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Applied Energy

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Towards uniform distributions of reactants via the aligned electrode designfor vanadium redox flow batteriesJ. Suna,1, H.R. Jianga,1, B.W. Zhangb, C.Y.H. Chaoc, T.S. Zhaoa,⁎

a Department of Mechanical and Aerospace Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong SpecialAdministrative Region, Chinab State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an 710049, Chinac Department of Mechanical Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong Special Administrative Region, China

H I G H L I G H T S

• Electrodes with aligned electrospun carbon fibers are developed.

• Uniform in-plane distribution of reactants is achieved with aligned electrodes.

• The ordered electrodes exhibit an energy efficiency of 79.1% at 150 mA cm−2.

• The aligned electrodes enable a limiting current density of 900 mA cm−2.

A R T I C L E I N F O

Keywords:Aligned fiberUniform distributionConcentration polarizationElectrospinningVanadium redox flow battery

A B S T R A C T

Enhancing the hydraulic permeability of electrodes along both the through-plane and in-plane directions isessential in flow-field structured vanadium redox flow batteries, as it can promote uniform distributions ofreactants, lower the concentration overpotential, and therefore improve battery performances. In this work,uniaxially-aligned carbon fiber electrodes with the fiber diameter ranging from 7 to 12 µm (average ~10 µm) arefabricated by electrospinning method. Attributed to the enhanced permeability of the aligned structure, thebattery assembled with the prepared electrodes exhibits an energy efficiency of 84.4% at a current density of100 mA cm−2, which is 13.2% higher than that with conventional electrospun fiber electrodes. The permeabilityin the in-plane direction is further tailored by adjusting the orientation of aligned fibers against the flowchannels. Results show that when the orientation of aligned fibers is perpendicular to the direction of flowchannels, the battery delivers the largest discharge capacity and the highest limiting current density(~900 mA cm−2). Such an enhancement in the battery performance can be ascribed to the more uniform in-plane distribution of reactants and current by maximizing the permeability along the direction vertical to theflow channels, as evidenced by a three-dimensional model.

1. Introduction

Renewable sources such as wind and solar are alternatives to ad-dress the issues including fossil fuel shortage and environmental pol-lution [1,2]. However, the contradiction between the continuous de-mand for electricity and the intermittent nature of renewablesnecessitates the development of electrical energy storage systems [3].Benefitted from the decoupled energy and power, the redox flow bat-teries (RFBs) represent a promising approach for large-scale energystorage, as the energy is decided by the volume and concentration of

electrolyte while the power is determined by the size of the power stack[4,5]. Other advantages of RFBs include long cycle life, low operationcost, and adjustable design [6,7]. Among the existing flow batterysystems [8–10], vanadium redox flow batteries (VRFBs) gain the mostattention due to the employment of the same element in both anolyteand catholyte, which can eliminate the cross-contamination issue ofelectroactive species existed in many other RFBs [11]. However, thebroad market penetration of VRFB is still hindered by its high capitalcost, the reduction of which requires the development of VRFBs thatcan be operated at high current densities with high energy efficiency

https://doi.org/10.1016/j.apenergy.2019.114198Received 10 June 2019; Received in revised form 21 October 2019; Accepted 18 November 2019

⁎ Corresponding author.E-mail address: metzhao@ust.hk (T.S. Zhao).

1 These authors contributed equally to this work.

Applied Energy 259 (2020) 114198

Available online 25 November 20190306-2619/ © 2019 Elsevier Ltd. All rights reserved.

T

[12,13].The electrode is a crucial component to determine the battery per-

formance, which is evaluated in terms of the coulombic efficiency,voltage efficiency, and energy efficiency, as it is the main contributor tothe cell voltage losses, including the activation loss, ohmic loss, andconcentration loss [14,15]. Typically, the commercial carbon materialssuch as carbon felts and carbon papers have been employed as elec-trodes in VRFBs, due primarily to their high electrical conductivity andgood chemical stability [16,17]. However, such electrodes always sufferfrom relatively low electrochemical activity, leading to a high activa-tion loss. Therefore, lots of work has been done to tailor the surfaceproperties of carbon electrode through heteroatom doping [18], cata-lyst deposition [19,20], and surface etching [21,22].

Apart from the efforts done to modify the electrodes to improve thereaction kinetics, attention should also be paid to reduce the ohmic loss.Previously, the flow-through architectures were constructed in RFBcells. In such architectures, to maintain a relatively low pressure drop,thick electrodes with a small compression ratio should be applied,which, however, results in a large ohmic loss and thereby causes poorbattery performances [23]. A remarkable reduction in ohmic loss can beachieved by replacing the flow-through architecture with the flow-byarchitecture [24–26]. However, mass transport is sacrificed in the flow-by structure according to the principles of convective mass transfer[27,28]. In addition, due to the co-existence of under-channel andunder-rib regions in the flow-by architecture, the distribution of re-actants, which is achieved by the convection and diffusion of electrolytefrom the flow channels to the porous electrode, is non-uniform. Thenon-uniform distribution of reactants would not only enhance con-centration polarization but also lead to local overcharge and gas evo-lutions. Therefore, seeking effective strategies to promote the uniformdistribution of reactants is imperative for the flow-by structured VRFBs.

Achieving the uniform distribution of electrolyte requires to designthe geometrical structures of porous electrodes [29]. Unfortunately, thecommercial carbon materials which are used as the typical electrodesfor VRFBs, have fixed intrinsic geometrically structural properties such

as the fiber diameter, fiber arrangement, porosity, and pore size. Up tonow, only a trace of work has experimentally studied the effect of theabovementioned structural properties on the hydraulic permeability ofthe electrodes. Mayrhuber et al. demonstrated that introducing per-forations to the carbon paper using CO2 laser can enhance the acces-sibility of electrolyte and thereby improve the battery performances[30]. However, applying such a method to generate holes was at thesacrifice of active surface area. More importantly, the intrinsic porestructures among the fibers remained the same after laser treatment,leaving limited space for further enhancement. Another more promisingmethod to bottom-to-up design the electrode structure is electrospin-ning technology. However, due to the stack of densely woven fiber withthe diameter in the range of several hundreds of nanometers to around1 µm, the conventional electrospun carbon material suffers from lowhydraulic permeability and thus reduced electrode utilization [31]. Toaddress this issue, researchers have proposed several strategies to tunethe structures of the electrospun carbon material. For example, a mix-ture of polyacrylonitrile (PAN) and polyvinylpyrrolidone (PVP) binaryfiber web was prepared using a horizontally-opposed blending elec-trospinning method, and the pores were expanded while the fiber dia-meter was kept unchanged by later dissolving the PVP fibers [32].Additionally, by forming fiber bundles, the pore sizes and fiber dia-meter were augmented simultaneously, promoting the transport ofelectrolyte to the surface of fibers [33]. Even progress has been made;previous methods only focused on the through-plane hydraulic per-meability of the electrode; the in-plane hydraulic permeability so farhas not been tailored. Enhancing the in-plane hydraulic permeabilitycan strengthen the mass transport from the under-channel to the under-rib regions, which is effective to achieve the uniform in-plane dis-tribution of reactants, and thus reduce the concentration polarizationand benefit the battery performance. Therefore, seeking effectivemethods to tailor the hydraulic permeability of the electrode in the in-plane direction is in urgent demand.

In this study, to simultaneously enhance the mass transport ofelectrolyte in the through-plane and in-plane directions, we designed

Nomenclature

List of symbols

u velocity vector [m s−1]p pressure [Pa]f volume force vector [N m−3]k permeability [m2]df fiber diameter [µm]kck dimensionless Carman-Kozeny constant [-]N species molar flux [mol m−2 s−1]D diffusive of ions [m2 s−1]c molar concentration [mol m−3]z charge number [-]F Faraday constant [C mol−1]R universal gas constant [J mol−1 K−1]T temperature [K]i current density [mA cm−2]k0 reaction rate constant [m s−1]a active area [m−1]E equilibrium potential [V]km mass transport coefficient [m s−1]SOC state of charge [-]

Greek symbols

ρ density of electrolyte [kg m−3]µ viscosity [Pa s]

ε porosity of the electrode [-]βF Forchheimer drag coefficient [m−1]θ angle of fiber to the x-axis [°]σ electric conductivity [S m−1]ϕ potential [V]η overpotential [V]ω flow rate [mL min−1]α charge transfer coefficient [-]

Superscripts

eff effective propertiess surface0 standard condition or initial state

Subscripts

i i-th chemical speciesl liquid phases solid phasec cathodea anodeneg negative sideV2+ V2+ ionV3+ V3+ ionH+ H+ ionHSO4

− HSO4− ion

J. Sun, et al. Applied Energy 259 (2020) 114198

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and fabricated aligned electrospun carbon fiber (ECF) mat with a fiberdiameter of around 10 µm for the first time [34,35], which can beapplied as free-standing electrodes in VRFBs. Firstly, the as-synthesizedaligned electrodes and conventional electrospun carbon electrodes werecompared in the battery tests. Secondly, by varying the orientations ofaligned fiber against the serpentine flow fields, the impact of in-planepermeability on the reactant transport and distribution was studied. Toget insights into the current density and reactant distributions in thealigned electrodes, a three-dimensional computational model wasconducted. The experimental and computational results show that byarranging the aligned fibers with the orientation perpendicular to theflow channels, the reactants can be uniformly distributed in the porouselectrodes, thus lowering the concentration polarization and improvingthe battery performances.

2. Experimental

2.1. Electrode materials

The electrode with aligned fibers was fabricated using the electro-spinning method. Polyacrylonitrile (PAN, MW 150,000, Sigma-Aldrich)polymer solution was prepared by dissolving 4.5 g PAN in 25.5 g N, N-dimethylformamide (DMF, ≥99%, Sigma-Aldrich) at 70 °C for 12 hwith vigorous stirring to form the 15 wt% solution. Then the resultingsolution was loaded to a syringe with a flow rate of 1 mL h−1 forelectrospinning. The distance between the needle and the aluminum-foil-covered collector is 16 cm with a high voltage of 16 kV appliedbetween the tip of the needle and the collector. The conventionalelectrospun fibers were prepared in the environment of around 40%relative humidity and the rotating rate of the collector of 100 rpm. Thealigned electrospun fibers were fabricated with the same polymer so-lution under the relative humidity to be around 55% and the rotatingrate to be 200 rpm. After electrospinning, the as-prepared electrospunfibers were preoxidized at 250 °C for 2 h in the air to stabilize thepolymer fiber by intermolecular crosslinking, so that the PAN fiber cansurvive high-temperature pyrolysis without decomposing [36]. Then,the as-stabilized polymer mat was carbonized at 1100 °C for 1 h in thenitrogen atmosphere to get the conventional ECF and aligned ECF.

2.2. Material characterizations

The arrangement of conventional and aligned ECFs with respect tothe flow fields was recorded by a high-resolution camera. The mor-phology of the as-prepared ECFs and the commercial carbon paper wascharacterized by a scanning electron microscope (SEM, JEOL 6390).The X-ray photoelectron spectroscopy (XPS) was performed by aPhysical Electronics PHI 5600 multi-technique system using an Almonochromatic X-ray with a power of 350 W.

2.3. Single-cell performance

All the battery performances were evaluated in a homemade flow-by battery set up with the serpentine flow field [37]. Three differentarrangements of the fiber direction with respect to the flow field

direction were examined which were denoted as parallel direction,diagonal direction, and vertical direction. The electrodes were cut intosquares (2 cm × 2 cm) with an uncompressed thickness of 700 µm andwere employed as electrodes on both positive and negative sides with acompression ratio of 30%. Nafion 212 (3.5 cm × 3.5 cm, Dupont) wasused as the membrane. The catholyte containing 1 M V(IV) + 3 MH2SO4 and anolyte containing 1 M V(III) + 3 M H2SO4 were supplied tothe cell by a peristaltic pump (BT600-2J, Longerpump) with a flow rateof 20 mL min−1. The rate and cycling performance of the cell wasevaluated using a potentiostat/galvanostat (Arbin Instrument). Thebatteries were tested at constant current densities ranging from60 mA cm−2 to 250 mA cm−2 with cut-off voltages were 1.65 V and0.9 V for charge and discharge, respectively. The polarization curve wasconducted from the full charge state. Then, the battery underwent aquick discharge process at increasing current densities until the voltagereaches zero.

3. Computational model

3.1. Governing equations

In order to gain insights into the current and species distributioninside the electrodes under different arrangement orientations ofaligned ECFs with the serpentine flow field, a computational model wasconducted. The computational domain was constructed based on theexperimental set-up, which composes a flow field and a porous elec-trode with the projected area to be 2 cm × 2 cm. The flow field con-sisted of a serpentine flow channel with 1 mm wide by 1.5 mm deepchannels and 1 mm wide ribs as shown in Fig. 1(a) and (b).

The current three-dimensional model focused on the negative half-cell of vanadium redox flow battery during the charging process withthe electrochemical reaction written as:

+ +V e Vch e2 arg 3 (1)

Conservation of mass was applied in both the channel and porousmedia:

=u s· (2)

where ρ is the density of the electrolyte, u the velocity and s the sourceterm in the electrode which is related to the electrochemical reactions.

The momentum conservation of electrolyte flowing through theflow channel and the porous electrode was computed by employing theNavier-Stokes equation and Brinkman equation respectively:

= + + +u u p µ u u f( · ) ·[ ( ( ) )]T (3)

= + + + +u u p µ u u µk

u u f( · ) · ( ( ) ) | |TF

(4)

where ε is the porosity of the porous electrode, p is the pressure, µ is thedynamic viscosity of the fluid and k is the permeability of the porouselectrode which is calculated by the Carman-Kozeny equation.βF is theForchheimer drag coefficient which is neglected in the simulation. Andf is the body force acting on the flow, which is zero here as gravity is

Fig. 1. (a) Schematic of the 3D computational domain. (b) Cross-sectional views of the flow channel and electrode. (c) The permeability of flow to aligned fibers withan angle of θ to the x-axis.

J. Sun, et al. Applied Energy 259 (2020) 114198

3

not taken into consideration.For the aligned electrospun carbon fiber electrodes, the fiber geo-

metry was approximated as a set of cylinders with the diameter df equalto 10 μm, the value of which is averaged from the SEM measurements.The porosity of the material ε was determined experimentally usingmercury intrusion porosimetry, which is around 0.9. Thus, the perme-ability can be calculated using Carman-Kozeny relationship, which re-lates to the fiber diameter, material porosity, and the fiber morphology:

=kd

k16 (1 )f

ck

2 3

2 (5)

where kck is the dimensionless Carman-Kozeny constant, the value ofwhich is associated with the arrangement of fibers with the flow di-rection shown in Fig. 1(c). According to Ref. [38], the Carman-Kozenyconstant for flow parallel to the cylinder is expressed as:

=+

k 2(1 )[2 ln 3 4(1 ) (1 ) ]

ck,//3

11

2 (6)

While for flow perpendicular to the cylinder, the Carman-Kozenyconstant is expressed as

=+

kck,

2(1 )

11

1 (1 )1 (1 )

3

22 (7)

Thus the Carman-Kozeny constant for liquid flowing parallel to thecylinders and perpendicular to the cylinders can be calculated as 0.73and 11.03, respectively. In our simulations, the permeability tensor[39] of different arrangements of fiber to the flow field in the XY planecan be written as:

=+

+k kk k

k k k kk k k k

cos sin cos sin cos sincos sin cos sin sin cos

xx xy

y x yy

//2 2

//

// //2 2

(8)

where θ is the angle of fiber to the x-axis. Since the arrangement ofaligned electrode only varies on the XY plane, the flow along the z-axisis always perpendicular to the fiber; the permeability tensor can bewritten as

=

+

+

k kk k

k

k k k k

k k k kk

cos sin cos sin cossin

cos sin cos sin sin cos

xx xy

yx yy

zz

//2 2

//

// //2 2

(9)

Then the permeability tensor can thereby be calculated ase

ee

6.24 104.13 11

4.13 11for the vertical direction arrange-

ment ande

ee

4.13 116.24 10

4.13 11for parallel direction

arrangement, ande ee e

e

3.33 10 2.91 102.91 10 3.33 10

4.13 11for the diagonal

direction arrangement with θ equal to 45°.The transport of dilute species in the porous electrode was modeled

by the Nernst-Plank equation [40] which describes the flux of speciesfrom diffusive, migrative, and convective contributions:

= +N D c z c D FRT

u ci ieff

ii i i

eff

l i (10)

The conservation of each species can be expressed as

=N S· i i (11)

where the index i represents the species i ∈{ V2+, V3+, H+, HSO4−},

and Ni is the flux of the species. Si is the species molar source term,which is related to the electrochemical reactions. ci and zi are molarconcentration and charge number of species i, respectively. R is theideal gas constant, T is temperature, and F is Faraday’s constant. Theeffective diffusivity Di

eff is corrected according to the Bruggeman cor-rection =D Di

effi

3/2 [41]. ϕl is the potential in the liquid phase. Thedissociation of HSO4

− is neglected in this simulation.Charge conservation is solved in the porous electrode as

= =i i i· ·s l neg (12)

where is is the current density in the solid phase, il is the currentdensity in the liquid phase and the expressions of these two parametersare:

=is seff

s (13)

=i F z Nli

i i(14)

where = (1 )seff

s3/2 is the effective electric conductivity of the solid

electrode from the Bruggermann correction. s is the electronic con-ductivity of the electrode. The source term Si is dependent on theelectrochemical reaction rate ineg. For the negative electrode,

=+S i F/V neg2 , =+S i F/V neg3 . Meanwhile, the source term is obtainedby the Butler-Volmer equation [40]:

= + ++

+

+

+i aFk c c

cc

FRT

cc

FRT

exp expneg V VVs

V

c Vs

V

a0 c a

2 33

3

2

2 (15)

where k0 is the reaction constant of the negative half-reaction, a is thespecific surface area, αa and αc are anodic and cathodic charge transfercoefficient, respectively, and η = ϕs − ϕl − Eeq is the overpotential,

where the equilibrium potential = + +

+E E lneq

RTF

cc

0 V

V

3

2. E0 is the ne-

gative equilibrium potential at the standard condition. And the con-centration of vanadium ions on the surface of the electrode can bedetermined by solving the equation that describes the balance of masstransport flux and the electrochemical reaction rate.

= =+ + + +k c c k c ciaF

( ) ( )m V Vs m V V

s neg3 3 2 2 (16)

where km is the mass transfer coefficient described as [42]

= ×k u1.6 10m4 0.4 (17)

3.2. Numerical details

The inlet of the channel was supplied with a constant flow rate ofelectrolyte (20 mL min−1). The concentration of the species at the inletdepended on the state of charge (SOC) of the electrolyte.

=+c SOC c·V Vtotal2 0 , and =+c SOC c(1 )·V Vtotal3 0 , = ++c c c SOC c·H acid Vtotal Vtotal0 0 0 ,

= +c c c2HSO acid V0 0

total4 , where cV0total is the initial total vanadium con-

centration which is set to 1 M, and cacid0 is the initial sulfuric acid con-

centration and is assumed to 3 M. The outlet boundary is assumed to bezero pressure as the reference. Zero electric potential was applied at thecontact of the current collector and the porous electrode, and the po-tential was set to Eeq at the interface between the electrode and mem-brane. A uniform current was applied at the electrode boundary. All theother boundaries were assumed to be impermeable to the mass, elec-tron and ion transfer. The parameters for the battery structure, elec-trode, electrolyte, and operating conditions were listed in Table1.

The above equations were solved based on a finite-element methodwith a mesh that consists of 289,569 domain elements, 43,798boundary elements, and 3339 edge elements. The relative tolerance wasset to 1 × 10−6. The steady state of the battery during discharge at acurrent density of 100 mA cm−2 was simulated for the three different

J. Sun, et al. Applied Energy 259 (2020) 114198

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arrangements of the aligned electrode.Similar to the simulations conducted on the negative side, the cor-

responding positive side simulations are also carried out. Therefore, wecan get the charge-discharge curves of the full cell under different statesof charge (SOC). Fig. S4 indicates that the potential profile of the si-mulated results agrees well with the experimental data with only anaverage of 0.8% relative difference observed. The discrepancy may beresulted from neglecting the side reactions, especially at the final stagesof charge and discharge.

4. Results and discussion

4.1. Structure of vanadium redox flow batteries

In VRFBs, electrolytes containing the electroactive materials arecontinuously pumped from the external tanks into the cell during theoperation. For the serpentine flow-field-structured VRFBs (Fig. 1(a)),the electrolyte flows in the channels and convects and diffuses into theporous electrode where the redox reactions take place. Conventionalelectrode materials include carbon or graphite felt/paper due to thehigh electronic conductivity, excellent chemical resistance, and goodmechanical strength of these materials. The graphite felt can be clas-sified according to the raw materials as PAN-, rayon- and pitch-based.Among these, the most widely used graphite felt is the needle-punchedPAN-based graphite felt, which is light in weight and can stand high-temperature oxidization. In addition, the graphite felt is always as thickas several centimeters and exhibits a binder-free fibrous morphology.For the carbon or graphite electrode, the carbon remnants of the binderare visible in the structure and are usually thinner (280 μm, SGL, 39AA)

compared with the graphite felt. The commercial carbon materials havefixed geometrical structures and the structural properties are usuallytreated as isotropic. However, when these materials are applied aselectrodes in the flow-field-structured VRFBs, the co-existence of theunder-channel and under-rib regions in the serpentine flow field resultsin uneven distributions of reactants in the isotropic porous electrode.Therefore, to enhance the permeability along both the through-planeand in-plane directions, the novel aligned electrospun electrode withanisotropic properties were fabricated with modified electrospinningconditions.

4.2. Electrospun carbon fiber characterization

It is known that the diameter of the electrospun PAN fibers increasesas the concentration of polymer solution increases [34]. Therefore, toobtain the large fiber, PAN with a high concentration of 15 wt% wasused as the precursor solution for electrospinning. In the conventionalelectrospinning process, the ECF is generally fabricated at relatively lowhumidity (~40%) and a low rotating rate of the collector (100 rpm)[35], as illustrated in Fig. 2(a), which leads to a dense surface aftercarbonization (Fig. 2(b)). The SEM images of the conventional ECFunder different magnifications are displayed in Fig. 2(c)–(e). It is seenthat the mat is composed of randomly-arranged fine fibers with a dia-meter between 1 and 2 μm, forming small pores with the size around10 μm. Herein, even with one of the highest concentrations of PANsolution reported in the open literature [34,47,48], the ECF mat fab-ricated by the conventional method still results in a dense structure,which is unfavorable for the transport of electrolyte flow and may leadto a large concentration overpotential for VRFBs. On the contrary, it isinteresting to find that by increasing the relative humidity to ~55% andthe rotating rate of the collector to ~200 rpm while keeping otherconditions unchanged (Fig. 2(f)), the uniaxially aligned fibers can beobtained, which shows great potential to address the mass transportissues in conventional ECF. The digital photo of the uniaxially-alignedelectrospun fiber mat is shown in Fig. 2(g). It is seen that the fibers areorientated along the vertical direction, and the aligned ECF is muchlooser than the conventional one. Fig. 2(h)–(j) displays the SEM imagesof aligned ECF at different magnifications. The electrospun fibers showa strong uniaxially-aligned tendency, which is mainly determined bythe large fibers with a diameter ranging from ~7 µm to ~12 µm(average ~ 10 µm) (Fig. S1). In addition, the aligned ECF mat exhibitsgood flexibility and mechanical properties during repeated bending(Fig. S2), ensuring it to withstand the compression during battery as-sembly. The chemical compositions from X-ray photoelectron spectro-scopy (XPS) analysis of conventional ECF and aligned ECF show similarelement content of carbon, oxygen, and nitrogen (Table S1), whichdemonstrates that the two samples should have the same surfaceproperties.

4.3. Battery performance of aligned electrodes

Then we compared the battery performances of the cells assembledwith conventional ECF and novel aligned ECF, as shown in Fig. 3. Here,the orientation of the aligned ECF electrodes tested followed the par-allel direction arrangement (Fig. 4(a)). Fig. 3(a)–(c) show the charge-discharge profiles at the current densities of 60, 80, and 100 mA cm−2,respectively. It is found that the battery with aligned ECF electrodesoutperforms that with the conventional ECF electrodes, as evidenced bythe lower charge plateau and higher discharge plateau at all in-vestigated current densities. In addition, the discharge and chargecurves are obviously prolonged, especially at the final stages where themass transport dominates, indicating the enhanced transport propertiesof the aligned ECF. The coulombic efficiency (CE), voltage efficiency(VE) of the batteries with these two electrodes are compared in Fig. 3(d)and the corresponding energy efficiency (EE) are summarized inFig. 3(e). Notably, the battery assembled with aligned ECF electrodes

Table 1Modeling parameters related to operating conditions, electrolyte and electrodeproperties, electrochemistry, and cell structures.

Symbol Description Value

Operating conditionsT Operating temperature (K) 298.15i Current density (mA cm−2) 100ω Inlet volumetric flow rate (mL min−1) 20Pout Outlet pressure (Pa) 0Initial species concentrationsCII

0 Initial V(II) concentration (mol m−3) 500CIII

0 Initial V(III) concentration (mol m−3) 500C-,H

0 Initial H+ concentration in negative side (molm−3)

2500

C-,HSO40 Initial HSO4

− concentration in negative side (molm−3)

5000

Default values for constants related to the transport of charges and massDVII V(II) diffusion coefficient in electrolyte (m2 s−1) 2.40E−10 [43]DVIII V(III)diffusion coefficient in electrolyte (m2 s−1) 2.40E−10 [43]DH Proton diffusion coefficient (m2 s−1) 9.31E−09 [40]DHSO4 HSO4 diffusion coefficient (m2 s−1) 1.33E−09 [40]ρ Electrolyte density (kg m−3) 1.45E+03μ Electrolyte viscosity (Pa·s) 4.93E−03 [44]Default values of the constants related to the structureh Carbon electrode thickness (µm) 500h_channel Channel depth (mm) 1.5w_channel Channel width (mm) 1Le Electrode width (cm) 2df Carbon electrode fiber (µm) 10ε Carbon electrode porosity 0.9a Specific surface area (m−1) 2.00E+06 [41]σs Electrode conductivity (S m−1) 500 [41]Default values of constants related to electrochemistryk0 The standard reaction rate constant of the

negative side7.00E−08 [45]

αa Anodic charge transfer coefficient for the negativeside

0.5

αc Cathodic charge transfer coefficient for thenegative side

0.5

E0 Standard potential (negative) (V) −0.225 [46]

J. Sun, et al. Applied Energy 259 (2020) 114198

5

achieves an EE of 84.4% at 100 mA cm−2, which is 13.2% higher thanthat with conventional ECF electrodes. More prominently, a 79.1% EEcan be delivered at a current density of 150 mA cm−2 for the batterywith aligned ECF electrodes, but the battery with conventional ECFelectrodes fails to be operated at such a high current density due to theenlarged cell polarization. To clarify the origin of the enhanced

performance, polarization curves were further tested (Fig. 3(f)). It isseen that the two polarization curves almost coincide at the currentdensities lower than 100 mA cm−2, so the activation polarizationsvaried little for the batteries assembled with these two kinds of elec-trodes. As the current density increases, the concentration polarization,which is decided by the transport of reactants in the porous electrodes,

Fig. 2. (a) Schematic of electrospinning set up and the conditions to fabricate conventional ECF. (b) Digital photo of the conventional electrospun mat. (c)–(e) SEMimages of conventional ECFs under different magnifications. (f) Schematic of electrospinning set up and the conditions to fabricate aligned ECF. (g) Digital photo ofthe aligned electrospun mat. (h)–(j) SEM images of the aligned ECFs under different magnifications.

Fig. 3. (a)-(c) Charge-discharge profiles of the batteries with conventional ECF and aligned ECF electrodes at the current densities of 60, 80, and 100 mA cm−2. (d)CE and VE comparison of the two kinds of electrodes. (e) EE comparison of the two kinds of electrodes. (f) Polarization curves of batteries with conventional ECF andthe aligned ECF electrodes.

J. Sun, et al. Applied Energy 259 (2020) 114198

6

gradually dominates the voltage loss. It is found that the battery withconventional ECF reaches the concentration dominant region at only200 mA cm−2 and undergoes a rapid decay in voltage, resulting in alow limiting current density of 400 mA cm−2. On the contrary, untilreaching a high current density of 600 mA cm−2, the concentrationpolarization dominates the voltage loss for the battery with aligned ECFelectrodes, ensuring a limiting current density of 700 mA cm−2, whichis 75% higher than that with the conventional one. Therefore, the en-hanced performance of the aligned ECF can mainly be ascribed to itsexcellent transport properties.

4.4. Influence of the in-plane permeability on the battery performance

With the aligned structure, the influence of the in-plane hydraulicpermeability of the electrodes on battery performance was further ex-plored. It is known that in the flow-by structure, electrolyte transportsinside the porous electrode from the under-channel region to the under-rib region driven by the pressure drop between the neighboring

channels. Therefore, achieving a high permeability along the directionperpendicular to the flow channel can reduce the flow resistance andthus promote a more uniform distribution of electrolyte. As the per-meability along one direction is closely related to the correspondinglength for mass transport, the in-plane permeability is tailored by ad-justing the orientation of the aligned fibers against the flow channels. Inthis work, the interplay between the fiber orientation and the flow fieldwas examined in three different arrangements, as shown in Fig. 4.Fig. 4(a) and (d) show the parallel-direction arrangement, under whichcase the direction of the fibers is parallel to the orientation of electro-lyte flow in the vertical channels. Fig. 4(b) and (e) represent the diag-onal-direction arrangement with the orientation of aligned fibers alongthe diagonal line of the serpentine flow field, forming a 45° slantingangle. Fig. 4(c) and (f) depict the vertical direction arrangement withthe slanting angle to be 90°. Optical images of the as-prepared elec-trodes against flow fields are provided in Fig. S3. To directly char-acterize the in-plane permeability under different configurations, thefluorescence microscopy and particle tracking methods proposed by

Fig. 4. Schematic diagrams of the vertical direction, diagonal direction, and parallel direction configurations. (a)–(c): 3D view of the serpentine channels withdifferent orientations of aligned fiber electrodes. (d)–(f): Top views of three configurations: red line denotes the main flow direction in the channels, and the blackline represents the fiber orientation.

Fig. 5. Charge-discharge profiles of three different arrangements of aligned electrodes to flow field at current densities ranging from 60 to 250 mA cm−2.

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Wang and Aziz et al. [49] can be applied to visualize the flow ofelectrolyte in the in-plane direction and get the velocity field in ourfuture work.

To evaluate the battery performances of the cells employing dif-ferent arrangements of the aligned carbon fiber electrodes against theserpentine flow field, single-cell tests were conducted. As shown inFig. 5, the cells were charged and discharged at current densities ran-ging from 60 to 250 mA cm−2. Since the electrodes employed in thecells only differed in the orientation of fiber direction with respect tothe flow field, the variance in battery performances of these threeconfigurations can only be ascribed to the varied mass transport pro-cess. It is found that the cell with vertical direction arrangement out-performs the other two configurations, evidenced with the smallestcharge-discharge overpotential and the largest discharge capacity at allcurrent densities. Specifically, at low current densities(60–100 mA cm−2), the charge-discharge curves for the three config-urations almost coincide at initial stages since the cells are kineticallycontrolled when sufficient reactant is supplied to the electrode. How-ever, at the final stages of charge and discharge process when the activespecies are gradually depleted, the curves begin to diverge, and thebattery performances are dominantly affected by the mass transportprocess of the electrolyte inside the electrodes. More significantly, athigher current densities (150–250 mA cm−2), distinctions are amplifiedwith the charge-discharge curves diverging at an earlier time, and thedifference of the charge-discharge overpotentials become larger. Theimprovement trend of battery performance is witnessed when switchingthe fiber-to-electrode configurations gradually from the parallel direc-tion to the vertical direction at all current densities. The above analysisdemonstrates that the battery achieves the highest performance among

the three configurations when the aligned electrodes are vertically ar-ranged to the flow channels.

Aiming to quantify the battery performances, the coulombic effi-ciency (CE), voltage efficiency (VE), and energy efficiency (EE) of eachelectrode configuration were analyzed in Fig. 6. The CE of each cell isall above 97%, indicating a good airtightness of the battery set up. Asshown in Fig. 6(a)-(b), the battery with vertical direction arrangementof aligned electrodes exhibits the highest VE and EE among these threeconfigurations which can deliver an 81.2% VE and 80.7% EE at acurrent density of 150 mA cm−2, respectively. The polarization curveswere employed to compare the contribution of different types of voltagelosses in the three cells. The overlapping of the three polarizationcurves at the initial stages reveals similar activation overpotential andinternal resistance of the electrodes because the physicochemicalproperties of these electrodes are identical. However, these three curvesbegin to diverge at higher current densities when concentration po-larization begins to dominate the voltage loss, resulting in a significantvariance on the limiting current densities. As shown in Fig. 6(c), thevertical-direction configuration can reach a limiting current density of~900 mA cm−2, which is much higher than that of the parallel direc-tion arrangement (~700 mA cm−2). The enhancement in the limitingcurrent densities mainly results from the reduced concentration polar-ization, which indicates improved mass transport process inside thevertical direction arranged electrode. In addition, the discharge capa-cities of the three batteries with different electrode arrangements areanalyzed in Fig. 6(d). The battery with a vertical direction electrodeconfiguration gains the largest discharge capacity of 9.1 Ah L−1 at acurrent density of 80 mA cm−2. More importantly, an additional 56%depth of discharge is achieved by changing the fiber arrangement from

Fig. 6. (a) CE and VE of the batteries with three different aligned electrode arrangements. (b) EE of the batteries with three different aligned electrode arrangements.(c) Polarization curves and (d) Discharge capacity of the three different electrodes configurations.

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the parallel direction to vertical direction at the current density of200 mA cm−2. Therefore, it can be concluded from the above batteryperformance that when the aligned electrospun electrode is verticallyarranged against the flow direction in the serpentine flow field, themass transport properties of electrolyte inside the electrodes are en-hanced, resulting in increased energy efficiency and discharge capacity,as well as the prolonged limiting current density.

Subsequently, the cycling performances of vertical-direction cellswere evaluated by charging and discharging the battery for 200 cyclesat a current density of 100 mA cm−2. As shown in Fig. 7(a), the CE, VE,and EE remain stable during repeated charge and discharge processes.The discharge capacity is gradually declined over the cycles with adecay rate of 0.25% per cycle, which is mainly due to the imbalance ofthe active materials on the two sides resulting from the crossover ofactive species through the membrane. The cycling performances of thealigned electrospun electrodes confirm that the as-prepared electrodesare potentially stable over long battery cycles.

4.5. Computational analysis

To explain the results observed in the above experiments, the nu-merical simulations with the computational model were conductedwhich provide insights into the current distribution and active speciesdistribution in the electrode. In our simulations, all the conditions werekept the same except the permeability tensor for the three arrange-ments. When the aligned fibers were placed against the flow field withdifferent orientations, the corresponding hydraulic permeability tensorvaried, thereby affecting the electrolyte distribution and current dis-tribution. The calculated velocity field, current density distribution, andthe reactant distribution were plotted in Fig. 8.

The calculated velocity fields show that on the same cut plane alongthe z-axis, the vertical-direction arrangement brings about the largestvelocity magnitude (Fig. 8(a)–(c)) among the three configurations.Therefore, the electrode can be accessed with a large flow rate ofelectrolyte when it is placed with the vertical-direction arrangement. Inaddition, it is found that the velocity is higher in the under-rib regionsthan that of under channel regions for all the three configurationswhich is due to the existence of bypass flow. Additionally, the calcu-lated velocity field agrees well with the fiber direction arrangement.

By incorporating electrochemical reactions into the model, thecurrent density distribution and the species distribution can be calcu-lated. The current density is a function of the reactant concentrationand overpotential according to the Butler-Volmer equation. It is foundthat the current density reaches its maximum near the inlet where theconcentration of the reactants is the highest for all the three config-urations. As shown in Fig. 8(d), the current density is highly hetero-geneous for the parallel-direction arrangement with maxima appearedunder the ribs and minima under the channels. Compared with theparallel-direction arrangement, the diagonal-direction arrangementshows significantly improved uniformity of the current density dis-tribution with local maxima evidenced near the inlet and along thediagonal directions. When the aligned electrode is vertically placedwith the flow field, the current density gains the most homogeneousdistribution in the in-plane direction, as shown in Fig. 8(f).

The reactant shows similar in-plane distribution profiles(Fig. 8(g)–(i)) with the current density distributions (Fig. 8(d)–(f)). Adecrease in V2+ concentration from the inlet to the outlet in all threeconfigurations is observed because V2+ ions are gradually depletedduring the discharge process. To quantitatively describe the uniformityof the in-plane distribution of current and react distribution, we definethe uniformity factor for current density and reactant [23]:

=Uc A

c c A1 1¯

1d

( ¯ ) di loci loc

i loc i loc,,

, ,2

(18)

=++

+ +Uc A

c c A1 1¯

1d

( ¯ ) dcV

V V2

V22

2 2(19)

where Ui loc, (Ui loc, ∈[0,1])is the uniformity factor of current density,+UcV2 ( +UcV2 ∈[0,1])is the uniformity factor of V2+ concentration. When

both the two uniformity factors approach 1, the current density and thereactants reach homogenous distributions. It is found in Fig. S6 thatboth Ui loc, and +UcV2 are the largest for the vertical-direction arrange-ment. To be specific, on a fixed cut plane, for example, at z = 0.1 mm,Ui loc, for the parallel direction, diagonal direction and vertical directionarrangements are 0.437, 0.823, and 0.877 respectively and +UcV2 for thethree configurations are 0.899, 0.962, and 0.973 respectively, whichindicates that the more uniform distribution of reactants and currentare achieved in the vertical-direction configuration.

From the above analysis of the computational results, the vertical-direction arrangement of the electrode against the flow field facilitatesthe uniform distribution of current and reactants, which provides ex-planations for the higher limiting current density and increased dis-charge capacities examined in the battery with vertical direction ar-ranged electrodes.

4.6. Future electrode optimization and real application

Our work presented a novel electrode structure which is composedof aligned fibers of around 10 µm in diameter and was produced withthe electrospinning method. Extending from the abovementioned re-sults, we want to discuss the future electrode optimization and realapplications of this aligned electrode structure. Based on the improvedmass transport properties of the aligned electrode structure, futureelectrode optimization can be focused on surface modifications of thematerial to improve the kinetics and boost the battery performances.And for the real applications, this aligned structure can be adopted bythe fiber production industry when fabricating carbon materials for theelectrode in flow battery systems. In addition, the lab-scale productionof the electrospun carbon fibers shows potentials in large-scale fabri-cation which can be realized with industrial-scale electrospinningequipment [50].

5. Conclusions

In this work, the uniaxially-aligned fibers were fabricated to en-hance the through-plane and in-plane hydraulic permeability of

Fig. 7. Cycling performance of the vertical-direction assembly of the alignedelectrodes. (a) Efficiency and (b) specific capacity over 200 cycles.

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electrospun materials for the typical serpentine flow-by cell archi-tecture. Firstly, benefitting from the novel aligned electrode structurewith large fibers, the battery assembled with aligned ECFs achieved anenergy efficiency of 84.4% while the battery with conventional ECFonly delivered 71.2% EE at the current density of 100 mA cm−2.Secondly, the arrangement orientation of aligned fibers against the flowfield was optimized under three different configurations. The experi-mental results showed that the battery with vertical-direction ar-rangement achieved a limiting current density of 900 mA cm−2 whichwas 28.6% higher than that tested with the parallel-direction arrange-ment. Notably, the battery with vertical-direction arrangementachieved an additional 56% discharge depth compared with the par-allel-direction configuration at the current density of 200 mA cm−2.The enhanced limiting current density and discharge capacity demon-strated that the vertical direction arrangement can effectively lowerconcentration polarization. Such improvement in battery performanceswas further explained by the computational simulations which showedthat more homogenous in-plane distributions of reactant and currentwere achieved in the vertical direction arrangement. In summary, theelectrodes with aligned carbon fibers are promising for flow battery

systems which enable an improved mass transport of the electrolyte,and this structured design using the electrospinning method also pro-vides inspirations for future electrode design. Furthermore, the alignedelectrode fabricated with current lab-scale electrospinning equipmentcan be mass-produced with industrial-scale electrospinning productionline in the future, providing a new approach to manufacturing cost-effective carbon fibers with designed structures.

Declaration of Competing Interest

The authors declared that there is no conflict of interest.

Acknowledgments

The work described in this paper was supported by a grant from theResearch Grants Council of the Hong Kong Special AdministrativeRegion, China (Project No. T23-601/17-R) and HKUST Fund of Nanhai(Grant No. FSNH-18FYTRI01).

Fig. 8. (a)–(c) Velocity magnitude and vector on the cut plane z = 0.1 mm for the three arrangements. (d)–(f) Current density distribution on the cut planez = 0.1 mm for the three arrangements. (g)-(i) The distribution of concentration of species V2+ on the cut plane z = 0.1 mm.

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Appendix A. Supplementary material

Supplementary data to this article can be found online at https://doi.org/10.1016/j.apenergy.2019.114198.

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