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Optimal design of current collectors for microfluidic fuel cell withflow-through porous electrodes

Citation for published version:Li, L, Fan, W, Xuan, J, Leung, MKH, Zheng, K & She, Y 2017, 'Optimal design of current collectors formicrofluidic fuel cell with flow-through porous electrodes: Model and experiment', Applied Energy, vol. 206,pp. 413-424. https://doi.org/10.1016/j.apenergy.2017.08.175

Digital Object Identifier (DOI):10.1016/j.apenergy.2017.08.175

Link:Link to publication record in Heriot-Watt Research Portal

Document Version:Peer reviewed version

Published In:Applied Energy

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Download date: 11. Jun. 2022

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Optimal design of current collectors for microfluidic fuel cell with flow-through

porous electrodes: Model and experiment

Li Li a,b, Wenguang Fan a, Jin Xuan c, Michael K.H. Leung a, *, Keqing Zheng d, Yiyi She a

a Ability R&D Energy Research Centre, School of Energy and Environment, City University of

Hong Kong, Hong Kong, China

b School of Automotive and Traffic Engineering, Jiangsu University of Technology, Changzhou,

213001, China

c School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh, United Kingdom

d School of Electrical and Power Engineering, China University of Mining and Technology, Xuzhou,

221116, China

*Corresponding author, Tel: +852 3442 4626; Fax: +852 3442 0688; E-mail:

mkh.leung@cityu.edu.hk (M.K.H. Leung).

Abstract:

Design optimization of current collectors has been performed to reduce the significant ohmic

resistance observed in microfluidic fuel cell (MFC) with flow-through porous electrodes. A

three-dimensional computational model is developed to investigate the electron transport

characteristics in the porous electrodes, where lateral electron transport is found to encounter high

resistance. Influences of different current collector design parameters on the transport resistances

are examined and analyzed. The modeling results indicate that current collector position is the most

influential factor due to the non-uniform flow rate distribution. Optimal current collector position is

located at the high flow rate region instead of the conventional exposed end of the porous electrode.

Experimental studies are performed to support the modeling analysis. The experimental results

demonstrate that the optimized current collector position can boost the maximum power density by

61%. This study highlights the significance of the current collector design in achieving high

performance MFC with flow-through porous electrodes. Based on the results, some general rules

have been set for the current collector designs in this energy system, which can provide useful

guidance for the future development of MFC.

2

Keywords: Microfluidic fuel cell; Porous electrode; Current collector design; Lateral electron

transport; Electrical resistance

Nomenclature

𝑎 specific surface area, m−1

A center of the interface between external wire and current collector

B center of the interface between current collector and electrode

𝑐 bulk concentration, mol m−3

𝑐𝑠 surface concentration, mol m−3

𝑑 diameter, m

𝐷 diffusion coefficient, m2 s−1

𝐸 equilibrium potential vs. SCE, V

𝐸0 standard equilibrium potential vs. SCE, V

𝐹 Faraday constant, 9.65 x 104 C mol−1

ℎ thickness in the z-direction, mm

𝑖→ current density, A m−2

𝑖0 exchange current density, A m−2

𝑖 charge transfer current density, A m−2

𝐾 permeability, m2

𝑘 standard reaction rate constant, m s−1

𝑘𝑚𝑗 mass transfer coefficient of species 𝑗, m s−1

𝐿 length in the y-direction, mm

𝑃 pressure, Pa

3

𝑄 charge source term, A m−3

𝑅 universal gas constant, 8.314 J mol−1 K−1

𝑆 species source term, mol m−3s−1

𝑡 time, s

𝑇 temperature, K

�⃗⃗� velocity vector, m s−1

𝑉 vanadium species

𝑉𝑐𝑒𝑙𝑙 cell voltage, V

𝑊 width in the x-direction, mm

𝑧 charge number

Greek symbols

𝛼 charge transfer coefficient

γ constant

𝜀 porosity

𝜀𝑝 percolation threshold

𝜌 density, kg m−3

𝜎 electrical conductivity, S m−1

τ tortuosity

∅ potential, V

𝜇 viscosity, Pa s

ω constant

η overpotential, V

Superscript

𝑒𝑓𝑓 effective

4

Subscripts

1 anode

2 cathode

𝑎 anodic reaction

𝑐 cathodic reaction

𝑗 species {𝑉2+, 𝑉3+, 𝑉𝑂2+, 𝑉𝑂2+ and 𝐻+}, marked as {II, III, IV, V and H}

𝑓 fiber

𝑠 electrode

𝑙 electrolyte

𝑐𝑙 current collector

𝑒𝑤 external wire

1. Introduction

Microfluidic fuel cell (MFC) is a promising microscale power source for portable electronics [1].

In an MFC, the co-laminar nature of multi-stream flow in microchannels is utilized to maintain

separation between fuel and oxidant streams without the need of a physical barrier such as a

membrane while still allowing ionic transport [2]. This unique membraneless feature brings many

distinct advantages against conventional proton exchange membrane fuel cells, such as elimination

of membrane-related problems, easy fabrication and low cost [3].

By now, various MFC systems have been demonstrated using different fuel-oxidant

combinations [4-8], electrode materials [9-13] and micro-channel configurations [1, 14-16]. Among

all of these studies, the vanadium redox based MFC with flow-through porous electrodes

demonstrated a remarkably high power density (131 mW cm−2 at room temperature) [17]. The

outstanding performance was mostly due to the large reaction interfaces brought about by the

exceptionally high surface-to-volume ratio of the porous electrodes [18]. As the interest in MFC is

5

growing rapidly, a series of works were conducted to further ameliorate the design in various

aspects, including: optimization of the porous electrode volume [19], determination of kinetic

parameters of the vanadium redox reactions on carbon based electrodes [20], development of novel

porous electrode materials [9] and novel electrode configurations [2], introduction of new MFC

architectures [21, 22] and construction of MFC stacked systems [23].

Despite the high power density output feature of porous flow-through MFCs, high ohmic

resistance and associated voltage loss were often observed [24]. As the ionic resistance is fixed at a

small value (about 2Ω) by excess supporting electrolyte, the significant ohmic resistance was

mainly attributed to the electron transport in the cell. The electrons generated at the anode were

drawn to the external circuit via the anode current collector, and then transported to the cathode via

the cathode current collector. At this point, the current collectors should be designed carefully as

they must ensure an effective transport of electrons between the reaction sites and the external

circuit.

Work in search of an optimal current collector design has already been demonstrated in other

fuel cell systems, especially the passive direct methanol fuel cells (DMFCs) [25-27]. Unfortunately,

the current collector design principles derived for DMFC cannot be directly applied to MFC. In

DMFC, current collectors offer passages for reactant distribution and product removal, in addition

to providing good electrical contact for electron transport. Thus, the size of the current collector

should be large enough to cover the whole active area of the electrode to ensure an effective mass

transport. Open ratio (i.e. the ratio of the electrode area exposed to the reactant) is the most

influential factor in DMFC current collector design as a tradeoff must be considered between the

mass transport and electron transport [28]. In MFC, current collectors only serve to provide good

electrical contact between the electrodes and the external circuits. Hence planar current collector

with the open ratio equaling to zero is preferred. In addition, the current collector does not need to

cover all the active area of the electrode. It can be attached to different parts of the electrode’s active

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area, which offers room for optimization. However, by now, limited literature is available on the

optimal design of current collectors in MFCs [29]. Therefore, deriving effective principles for

current collector design is essential for future MFC design.

In this work, modeling studies are performed to accomplish design optimization of current

collectors for MFC with flow-through porous electrodes. A comprehensive three-dimensional

computational model has been developed for this purpose. Different from the existing models in the

literature, the present model has restored the geometries of the current collectors and part of the

external circuits in the modeling domain for the parametric analysis of the influences of current

collector design parameters on the cell performance. The studied parameters include the current

collector area, positioning, thickness, electrical conductivity and connecting position of the external

wire. After analysis and discussions, conclusions and recommendations are derived for optimal and

economical current collector design. Experimental verifications of the theoretical findings are also

carried out and good agreement is achieved between the experimental results and the modeling

predictions.

2. Numerical Model

A three-dimensional computational model of MFC with flow-through porous electrodes is built

up to perform the design optimization of current collectors. Fig. 1 shows the schematic of the

modeling domain. This is an all vanadium MFC with 𝑉2+/𝑉3+ sulfate solution as the anolyte,

𝑉𝑂2+/𝑉𝑂2+ sulfate solution as the catholyte and carbon paper as the porous electrode material. In

the operation, the anolyte and catholyte enter the fuel cell via two inlets on both sides passing

through the inlet reservoirs heading to the carbon paper electrodes. The two streams then flow

through the porous electrodes. Electrochemical reactions take place at the interface between the

electrode and electrolyte:

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Anode: 𝑉2+ → 𝑉3+ + 𝑒− E0 = −0.496 V vs SCE (1)

Cathode: 𝑉𝑂2+ + 2𝐻+ + 𝑒− → 𝑉𝑂2+ + 𝐻2𝑂 E0 = 0.75 V vs SCE (2)

After passing through the porous electrodes and undergoing redox reactions, the two streams

enter the common center channel, where they will make a 90°turn and flow towards the outlet in a

stratified, co-laminar format.

The followings are some general assumptions adopted in this analysis:

(1) Isothermal and steady state conditions;

(2) Incompressible fluid flow;

(3) Negligible effects of gravity;

(4) Dilute solution approximation [24, 30, 31], here, concentrated sulfuric acid (mass

fraction=98%) usually refers to 18-20 M solution;

(5) Negligible ionic migration.

2.1 Governing equations

With these general assumptions, the model is formulated and described by the following set of

governing equations.

2.1.1 Fluid flow

The continuity and Navier-Stokes equations are used to solve the steady-state, laminar flow in

the channel:

∇ ∙ (𝜌�⃗⃗� ) = 0 (3)

∂

∂𝑡�⃗⃗� + (�⃗⃗� ∙ ∇�⃗⃗� ) = −

1

𝜌∇𝑃 +

𝜇

𝜌∇2�⃗⃗� (4)

where ρ is the density, U⃗⃗ is the velocity vector, t is time, P is pressure and μ is the viscosity.

For the flow field in the porous electrodes, the Brinkman equation is employed instead of the

8

Navier-Stokes equation:

∇𝑃 = −𝜇

𝐾�̅� +

𝜇

𝜀∇2�⃗⃗� (5)

where K is the permeability and ε is the electrode porosity.

2.1.2 Mass transport

The governing equation for the mass transport can be written as:

U⃗⃗ ∙ ∇cj − Djeff∇2cj = Sj (6)

where the subscript j is used to indicate the species involved in the electrochemical reactions,

including V2+ , V3+ , VO2+ , VO2+

and H+ . The symbols {II, III, IV, V and H} refer to the

species { V2+, V3+, VO2+, VO2+ and H+} respectively in the following sections. The superscript

eff denotes effective, c is the bulk concentration, D is the diffusion coefficient, and S is the

species source term.

The species source term corresponds to the volumetric–basis species generation or depletion due

to the electrochemical reactions. Therefore it equals to zero in the channels as no electrochemical

reactions take place there. In the porous electrodes, the transport rate of vanadium species to or

from the electrode surface is proportional to the difference in concentration between the bulk and

the surface [24]. Thus the species source terms in the porous electrodes can be defined as

𝑆𝑗 = 𝑎𝑘𝑚𝑗(𝑐𝑗𝑠 − 𝑐𝑗) (7)

where a is the specific surface area of the porous elecrode, kmj and cjs are the mass transfer

coefficient and surface concentration of species j, respectively. Here, the mass transfer coefficient

kmj can be estimated by [24]:

𝑘𝑚𝑗 = 7𝐷𝑗

𝑑𝑓(𝜌|�⃗⃗� |𝑑𝑓

𝜇)0.4

(8)

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where df is the average diameter of the fibers in the porous electrodes.

2.1.3 Charge conservation

The charge conservation equations for the electrical potential in the porous electrodes, current

collectors and external wires are

∇ ∙𝑖𝑠→= 𝑄𝑠, =𝑖𝑠

→ − 𝜎𝑠𝑒𝑓𝑓

∇∅𝑠 (9)

∇ ∙𝑖𝑐𝑙→ = 𝑄𝑐𝑙, =𝑖𝑐𝑙

→ − 𝜎𝑐𝑙∇∅𝑐𝑙 (10)

∇ ∙𝑖𝑒𝑤

→ = 𝑄𝑒𝑤, =𝑖𝑒𝑤

→ − 𝜎𝑒𝑤∇∅𝑒𝑤 (11)

where →i

is the current density, Q is the charge source term, σ is the electrical conductivity and

∅ is the potential. The subscripts s, cl, and ew denote electrode, current collector and external

wire, respectively.

The charge conservation equation for the electrolyte potential in both the porous electrodes and

the channels is

∇ ∙il→= Ql , =il

→ − σleff∇∅l (12)

where l refers to electrolyte.

Similar to the species source term, the charge source term values in the current collectors,

external wires and fluid channels equal to zero as no electrochemical reactions happen there. In the

porous electrodes, the charge source terms 𝑄𝑠 and 𝑄𝑙 can be derived from the charge transfer

current densities 𝑖1 and 𝑖2, which are given by the Butler-Volmer equations,

𝑄1 = 𝑄𝑠 = −𝑄𝑙 = −𝑎𝑖1 (13)

𝑄2 = 𝑄s = −𝑄𝑙 = −𝑎𝑖2 (14)

𝑖1 = 𝑖10 {

𝑐II𝑠

𝑐IIexp (

𝛼1,𝑎𝐹ƞ1

𝑅𝑇) −

𝑐III𝑠

𝑐IIIexp (−

𝛼1,𝑐𝐹ƞ1

𝑅𝑇)} (15)

𝑖2 = 𝑖20 {

𝑐IV𝑠

𝑐IVexp (

𝛼2,𝑎𝐹ƞ2

𝑅𝑇) −

𝑐V𝑠

𝑐Vexp (−

𝛼2,𝑐𝐹ƞ2

𝑅𝑇)} (16)

10

where the subscripts 1 and 2 refer to the anode and cathode, the subscripts a and c refer to the

anodic and cathodic reactions, i0 is the exchange current density, F is Faraday constant, R is

universal gas constant, T is temperature, ƞ is the overpotential and α is the charge transfer

coefficient.

Related parameters and variables including the effective electrolyte conductivity, exchange

current density, overpotential and equilibrium potential are derived below:

𝜎𝑙𝑒𝑓𝑓

=𝐹2

𝑅𝑇∑ 𝑧𝑗

2𝑗 𝐷𝑗

𝑒𝑓𝑓𝑐𝑗 (17)

𝑖10 = 𝐹𝑘1𝑐II

𝛼1,𝑐𝑐III

𝛼1,𝑎 (18)

𝑖20 = 𝐹𝑘2𝑐IV

𝛼2,𝑐𝑐V

𝛼2,𝑎 (19)

ƞ1 = ∅𝑠 − ∅𝑙 − 𝐸1 (20)

ƞ2 = ∅𝑠 − ∅𝑙 − 𝐸2 (21)

𝐸1 = 𝐸10 +

𝑅𝑇

𝐹ln (

𝑐III

𝑐II) (22)

𝐸2 = 𝐸20 +

𝑅𝑇

𝐹ln (

𝑐V𝑐𝐻2

𝑐IV) (23)

where z is the number of electrons involved in a single electrochemical reaction, k is the standard

reaction rate constant, E is the equilibrium potential and E0 is the standard equilibrium potential.

At steady state, the rate at which a reactant is transported to or from the surface of the electrodes

equals to the rate of the electrochemical reaction. Hence, to couple the mass and charge transport,

their source terms can be expressed mathematically by

𝑆II = −𝑆III =𝑄1

𝐹 (24)

𝑆IV = −𝑆V = −𝑆𝐻

2=

𝑄2

𝐹 (25)

2.1.4 Contact resistance

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Contact resistance exists at the interface between the current collector and the porous electrode.

The reported values of the area specific contact resistance normally range from 1 to 10 mΩ cm2,

depending on the particular contact pressure, material properties and surface topography [32-36].

Thus, for the case with current collector area equal to 1 mm × 2 mm, corresponding total contact

resistance in the cell is in the range of 0.1 to 1 Ω. In an experiment conducted by us, the contact

resistance was measured to be 0.2 Ω with the current collector area equal to 1 mm × 1 mm. And

this value can be further reduced by increasing the current collector area. Thus, in this model, the

ohmic loss due to the contact resistance is ignored.

2.1.5 Anisotropic effective transport parameters of the porous electrode

Carbon paper is employed as the porous electrode material. The structures of carbon papers are

highly anisotropic, and thus the effective transport parameters of carbon papers are also found

anisotropic [37-39]. The effective electrical conductivity in the in-plane directions (directions

parallel to the x-y plane in this model) is commonly one order of magnitude higher than that in the

through-plane direction (z-axis direction in this model). The reported values of effective in-plane

conductivities normally range from 1000 to 10000 S m−1 and their counterparts in the

through-plane direction normally range from 100 to 1000 S m−1, depending on the bare carbon

paper used and the treatment it undergoes [37, 39, 40]. In the base case (specified in Section 2.2),

the effective electrical conductivity of the porous electrode is set to be 5000 S m−1 in the in-plane

directions and 500 S m−1 in the through-plane direction.

The effective diffusion coefficient 𝐷𝑗𝑒𝑓𝑓

is calculated based on previous modeling work of

carbon paper [41],

𝐷𝑗𝑒𝑓𝑓

= 𝐷𝑗𝜀

𝜏 (26)

𝜏 = 1 + 𝛾1−𝜀

(𝜀−𝜀𝑝)𝜔 (27)

12

where τ is the tortuosity, εp is the percolation threshold, γ and ω are constants which have

different values in the in-plane and through-plane directions. Finally, the effective electrolyte

conductivity in the porous electrodes can be obtained by Eq. (17).

2.2 Boundary conditions and input parameters

In the fluid flow model, non-slip condition is defined at the walls, constant inward velocity is

set at the inlets and constant pressure equaling to that in the ambient is specified at the outlet. For

the mass transport, non-flux conditions are considered everywhere except at the inlets and outlet. At

the inlets, constant concentrations are adopted, and at the outlet, pure convection boundary

condition is employed. To investigate effects of current collector designs on the cell performance, a

reference cell potential of 0 V is set at the upper surface (z = 2.1 mm cross-section, 1.5 mm from

the (current collector) – (external wire) interface) of the anodic external wire included in the

computational domain, and the electrical potential at the upper surface of the cathodic external wire

is set to be the cell voltage (𝑉𝑐𝑒𝑙𝑙). All other boundaries are set to be electrically insulated. A base

case is defined as the normal working condition. In the base case, the dimensions of the cell follow

the experimental study in Ref. [17]. The parameter values of the electrode properties are based on

commonly employed carbon paper (TGPH-090, Toray) and the most commonly adopted settings in

the fuel cell research. Stock electrolyte (50/50 V3+/VO2+) in 4 mol L−1 sulfuric acid is recharged

to produce V2+ and VO2+ as the anolyte and catholyte. The initial concentrations of V2+ and

VO2+ are 1.89 and 1.84 mol L−1, respectively. The flow rate is 60 μL min−1, which is a laminar

flow with small Reynolds number (Re < 10). Table 1 lists the key input parameters for the base

case referred as base values in the following content.

2.3 Numerical procedure

The conservation equations constrained by the boundary conditions are solved by the Finite

13

Element Method (FEM) using the commercial software COMSOL MULTIPHYSICS Version 4.3.

The segregated solver is used to accelerate the convergence since the coupling of the source terms

between the species and charge transports makes the problem strongly non-linear. The following

problem-solving procedure is adopted: the continuity and momentum conservation equations are

first solved based on the initial setting. The results are consequently used for solving species and

charge transports. A relative convergence tolerance of 1 × 10−4 is set. Structural meshes are

generated and then a grid independence study is carried out on the base case. Three different grids

are generated in the porous electrodes as shown in Fig. 2a. The cell sizes for Grid 1, Grid 2 and

Grid 3 are 67 μm × 83 μm × 20 μm, 50 μm × 67 μm × 15 μm and 40 μm × 55 μm × 12 μm

(in x × y × z form), respectively. For each case, cell sizes in the channels are the same as those in

the porous electrodes in the y and z directions but different in the x direction with 100 μm/cell.

The distribution of the y-component of the electrode current density along the midline of the anode

upper surface is selected to evaluate the grid independence (Fig. 2a). It can be clearly seen that Grid

2 appears to be as close to complete grid independence as is practicable and necessary. Thus Grid 2

is chosen for performing further analysis.

In the simulation procedure, the total current is obtained by numerical integration of the normal

electrode current density over the z = 2.1 mm cross-section of the anodic external wire. The final

output current density is normalized by the upper surface area of the anode active region (from y =

0 mm to y = 12 mm where the electrolyte streams flow through) to facilitate comparison among

different cases.

2.4 Model validation

The pioneer experiment work in [17] in conjunction with a series of studies in [18-24, 29]

established a both experimentally and computationally well-defined system of flow-through porous

electrode incorporated MFC. As we validate our model with the experimental results in [17], not

14

only the values of the parameters needed in the modeling simulations are available in the literature

[17, 20, 24, 29], but also the findings we obtain can benefit a wider span of researchers who are

following this classical system. Therefore, the validation of the present model is conducted by

comparing the numerically predicted cell performance with the experimental results in [17]. The

geometric and operating conditions of the simulation follow the experimental study. Toray carbon

paper (TGPH-090) was used as the porous electrode material. Stock electrolyte (50/50, 𝑉3+/𝑉𝑂2+)

in 4 M aqueous H2SO4 solution was recharged to produce 𝑉2+ and 𝑉𝑂2+, the latter being the

anolyte and catholyte, respectively. Fig. 2b shows the comparison between the simulated and

measured polarization curves of the cell. Good agreement is obtained between the simulated and

experimental data. The validated model is further used to perform the investigation of the current

collector designs in MFC. All the parameter values used in the following studies are the same as

those in the base case unless specifically mentioned.

3. Results and discussion

3.1 Characteristics of fluid field and charge transport in MFC

For the fluid field, axially symmetric flow patterns are observed due to the symmetric cell

arrangement. Magnitude distribution curves of the flow velocity along the anode and cathode

mid-lines are shown in Fig. 3a. The velocity distribution profiles have two distinctive sections: in

the inactive region (from y = −8 mm to y = 0 mm), the velocity is near to zero; in the active

region (from y = 0 mm to y = 12 mm), the velocity increases significantly along the positive y

direction from 7 × 10−5 m s−1 to 8.8 × 10−4 m s−1.

Corresponding local current density profile is presented in Fig. 3b. It can be seen that

electrochemical reactions mainly take place in the active region, which is in consistent with the

results in Fig. 3a. Interestingly, in the active region, a relatively uniform local current density

distribution is observed in spite of the non-uniform velocity. To facilitate explaining this,

15

streamlines of the electron transport paths and distribution patterns of the associated electrode

potential in the anode are presented in Fig. 3c&d, respectively. Electrons generated in the active

region first flow laterally in the y-direction to the region covered by the current collector, and then

flow in the z-direction to the external wire via the current collector. Due to the small cross-section

area (0.3 mm × 1 mm) of the electrode in the x-z plane, the lateral electron transport in the

y-direction encounters significant resistance, which causes the electrode potential to decrease along

the positive y-direction, as shown in Fig. 3d. In the base case, the associated voltage loss due to the

electrical resistance is 0.174 V. The decreased electrode potential is a counterforce of the

electrochemical reaction. Therefore, a relatively uniform local current density distribution curve is

observed in the active region as a competitive balance of the increased flow rate and decreased

electrode potential along the positive y-direction.

The internal ohmic loss can be reduced by optimizing the current collector design, as the current

collector dominates the shape of the electron transport paths. In the following section, the impacts

of different current collector design parameters on the cell performance are evaluated.

3.2 Parametric studies

In the analysis, rectangular-shaped current collectors are attached to the upper surfaces of the

anode and cathode. Designs of the anode and cathode current collectors are set to be symmetric

about the cell mid-plane (x = 0 mm) due to the symmetric flow pattern. We firstly investigate the

effect of the current collector area. Considering that the upper surface of the porous electrode is

long and narrow, the area is shifted by increasing the length of the current collector from 2mm to

20mm. Two situations are simulated: if one side of the current collector is fixed at y = −8mm

(Fig. 4a inset), an increase of 80% in the maximum output power is obtained with the increased

current collector length (Fig. 4b), which is consistent with previous experimental work [29];

differently, if we fix the other side of the current collector at y = 12mm (Fig. 4c inset), increasing

the current collector length exhibits negligible effect on the cell performance as shown in Fig. 4d.

16

This difference can be attributed to the non-uniform velocity distribution in the porous electrodes.

As shown in Fig. 3a, along the positive y-direction, the velocity magnitude in the active region

increases in an accelerating manner to the peak value at the end of the electrode. Therefore, for the

situation of Fig. 4c, the high flow rate region, where the local electrochemical reaction rate is more

sensitive to the electrode potential, is covered by the current collector. Voltage loss in the high flow

rate region due to the lateral electron transport is almost zero, where corresponding inhibitions to

the electrochemical reactions are eliminated and hence similar cell performances are observed (see

Fig. 5). It can be derived from Fig. 4 and Fig. 5 that the positioning of the current collector is a

more influential factor than the area, due to the non-uniform velocity distribution.

The numerical simulation results of the effects of the current collector positioning on the cell

performance are plotted in Fig. 6. The size (L = 2mm, W = 1mm, h=0.3mm) of the current collector

is kept unchanged while the position of the current collector center varies from yB = −7 mm to

yB = 11 mm. An increase of 67% is observed in the maximum output power in this process. The

optimal position is in the high flow rate region which locates close to the outlet. Since the impact of

current collector positioning is significant, we have carried out experiments to verify this result. An

MFC with flow-through porous electrodes, as shown in Fig. 7, was fabricated. Hesen carbon paper

(HCP020N) was employed as the porous electrode material. 2 mol L−1 V2+ in 4 mol L−1 sulfuric

acid was used as anolyte and 2 mol L−1 VO2+ in 4 mol L−1 sulfuric acid was used as catholyte.

Three pairs of ports (marked with A1, B1, A2, B2, A3, B3) were simultaneously planted at different

positions along the porous electrodes (Fig 7 (b) and (c)) in a single cell to eliminate the deviations

from cell fabrication. More experimental details are provided in the Supplemental Materials. In the

experiment, the cell was operated at flow rate spanning from 60 μL min−1 to 300μL min−1. The

current collector size was kept unchanged (𝐿 = 1mm,𝑊 = 1mm, ℎ = 5mm) while the position of

the current collector center varied from yB = −7.5 mm to yB = 11.5 mm. This was realized by

connecting the external circuit to the cell via the port-pairs A1-B1, A2-B2, and A3-B3, respectively.

17

The polarization curves were recorded with a potentiostat, as shown in Fig. 8. The experimental

results shown in Fig. 8 exhibited the same trend as that in Fig. 6: increases by 26% and 61% in the

maximum output power with optimized current collector position were observed for the cases with

flow rates of 60 μL min−1 and 300 μL min−1, respectively. The main reason for the discrepancies

in the specific current density values between the experimental data in Fig. 8 and simulated data in

Fig. 6 is the difference in the carbon paper used for the porous electrodes. According to our

previous electrochemical analysis in [2], the rate constants of the vanadium redox reactions on

HCP020N, the one used in our experiment, are 1 × 10−8 m s−1 for V2+ oxidation and 7.5 ×

10−8 m s−1 for VO2+ reduction, which are much lower than those on TGPH-090 (in [17], 1.7 ×

10−7 m s−1 for V2+ oxidation and 6.8 × 10−7 m s−1 for VO2+ reduction ). As a result, under the

same operating conditions, the current density values in Fig. 8 (experimental results with HCP020N

as the porous electrode material) are generally smaller than those in Fig. 6 (modeling results with

TGPH-090 as the porous electrode material). Besides, the smaller thickness (2mm) of HCP020N

comparing to that (3mm) of TGPH-090 also yields lower cell performance. However, this does not

conflict with the conclusion we can draw, that the current collector position has a significant effect

on the cell performance and the optimal position locates close to the outlet where the flow rate is

higher and the local electrochemical reaction rate is more sensitive to the electrode potential.

Moreover, the results of the numerical simulation suggested that lateral electron transport in the

porous electrode encounters high resistance (Section 3.1), which was often ignored in previous

studies [29]. This conclusion is also validated by the experiment in which an ohmic resistance as

large as 8.7 Ω was measured along the lateral direction of the porous electrode.

Effects of current collector thickness were studied while keeping the current collector length

and width unchanged (𝐿 = 20mm and 𝑊 = 1mm to cover the whole upper surface of the

eledctrodes), and decreasing the current collector thickness from ℎ = 3 × 10−1 mm to ℎ = 4 ×

10−4 mm as employed in Ref. [29]. The results are plotted in Fig. 9a&b. When the thickness

18

decreases from 3 × 10−1 mm to 1.5 × 10−1 mm, no evident change in the polarization curves is

observed. From the inset of Fig. 9a it can be seen that till the thickness decreases from 3 × 10−1

mm to 3 × 10−3 mm, the maximum power can retain at 99% of the original value, and further

decrease in the thickness will result in a rapid drop in the cell performance. When the thickness

decreases to 4 × 10−4 mm, a 16% drop in maximum output power is resulted compared to the

3 × 10−1 mm case. At this condition, the lateral electron transport in the current collector has no

apparent priority over that in the porous electrode, electrode potential becomes non-uniform along

the y-direction, electrochemical reaction rate decreases, especially in the high flow rate region and

accordingly the cell performance diminishes. Thus, the current collector thickness should be kept no

lower than a certain value (3 × 10−3 mm in this case). On the other hand, since increasing the

thickness from 3 × 10−3 mm to 3 × 10−1 mm doesn’t bring any noticeable increase in the cell

output, there is no need to make it thicker, for cost-effectiveness.

The conductivity of the current collector material is another factor we studied. The results are

shown in Fig. 9c&d. Keeping the other factors unchanged (𝐿 = 20mm,𝑊 = 1mm, ℎ = 0.3mm

and the current collector covers the whole upper surface of the electrode), the setting of the

conductivity is decreased from 1 × 107 S m−1 to 5 × 103 S m−1. Here 1 × 107 S m−1 represents

the magnitude of typical conductivity values for conductive metallic current collectors (Au, Ag, Cu,

etc.), while 5 × 103 S m−1 for the carbon based materials. For the case of metallic current

collector being employed, the conductivity of the current collector (1 × 107 S m−1) is much larger

than that of the porous electrode (5 × 103 S m−1), electrons generated in the porous electrode will

first flow in the z-direction towards the current collector and then flow laterally within the current

collector to the external circuit. Thus, electrode potential loss due to the lateral electron transport in

the porous electrode is significantly reduced. In the other case, when the current collector

conductivity decreases to 5 × 103 S m−1, which is similar to that of the porous electrode, electron

transport in the current collector has no apparent priority over that in the porous electrode. Electrons

19

generated in the porous electrode show similar lateral flow behavior to the external wire in both the

electrode and the current collector. The non-uniform electrical potential in the electrode and the

current collector leads to decreased electrochemical reaction rates, especially in the high flow rate

region. A decrease of 35.2% is observed in the maximum output power. Thus, in order to optimize

the cell output, the current collector material should possess a much larger electrical conductivity

than that of the electrode material.

Normally, potential distribution within the current collector is uniform due to the high electrical

conductivity. However, in the cases where the current collector has low conductivity and/or a small

thickness, non-uniform potential distribution can also be observed within the current collector,

which is because the electrical resistance due to the lateral electron transport in the current collector

cannot be ignored. As a result, the connecting position between the external wire and the current

collector becomes critical as the electron transport in the z-direction towards the external circuit will

be more concentrated to the region covered by the external wire. Effects of the external wire

positioning are examined and the results are presented in Fig. 9e&f for the cell with a low current

collector conductivity (5 × 103 S m−1). In these cases, the whole electrode upper surfaces are also

totally covered by current collectors (20 mm × 1 mm). An increase of 18.9% in the maximum

power is observed when we move the external wire position along the electrode midline from yA =

−7 mm to yA = 11 mm. Thus, in the cases with a low current collector conductivity or a small

current collector thickness, effects of the current collector are weakened and external wire plays the

role of the current collector alternatively. To reduce the electrical resistance, the external wires need

to be attached to the high flow rate region.

4. Conclusions

From the investigations above, some basic principles in the current collector design for MFCs

can be drawn: The most important point is that the current collector should be located at the high

20

flow rate region; As for the size of the current collector, as long as it can cover the high flow rate

region and be thick enough (>10-3 mm), there should be no further need to increase the size as it

won’t significantly improve the output; The conductivity of the current collector material should be

larger than the electrode material, and highly conductive metallic materials are preferred; The

wiring position is insignificant if the above criteria are met, otherwise, if low conductivity material

has to be used and/or the thickness is limited, the external wire should also be attached to the

current collector at the high flow rate region. Overall, the present study concludes that optimal

current collector design can effectively reduce the ohmic resistance observed in MFC with

flow-through porous electrodes and, consequently, boost the cell performance. The derived findings

about the current collector design can provide useful guidance for the future development and

manufacturing planning of MFC.

Acknowledgements

The research presented in this paper is funded by a grant from the Research Grants Council in

Hong Kong (CityU 11207414), Natural Science Foundation of Jiangsu Province (BK20170314) and

Jiangsu University of Technology (KYY17008).

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24

List of Tables

Table 1. Input parameters for the base case

Parameter Value Units Reference

𝐸10 (vs. SCE) −0.496 V [24]

𝐸20 (vs. SCE) 0.75 V [24]

𝛼1,𝑎 0.5 - [24]

𝛼1,𝑐 0.5 - [24]

𝛼2,𝑎 0.5 - [24]

𝛼2,𝑐 0.5 - [24]

𝑘1 1.7 × 10−7 m s−1 [42]

𝑘2 6.8 × 10−7 m s−1 [43]

𝜎𝑠 (in-plane) 5 × 103 S m−1 Assumed

𝜎𝑠 (through-plane) 5 × 102 S m−1 Assumed

𝜎𝑐𝑙 1 × 107 S m−1 Assumed

𝜎𝑒𝑤 1 × 107 S m−1 Assumed

𝛾 (in − plane) 0.326 - [41]

𝛾 (through − plane) 0.714 - [41]

𝜔 (in − plane) 0.863 - [41]

𝜔 (through − plane) 0.543 - [41]

𝜀 0.78 - [44]

𝜀𝑝 0.11 - [41]

𝜌 1200 kg m−3 [45]

𝜇 0.008 Pa s [46]

𝐷II 2.4 × 10−11 m2 s−1 [24]

𝐷III 2.4 × 10−11 m2 s−1 [24]

𝐷IV 3.6 × 10−11 m2 s−1 [46, 47]

𝐷V 3.6 × 10−11 m2 s−1 [46, 47]

𝐷𝐻 9.312 × 10−9 m2 s−1 [48]

𝑑𝑓 7 × 10−6 m [44]

𝐾 2.375 × 10−11 m2 [44]

𝑎 8.333 × 104 m−1 [24]

𝑉𝑐𝑒𝑙𝑙 0.8 V - 𝑇 298 (room temp.) K - 𝐿𝑐𝑙 2.4 × 10−3 m - 𝑊𝑐𝑙 1 × 10−3 m - ℎ𝑐𝑙 3 × 10−4 m - 𝑑𝑒𝑤 4 × 10−4 m - ℎ𝑒𝑤 1.5 × 10−3 m - yA −4 × 10−3 m - yB −4 × 10−3 m -

25

List of Figures

Fig. 1 Schematic illustrations of the MFC with flow-through porous electrodes: (a) 3D diagram, (b)

plan view and (c) front view.

26

Fig. 2 (a) Grid independence check: distributions of the y-component of the electrode current

density along the midline of the anode upper surface with three different grid sizes. (b) Comparison

between fuel cell polarization curves predicted by the present model and experimental data in [17]

at the flow rate of 60 μL min−1.

27

Fig. 3 (a) Velocity magnitude and (b) local current density along the anode and cathode mid-lines

(Anode: x = −1 mm , z = 0.15 mm ; Cathode: x = 1 mm , z = 0.15 mm). (c) Streamlines of

electron transport paths and (d) electrical potential in the anode mid-plane at x = −1 mm.

28

Fig. 4 Effects of current collector length: (a) polarization curves and (b) power density curves for

the cases with one side of the current collector fixed at y = −8 mm; (c) polarization curves and (d)

power density curves for the cases with one side of the current collector fixed at y = 12 mm.

29

Fig. 5 (a) Electrical potential and (b) local current density in the anode mid-plane at x = −1 mm

for the cases with (1) one side of the current collector fixed at y = −8 mm; yA = −7 mm and (2)

one side of the current collector fixed at y = 12 mm; yA = 11 mm. Here 𝐿 = 6 mm.

30

Fig. 6 Effects of current collector position on (a) polarization curves and (b) power density curves.

31

Fig. 7 Schematic illustration of the fabrication of microfluidic fuel cell architecture with

flow-through porous electrodes: (a) exploded-view. Photographs of the assembled cell for the

assessment of current collector design on the cell performance: (b) plan view; (c) 3D diagram. The

red (marked with A1, A2 and A3) and black (marked with B1, B2 and B3) lines are the external

wires connected to the porous electrodes.

32

Fig. 8 Effects of current collector positions on cell performance: (a) polarization curves and (b)

power density curves measured at the flow rate of 60 μL min−1; (c) polarization curves and (d)

power density curves measured at the flow rate of 300 μL min−1.

33

Fig. 9 Effects of current collector design parameters on cell performance: (a) polarization curves

and (b) power density curves under different current collector thicknesses; (c) polarization curves

and (d) power density curves under different current collector electrical conductivities; (e)

polarization curves and (f) power density curves under different external wire positons.