optimal design of current collectors for microfluidic fuel
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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:
[email protected] (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.
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Keywords: Microfluidic fuel cell; Porous electrode; Current collector design; Lateral electron
transport; Electrical resistance
Nomenclature
π specific surface area, mβ1
A center of the interface between external wire and current collector
B center of the interface between current collector and electrode
π bulk concentration, mol mβ3
ππ surface concentration, mol mβ3
π diameter, m
π· diffusion coefficient, m2 sβ1
πΈ equilibrium potential vs. SCE, V
πΈ0 standard equilibrium potential vs. SCE, V
πΉ Faraday constant, 9.65 x 104 C molβ1
β thickness in the z-direction, mm
πβ current density, A mβ2
π0 exchange current density, A mβ2
π charge transfer current density, A mβ2
πΎ permeability, m2
π standard reaction rate constant, m sβ1
πππ mass transfer coefficient of species π, m sβ1
πΏ length in the y-direction, mm
π pressure, Pa
3
π charge source term, A mβ3
π universal gas constant, 8.314 J molβ1 Kβ1
π species source term, mol mβ3sβ1
π‘ time, s
π temperature, K
οΏ½ββοΏ½ velocity vector, m sβ1
π vanadium species
πππππ cell voltage, V
π width in the x-direction, mm
π§ charge number
Greek symbols
πΌ charge transfer coefficient
Ξ³ constant
π porosity
ππ percolation threshold
π density, kg mβ3
π electrical conductivity, S mβ1
Ο tortuosity
β potential, V
π viscosity, Pa s
Ο constant
Ξ· overpotential, V
Superscript
πππ effective
4
Subscripts
1 anode
2 cathode
π anodic reaction
π cathodic reaction
π species {π2+, π3+, ππ2+, ππ2+ and π»+}, marked as {II, III, IV, V and H}
π fiber
π electrode
π electrolyte
ππ current collector
ππ€ 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 cmβ2 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
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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 2Ξ©) 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 electrodeβs 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 π2+/π3+ sulfate solution as the anolyte,
ππ2+/ππ2+ 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: π2+ β π3+ + πβ E0 = β0.496 V vs SCE (1)
Cathode: ππ2+ + 2π»+ + πβ β ππ2+ + π»2π 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 90Β°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:
β β (ποΏ½ββοΏ½ ) = 0 (3)
β
βπ‘οΏ½ββοΏ½ + (οΏ½ββοΏ½ β βοΏ½ββοΏ½ ) = β
1
πβπ +
π
πβ2οΏ½ββοΏ½ (4)
where Ο is the density, Uββ is the velocity vector, t is time, P is pressure and ΞΌ is the viscosity.
For the flow field in the porous electrodes, the Brinkman equation is employed instead of the
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Navier-Stokes equation:
βπ = βπ
πΎοΏ½Μ οΏ½ +
π
πβ2οΏ½ββοΏ½ (5)
where K is the permeability and Ξ΅ is the electrode porosity.
2.1.2 Mass transport
The governing equation for the mass transport can be written as:
Uββ β βcj β Djeffβ2cj = 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 volumetricβbasis 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
ππ = ππππ(πππ β ππ) (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]:
πππ = 7π·π
ππ(π|οΏ½ββοΏ½ |ππ
π)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
β βππ β= ππ , =ππ
β β ππ πππ
ββ π (9)
β βπππβ = πππ, =πππ
β β πππββ ππ (10)
β βπππ€
β = πππ€, =πππ€
β β πππ€ββ ππ€ (11)
where βi
is the current density, Q is the charge source term, Ο is the electrical conductivity and
β 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
β βilβ= Ql , =il
β β Οleffββ 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 ππ and ππ can be derived from the charge transfer
current densities π1 and π2, which are given by the Butler-Volmer equations,
π1 = ππ = βππ = βππ1 (13)
π2 = πs = βππ = βππ2 (14)
π1 = π10 {
πIIπ
πIIexp (
πΌ1,ππΉΖ1
π π) β
πIIIπ
πIIIexp (β
πΌ1,ππΉΖ1
π π)} (15)
π2 = π20 {
πIVπ
πIVexp (
πΌ2,ππΉΖ2
π π) β
πVπ
πVexp (β
πΌ2,ππΉΖ2
π π)} (16)
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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, Ζ is the overpotential and Ξ± is the charge transfer
coefficient.
Related parameters and variables including the effective electrolyte conductivity, exchange
current density, overpotential and equilibrium potential are derived below:
πππππ
=πΉ2
π πβ π§π
2π π·π
πππππ (17)
π10 = πΉπ1πII
πΌ1,ππIII
πΌ1,π (18)
π20 = πΉπ2πIV
πΌ2,ππV
πΌ2,π (19)
Ζ1 = β π β β π β πΈ1 (20)
Ζ2 = β π β β π β πΈ2 (21)
πΈ1 = πΈ10 +
π π
πΉln (
πIII
πII) (22)
πΈ2 = πΈ20 +
π π
πΉln (
πVππ»2
πIV) (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
πII = βπIII =π1
πΉ (24)
πIV = βπV = βππ»
2=
π2
πΉ (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 mΞ© 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 Γ 2 mm, corresponding total contact
resistance in the cell is in the range of 0.1 to 1 Ξ©. In an experiment conducted by us, the contact
resistance was measured to be 0.2 Ξ© with the current collector area equal to 1 mm Γ 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 mβ1 and their counterparts in the
through-plane direction normally range from 100 to 1000 S mβ1, 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 mβ1 in the in-plane
directions and 500 S mβ1 in the through-plane direction.
The effective diffusion coefficient π·ππππ
is calculated based on previous modeling work of
carbon paper [41],
π·ππππ
= π·ππ
π (26)
π = 1 + πΎ1βπ
(πβππ)π (27)
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where Ο is the tortuosity, Ξ΅p is the percolation threshold, Ξ³ and Ο 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) β (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 (πππππ). 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 Lβ1 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 Lβ1, respectively. The flow rate is 60 ΞΌL minβ1, 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
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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 Γ 10β4 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 ΞΌm Γ 83 ΞΌm Γ 20 ΞΌm, 50 ΞΌm Γ 67 ΞΌm Γ 15 ΞΌm and 40 ΞΌm Γ 55 ΞΌm Γ 12 ΞΌm
(in x Γ y Γ 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 ΞΌm/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
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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, π3+/ππ2+)
in 4 M aqueous H2SO4 solution was recharged to produce π2+ and ππ2+, 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 = β8 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 Γ 10β5 m sβ1 to 8.8 Γ 10β4 m sβ1.
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,
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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 Γ 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 = β8mm
(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.
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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 = β7 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 Lβ1 V2+ in 4 mol Lβ1 sulfuric
acid was used as anolyte and 2 mol Lβ1 VO2+ in 4 mol Lβ1 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 ΞΌL minβ1 to 300ΞΌL minβ1. The
current collector size was kept unchanged (πΏ = 1mm,π = 1mm, β = 5mm) while the position of
the current collector center varied from yB = β7.5 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 ΞΌL minβ1 and 300 ΞΌL minβ1, 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 Γ 10β8 m sβ1 for V2+ oxidation and 7.5 Γ
10β8 m sβ1 for VO2+ reduction, which are much lower than those on TGPH-090 (in [17], 1.7 Γ
10β7 m sβ1 for V2+ oxidation and 6.8 Γ 10β7 m sβ1 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 Ξ© 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 (πΏ = 20mm and π = 1mm to cover the whole upper surface of the
eledctrodes), and decreasing the current collector thickness from β = 3 Γ 10β1 mm to β = 4 Γ
10β4 mm as employed in Ref. [29]. The results are plotted in Fig. 9a&b. When the thickness
18
decreases from 3 Γ 10β1 mm to 1.5 Γ 10β1 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 Γ 10β1
mm to 3 Γ 10β3 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 Γ 10β4 mm, a 16% drop in maximum output power is resulted compared to the
3 Γ 10β1 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 Γ 10β3 mm in this case). On the other hand, since increasing the
thickness from 3 Γ 10β3 mm to 3 Γ 10β1 mm doesnβt 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 (πΏ = 20mm,π = 1mm, β = 0.3mm
and the current collector covers the whole upper surface of the electrode), the setting of the
conductivity is decreased from 1 Γ 107 S mβ1 to 5 Γ 103 S mβ1. Here 1 Γ 107 S mβ1 represents
the magnitude of typical conductivity values for conductive metallic current collectors (Au, Ag, Cu,
etc.), while 5 Γ 103 S mβ1 for the carbon based materials. For the case of metallic current
collector being employed, the conductivity of the current collector (1 Γ 107 S mβ1) is much larger
than that of the porous electrode (5 Γ 103 S mβ1), 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 Γ 103 S mβ1, 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 Γ 103 S mβ1). In these cases, the whole electrode upper surfaces are also
totally covered by current collectors (20 mm Γ 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 =
β7 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
wonβt 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
πΈ10 (vs. SCE) β0.496 V [24]
πΈ20 (vs. SCE) 0.75 V [24]
πΌ1,π 0.5 - [24]
πΌ1,π 0.5 - [24]
πΌ2,π 0.5 - [24]
πΌ2,π 0.5 - [24]
π1 1.7 Γ 10β7 m sβ1 [42]
π2 6.8 Γ 10β7 m sβ1 [43]
ππ (in-plane) 5 Γ 103 S mβ1 Assumed
ππ (through-plane) 5 Γ 102 S mβ1 Assumed
πππ 1 Γ 107 S mβ1 Assumed
πππ€ 1 Γ 107 S mβ1 Assumed
πΎ (in β plane) 0.326 - [41]
πΎ (through β plane) 0.714 - [41]
π (in β plane) 0.863 - [41]
π (through β plane) 0.543 - [41]
π 0.78 - [44]
ππ 0.11 - [41]
π 1200 kg mβ3 [45]
π 0.008 Pa s [46]
π·II 2.4 Γ 10β11 m2 sβ1 [24]
π·III 2.4 Γ 10β11 m2 sβ1 [24]
π·IV 3.6 Γ 10β11 m2 sβ1 [46, 47]
π·V 3.6 Γ 10β11 m2 sβ1 [46, 47]
π·π» 9.312 Γ 10β9 m2 sβ1 [48]
ππ 7 Γ 10β6 m [44]
πΎ 2.375 Γ 10β11 m2 [44]
π 8.333 Γ 104 mβ1 [24]
πππππ 0.8 V - π 298 (room temp.) K - πΏππ 2.4 Γ 10β3 m - πππ 1 Γ 10β3 m - βππ 3 Γ 10β4 m - πππ€ 4 Γ 10β4 m - βππ€ 1.5 Γ 10β3 m - yA β4 Γ 10β3 m - yB β4 Γ 10β3 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 ΞΌL minβ1.
27
Fig. 3 (a) Velocity magnitude and (b) local current density along the anode and cathode mid-lines
(Anode: x = β1 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 = β1 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 = β8 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 = β1 mm
for the cases with (1) one side of the current collector fixed at y = β8 mm; yA = β7 mm and (2)
one side of the current collector fixed at y = 12 mm; yA = 11 mm. Here πΏ = 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 ΞΌL minβ1; (c) polarization curves and (d)
power density curves measured at the flow rate of 300 ΞΌL minβ1.
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.