by both regular and singular pressure drops. Polarization,power and Electrochemical Impedance Spectroscopy show the robustness and the efficiency of the cell,and therefore the potential of the constructal approach. Routes towards improvements are suggestedin terms of design evolutions.

� 2014 Elsevier Ltd. All rights reserved.

1. Introduction

Reducing the environmental impact of human activitiestogether with contributing to energy production with the help ofnatural entities is a challenge that is becoming a reality with therecent development of Microbial Fuel Cells (MFCs). MFCs are ableto reduce organic charge in wastewater. They simultaneously and

directly produce electrical energy, although still in limitedquantities at the present time (Rabaey and Verstraete, 2005; Loganet al., 2006; Logan and Regan, 2006; Kim et al., 2007; Lovley, 2008;Rinaldi et al., 2008; Watanabe, 2008; Du et al., 2007; Oliviera et al.,2013). Organic wastes and wastewaters are among the most sus-tainable and cost-effective feedstocks for MFCs (Hawkes et al.,2010). Practical implementation in wastewater treatment plantscan now be considered, however some technological, microbiolog-ical and economic challenges are to be solved (Rozendal et al.,2008; Oh et al., 2010).

The reactor design is one of the key features for wastewaterdepollution and electricity production efficiency. One approach

Fig. 1. Principle of the constructal series. Dhi are the hydraulic diameters and wi andL are respectively the widths (equal to the depths) and the lengths for each fork.

124 G. Lepage et al. / Bioresource Technology 162 (2014) 123–128

consists in observing and copying Nature’s great successes in min-imizing resistances and optimizing mass and energy transfers;treelike shapes in the vegetable world or in lungs’ bronchi andalveoli architecture in physiology are examples.

Based on these observations, the constructal approach was ini-tially developed in order to improve heat transfers (Bejan, 1997).This approach has been used for solving flow distribution problemsby optimizing branching, lengths and diameters ratios in two orthree dimensions (Wechsatol et al., 2002; Tondeur and Luo, 2004;Luo and Tondeur, 2005). This concept can be applied to various sys-tems, among them fuel cells (Liu et al., 2010). The geometry ofwater or gas delivery channels can be tackled by simulation thanksto this approach (Ramos-Alvarado et al., 2012; Arvay et al., 2013).

To our knowledge, this is the first time that the design of a MFCis undertaken via a constructal or similar approach (Lepage et al.,2011). Tsan et al. (2011) studied the effect of biometrics flow chan-nels with various obstacles in a rumen MFC at different Reynoldsnumbers. The presence of obstacles provides better mixing andstandardization of the flow together with power output enhance-ment. In the early times of MFCs, Min and Logan (2004) testedthe ability of a single channel flat plate air–cathode MFC.

In the present work, the constructal approach is used in a feed-through MFC as a tool to improve mass and energy transfers bydecreasing the pressure loss between the input and the output ofthe system. As a first step, a two-dimensional system with fourparallel channels is described. The double chamber system is runwith Reticulous Vitreous Carbon (RVC) as electrode material undercontinuous flow. Polarization and power curves are presented, to-gether with Electrochemical Impedance Spectroscopy (EIS) analy-ses for a broad description of the system.

2. Methods

2.1. Calculations

The constructal approach is a recent theory aiming at improvingsystems efficiencies by minimizing entropy generated by masstransfer resistances. This approach is particularly well adapted tothe study of flow distribution and collection problems in multi-channel reactors. It appears of high interest for the geometricaloptimization in the case of Microbial Fuel Cells, because of the highresident time that is needed in the reaction chamber. By the way,the resort to multichannel reactors should help managing high or-ganic flows in future compact microbial reactors.

For Hagen–Poiseuille flows, the hydraulic resistance Rhi causedby a regular pressure drop DPreg

i in a tube of diameter Di and lengthLi is written as:

Rhi ¼DPreg

i_mi¼ 128m

pLi

D4i

ð1Þ

where _mi is the mass flow in kg s�1 and m the kinematic viscosity inPa s when the geometric variables are expressed in meters (SIunits).

In the case of rectangular channels (width wi and depth di), thehydraulic diameter Dhi is used to assimilate the section to that of acircular channel through the relation:

Dhi ¼ 4Ai

Pi¼ 2

wi � di

wi þ dið2Þ

with being the channel cross section area and Pi the wet perimeter.For right angles and bifurcations the singular pressure drops

DPsingi have to be taken into account by the addition of an equiva-

lent length Leq,i:

Leq;i ¼Ksing

i Dh;i

64=Reið3Þ

with Rei the Reynolds number. Ksingi is the singular pressure drop

coefficient. According to fluid mechanics literature (Idelchik,2008) and to basic experiments, this parameter is set to 1.13 forright angles and 1.57 for tees. Thus, the global hydraulic resistancecaused by the regular and singular pressure drops in a tube of diam-eter Dhi and length Li can be written:

Rhi ¼DPreg

i þ DPsingi

_mi¼ 128m

pðLi þ Leq;iÞ

Dh4i

ð4Þ

In the case where DP << P and after linearization, q being the den-sity of the fluid, the associated generated entropy Si in the tube i isexpressed as (in W K�1):

Si ¼DPi _mi

qT¼ Rhi _m2

i

qTð5Þ

The goal is optimal flow network design by minimizing entropygeneration along the flow path. In the case of negligible singularpressure drops, this leads to the Hess–Murray law that links thelength and the hydraulic diameter of one given channel to the fol-lowing one (Wechsatol et al., 2002):

Li

Liþ1¼ Dhi

Dhiþ1¼ 2�1 3= ð6Þ

Let us now consider the flow network of Fig. 1, corresponding to afour-channel distributor (or collector), the approach developed herefor the distributor being applicable to the collector with the help ofsymmetry considerations.

In this distribution scheme, Qtot being the global flow at boththe inlet and the outlet, the electrolyte volumetric flows Qi throughthe subsequent channels are interconnected by:

Q5 ¼ Q tot;Q 4 ¼ Q 3 ¼ Q tot=2 and Q2 ¼ Q 1 ¼ Q tot=4 ð7Þ

2.2. Design

A first prototype of a Microbial Fuel Cell inspired from the con-structal theory has been dimensioned in order to highlight systemefficiency gain in multichannel reactors and to validate the ap-proach (Fig. 2). Optimal design was not able to be reached in thisfirst stage because of technical limitations (square sections, con-stant depth and right angles). However, in a first approximation,channels lengths and square section sides are set using Hess–Mur-ray law and rounded to the next millimeter. The reported dimen-sions in Table 1 show that the Hess–Murray ratio is wellpreserved for widths and lengths in every fork. It is then believedthat the principle of the constructal approach remains the connect-ing thread for this first attempt in MFCs.

As the reactive area of the system is related to channel 1, itslength L1 was chosen to ensure a sufficient residence time for theelectrolyte in the reaction chamber. Indeed, in such living systems,

i

Fig. 2. Top view of the constructal plate with engraving dimensions in mm. In gray:the 8-mm-depth channels with electrodes on their bottom. In black: the 5-mm-depth distributing and collecting ducts. The circles represent the drill holes forclamping bolts.

Fig. 3. Schematic section of the channels showing the anodic and cathodiccompartments separated by the Proton Exchange Membrane. The flow is perpen-dicular to this cross section.

G. Lepage et al. / Bioresource Technology 162 (2014) 123–128 125

the bio-kinetic processes are quite long (regarding to the acetateremoval rate (Zeng et al., 2010)). The volumetric flow Q1 in thereactive channels imposes a minimal channel length L1 of 120 mmin our case of a square section area A1 = w1�d1 = (510�3)2 m2, with aresidence time of about 30 s.

As seen in Fig. 2, the prototype is a flat double-chamber reactorconsisting of four parallel channels. The series of the distributor,channels and collector are identically engraved on two facing20 mm-thick PMMA plates. For practical manufacturing reasons,the depth is kept constant at 5 mm, except for the four linear chan-nels (depth 8 mm) that are intended to receive the 3 mm-thickelectrode materials at their bottom.

The following experimental conditions for the dimensionalcalculations to be getting started then apply: Qtot = 6.7 ml min�1 =1.12 � 10�7 m3 s�1; w1 = d1 = Dh1 = 5 � 10�3m; L2 = 24 � 10�3 m.

Together with the dimensional characteristics of the prototype,Table I gives the hydraulic resistances and entropy generations cal-culated for each channel of the cell for the actual case, for a basiccase (square sections with constant widths and depths) and for aquasi-ideal case. The quasi-ideal case is considered using Hess–Murray law (ideal), but does include singular pressure drops dueto bifurcations and right angles.

Note that in the quasi-ideal case, generated entropy is almostconstant for all parts i, with a mean value of 2.4 � 10�12 W K�1.The entropy generated in our prototype is still 2.7 times higherthan that in the quasi-ideal case, but presents a significant gainof 2.9 as compared to the case of a constant square section of5 � 5 mm2. An entropy generation decrease of more than 8 timescan thus be expected from the basic case to the quasi-ideal case.

Table 1Hydraulic resistances Rhi and entropy generations Si (in 10�12 W K�1) for the three designsquasi-ideal respecting the Hess–Murray law apart for the right angles bifurcations, and ouri is the order of the element (see Fig. 2) and Qi (in 10�8 m3 s�1) is the flow rate for each odefined as Stot = S5 + 2(S4 + S3) + 4(S2 + S1).

Basic case Qu

i Qi Li Dhi Rhi Si Dh

5 11.2 49 5 3150 131 134 5.58 38 5 2350 25 103 5.58 30 5 1900 20 82 2.79 24 5 1470 3.8 61 2.79 18 5 1070 2.8 5

Stot 247

2.3. Experimental

The RVC material (Goodfellow, 24 pores per cm), used for bothanode and cathode, is a 3.2-mm-thick open-pore foam (Lepageet al., 2012). This foam electrode is pasted, with electrically con-ductive glue, with carbon felt at its bottom. The electrical currentis collected through a stainless steel screw connected to a brass ba-nana female plug crossing the plate. Good electrical conduction(resistance 10–25 X as measured with tips) is then ensured be-tween all points of the electrode and the collecting plug. The twoplates are carefully clamped together and the waterproofness is gi-ven by a 1-mm-thick rubber sheet presenting four windows for thechannels. Between the channels, anolyte and catholyte are sepa-rated by a Nafion™ N-117 cation exchange membrane (Fig. 3).

The total area of the membrane in contact with the electrolytesis 52 cm2, and exceeds for construction reasons the total apparentarea which is 24 cm2 for each electrode. The total volume of thereactor, including the inlet and outlet ducts, is 75 cm3 (5 cm3 forone half-channel (anodic or cathodic), giving 20 cm3 for eachchamber and 40 cm3 for the whole active cell). The distance be-tween the two electrodes is about 1.2 cm, close to literature-basedideal distance (Cheng et al., 2006).

The sowing phase of the reactor starting is boosted as follows. Along-running MFC is kept in the laboratory for maintaining anelectroactive bacterial culture. In this setup, the anolyte is stirredand pumped to the anodic chamber of the constructal MFC, andthe two MFCs are kept running together for inoculation during

considered, a square-section basic case with constant depths and widths (Dhi = 5), acase. Lengths Li, widths wi, depths di and hydraulic diameters Dhi are expressed in mm.rder. In the basic and quasi-ideal cases, wi = di = Dhi. The total entropy generation is

asi-ideal case Actual case

i Rhi Si wi di Dhi Rhi Si

69 2.9 13 5 7.2 723 30147 1.5 10 5 6.7 744 7.8290 3 8 5 6.2 829 8.6711 1.9 6 5 5.5 1040 2.7

1070 2.8 5 5 5 1070 2.831 85

126 G. Lepage et al. / Bioresource Technology 162 (2014) 123–128

5 days under a 120 X-external resistor. The two reactors are thendisconnected and the constructal reactor is let to run in autonomy.The reactor is then fed with continuous flowing electrolytes at aflow rate of 6.7 mL min�1. The anolyte is a modified M9 mediumwhose composition is Na2HPO4 6 g L�1; KH2PO4 3 g L�1; NH4Cl0.1 g L�1; NaCl 0.5 g L�1; MgSO4�6H2O 0.1 g L�1; CaCl2�2H2O0.015 g L�1. Its conductivity is 11.9 ± 0.1 mS cm�1 at pH 7 and25 �C. The sodium acetate substrate is added with a concentrationof 24.4 mM, together with 0.05 g L�1 yeast extract. The catholyte isa phosphate buffer consisting of Na2HPO4 8.16 g L�1 and KH2PO4

5.78 g L�1, having a conductivity of 9.6 ± 0.1 mS cm�1 at pH 7 and25 �C. The catholyte is stirred and bubbled with a ceramic diffusorand an aquarium pump to keep dissolved oxygen up to saturation.The reactor is kept standing up to prevent gas accumulation.

The global cell voltage is measured and recorded every 10 min(Agilent 34970A Datalogger). A voltage drop is the sign of the endof the batch cycle, and the electrolytes are then fully renewed.pH and conductivity of the used media are measured for control.

Polarization curves are regularly drawn. The voltage and cur-rent measurements are undergone after a 3 h-open-circuit period.The voltage is scanned (Metrohm Autolab PGSTAT128N with NOVA1.7 software) from Open-Circuit Voltage (OCV) to 0 V at 0.5 mV s�1,sampling one point per second. From this analysis are extracted thecurrent density jsc, the maximum electric power PMAX and the inter-nal resistance RINT of the reactor. The external variable resistance isregularly set to the last determined value of RINT in order to keepthe reactor as close as possible to its maximum power operationconditions. The reference electrode (Unisense – REF 100 microSCE,EREF = +236 mV/ENH at 25 �C) is located in the catholyte bottle. Fara-daic and energetic conversion efficiencies are calculated for eachbatch. EIS measurements are done with a FRA2 (Metrohm Autolab)module connected to the potentiostat, with an over imposed po-tential of 30 mV, and simulations through the Equivalent ElectricalCircuit formalism were conducted with ZView2 (ScribnerAssociates).

3. Results and discussion

Fig. 4 gives an overview of the constructal MFC general behaviorin terms of generated electrical power for about 10 weeks. It can be

Ω Ω Ω

μ

0

5

10

15

20

25

30

35

Fig. 4. Cell power versus time for the first weeks of operation. Time 0 is for the starting onew batch. Vertical lines are for electrochemical measurements, and lines a, b and c are foand 72, respectively. The values of REXT are listed on top.

noticed that, with the help of the long-running reactor, an electri-cal output is already noticeable at day 3 after sowing. Such astarting period is very brief, and is quite shorter as compared tothe 15-day period for the same electrode material in regular condi-tions (Lepage et al., 2012).

Unwanted events such as breakdowns in power supply (days 9–10, 29–30, 63) or in measurements backup (18–20) are shown tohave only little consequences on the cell, denoting a great robust-ness of the microbial film. The external resistance was set to 1000at day 14 in order to put the cell as close as possible to maximumpower conditions. If we except the repeated drops due to acetatebatch consumption, the global power of the cell is seen to regularlyincrease in this 10-week period. Besides the great robustness al-ready noted, this denotes a positive evolution with time of the ano-dic microbial film, which was already noticed for the sameelectrode material in the conventional RVC-MFC (Lepage et al.,2012).

The positive evolution of the cell parameters with time can alsobe seen to move in the same way on the polarization and powercurves (Fig. 5a and b). The quasi linear polarization curves andsymmetrical power curves are typical of a fuel cell reactor wherethe ohmic resistance is dominant. It is shown that the cell contin-ues to improve its performances over a long period (see day 72).The cell power density is low, being about 10–20 mW m�2 in thestationary state after day 65 (22 mW m�2 for day 72). However,this value is twice as that produced by the conventional doublechamber MFC using the same electrode material, which was9 mW m�2. Arguing on a volume level, this ratio is roughly thesame (2.7 versus 1.7 W m�3).

Fig. 5c (complex plan) and 5d (phase angle diagram) reflect thecomplex electrical behavior of the whole cell. It is noticeable, espe-cially from the Bode representation of the phase angle with fre-quency, that at least three distinct phenomena are successivelypresent in the studied frequency domain, as it was the case forour conventional MFC with the same electrode material. Thesethree maxima lie around respectively 100 mHz, 100 Hz and10 kHz, these positions being shifted slightly towards higher fre-quencies as compared to the reference RVC MFC. An overall resis-tance of about 1200 X is seen for the entire cell, evaluated byextrapolation of the curve in Fig. 5c up to its intercept with the

Ω Ω Ω

f the autonomy run after the 5 day-sowing period. Arrows are for the beginning of ar the polarization and power measurements reported in Fig. 5a and b for days 24, 35

0

0.1

0.2

0.3

0.4

0.5

0 100 200 300 400

day 24day 35day 72

Cell

pote

n�al

(V

)

Cell current density (mA.m-2)

0

5

10

15

20

25

0 100 200 300 400

day 24day 35day 72

Cell current density (mA.m-2)

Cell

pow

er d

ensi

ty (

mW

.m-2

)

log f (Hz)

phas

e an

gle

(deg

ree)

Z’ (Ω)

-Z’’

(Ω)

(a) (c)

(b) (d)

Fig. 5. Electrochemical characteristics of the constructal MFC cell. Polarization (a) and power (b) curves for days 24, 35 and 72. EIS Nyquist complex plan (c) and time-resolved Bode phase (d) diagrams at day 27.

G. Lepage et al. / Bioresource Technology 162 (2014) 123–128 127

x-axis, which is lower than for the same reference MFC (about2100 X). Simulations of the frequency and complex responseswere conducted with the formalism of Equivalent ElectricalCircuits and led to a 3-element EEC identical to that found forthe global response of our conventional RVC cell. This is not sur-prising as the nature of the electrodes and the chemical mediaare the same in both MFC. More, the procedure used for the sowingperiod certainly results in an anodic biofilm colonization that canbe very similar. For its part, the series resistance, accounting forwires, contacts, etc., is as low as 6 X, showing the good global con-ception of this constructal-inspired Microbial Fuel Cell prototype.

It is expected that the design could be improved, althoughrequiring more sophisticated machining, on the basis of the follow-ing observations:

– Channel lengths and hydraulic diameters can be more properlydimensioned thanks to the global model presented in thispaper, including the singular pressure drops (Eqs. (4) and (5)).

– Circular cross-sections can be used as they present less resis-tance to flow than square cross-sections (Serrenho and Miguel,2013).

– Circular turning, instead of right angle turning, must decreasethe hydraulic resistance by decreasing the singular pressuredrops at corners (Liu et al., 2010).

– Y-shaped, instead of T-shaped, architecture must decreasehydraulic resistance by decreasing singular pressure drops atthe junctions (Azoumah et al., 2012).

Besides, the disassembly of the cell revealed some possibleleaks between the anolyte and catholyte chambers, due to a lackof rigidity of the rubber sheet. This is suspected to having reducedthe performance of this first prototype. In order to overtake thislimitation and to test the carbon foam in a traverse flow design,single-room through-flow air–cathode channels are under study.The first results obtained with this type of configuration showeda power higher by 50% as compared to this first prototype.

4. Conclusion

The constructal approach brings new optimization paths in fuelcells through efficient distribution of mass transfers between thedistributor inlet and the collector outlet. This approach has beenapplied for the first time to a Microbial Fuel Cell, constituted of fourRVC electrodes channels with a transverse flowing. Results showthat the principle of the constructal approach is validated for thisnovel cell, with power densities of 22 mW m�2 or 2.7 W m�3.Although requiring more sophisticated machining, the efficiencyof such a MFC should be improved through geometric improve-ments and through substrate feeding using traverse flow in theRVC electrodes.

References

Arvay, A., French, J., Wang, J.-C., Peng, X.-H., Kannan, A.M., 2013. Nature inspiredflow field designs for proton exchange membrane fuel cell. Int. J. HydrogenEnergy 38, 3717–3726.

Azoumah, Y., Bieupoude, P., Neveu, P., 2012. Optimal design of tree-shaped waterdistribution network using constructal approach: T-shaped and Y-shapedarchitectures optimization and comparison. Int. Commun. Heat Mass Transfer39, 182–189.

Bejan, A., 1997. Constructal-theory network of conducting paths for cooling a heatgenerating volume. Int. J. Heat Mass Transfer 40, 799–816.

Cheng, S., Liu, H., Logan, B.E., 2006. Increased power generation in a continuous flowMFC with advective flow through the porous anode and reduced electrodespacing. Environ. Sci. Technol. 40, 2426–2432.

Du, Z., Li, H., Gu, T., 2007. A state of the art review on microbial fuel cells: apromising technology for wastewater treatment and bioenergy. Biotechnol.Adv. 25, 464–482.

Hawkes, R.F., Kim, J.R., Kyazze, G., Premier, G.C., 2010. Feedstocks for BESconversions. In: Rabaey, K., Angenent, L., Schroder, U., Keller, J. (Eds.),Bioelectrochemical Systems. IWA Publishing, London, pp. 369–392.

Idelchik, I.E., 2008. Handbook of Hydraulic Resistance. Jaico Publishing House (790pages).

Kim, B.H., Chang, I.S., Gadd, G.M., 2007. Challenges in microbial fuel celldevelopment and operation. Appl. Microbiol. Biotechnol. 76, 485–494.

Lepage, G., Merlin, G., Perrier, G., 2011. Microbial fuel cells meet constructalgeometry. 3rd Microbial Fuel Cells Conference, Leeuwarden (Netherlands), June6–8.

128 G. Lepage et al. / Bioresource Technology 162 (2014) 123–128

Lepage, G., Ovenhausen Albernaz, F., Perrier, G., Merlin, G., 2012. Characterization ofa microbial fuel cell with reticulated carbon foam electrodes. Bioresour.Technol. 124, 199–207.

Liu, H., Li, P., Lew, J.V., 2010. CFD study on flow distribution uniformity in fueldistributors having multiple structural bifurcations of flow channels. Int. J.Hydrogen Energy 35, 9186–9198.

Logan, B.E., Hamelers, B., Rozendal, R., Schröder, U., Keller, J., Freguia, S., Aelterman,P., Verstraete, W., Rabaey, R., 2006. Microbial fuel cells: methodology andtechnology. Environ. Sci. Technol. 40, 5181–5192.

Logan, B.E., Regan, J.M., 2006. Electricity-producing bacterial communities inmicrobial fuel cells. Trends Microbiol. 14, 512–518.

Lovley, D.R., 2008. The microbe electric: conversion of electric matter to electricity.Curr. Opin. Biotechnol. 19, 564–571.

Luo, L., Tondeur, D., 2005. Optimal distribution of viscous dissipation in a multi-scale branched fluid distributor. Int. J. Therm. Sci. 44, 1131–1141.

Min, B., Logan, B.E., 2004. Continuous electricity generation from domesticwastewater and organic substrates in a flat plate microbial fuel cell. Environ.Sci. Technol. 38, 5809–5814.

Oh, S.T., Kim, J.R., Premier, G.C., Lee, T.H., Kim, C., Sloan, W.T., 2010. Sustainablewastewater treatment: how might microbial fuel cells contribute. Biotechnol.Adv. 28, 871–881.

Oliviera, V.B., Simoes, M., Melo, L.F., Pinto, A.M.F.R., 2013. Overview on thedevelopments of microbial fuel cells. Biochem. Eng. J. 73, 53–64.

Rabaey, K., Verstraete, W., 2005. Microbial fuel cells: novel technology for energygeneration. Trends Biotechnol. 23, 291–298.

Ramos-Alvarado, B., Hernandez-Guerrero, A., Juarez-Robles, D., Li, P., 2012.Numerical investigation of the performance of symmetric flow distributors asflow channels for PEM fuel cells. Int. J. Hydrogen Energy 37, 436–448.

Rinaldi, A., Mecheri, B., Garavaglia, V., Licoccia, S., di Nardo, P., Traversa, E., 2008.Engineering materials and biology to boost performance of microbial fuel cells:a critical review. Energy Environ. Sci. 1, 417–429.

Rozendal, R.A., Hamelers, H.V.M., Rabaey, K., Keller, J., Buisman, C.J.S., 2008. Towardspractical implementation of bioelectrochemical wastewater treatment. Trends.Biotechnol. 26, 450–459.

Serrenho, A., Miguel, A.F., 2013. Accessing the influence of Hess–Murray law onsuspension flow through ramified structures. Defect Diffus. Forum 334–335,322–328.

Tondeur, D., Luo, L., 2004. Design and scaling laws of ramified fluid distributors bythe constructal approach. Chem. Eng. Sci. 59, 1799–1813.

Tsan, W.C., Ming, Y.C., Sheng, C.Z., Shuai, T., 2011. Effect of biometric flow channelon the power generation at different Reynolds numbers in the single chamber ofrumen microbial fuel cells (RMFCs). Int. J. Hydrogen Energy 36, 9242–9251.

Watanabe, K., 2008. Recent developments in microbial fuel cell technologies forsustainable bioenergy. J. Biosci. Bioeng. 106, 528–536.

Wechsatol, W., Lorente, S., Bejan, A., 2002. Optimal tree-shaped networks for fluidflow in a disc shaped body. Int. J. Heat Mass Transfer 45, 4911–4924.

Zeng, Y., Choo, Y.F., Kim, B.-H., Wu, P., 2010. Modelling and simulation of two-chamber microbial fuel cell. J. Power Sources 195, 79–89.