Flow Field Effect on the Performance of Direct Formic Acid Membraneless Fuel Cells: a Numerical Study

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Article Flow Field Effect on the Performance of Direct Formic Acid Membraneless Fuel Cells: A Numerical Study

Jin-Cherng Shyu * and Sheng-Huei Hung

Department of Mechanical Engineering, National Kaohsiung University of Science and Technology, Kaohsiung 80778, Taiwan; [email protected] * Correspondence: [email protected] or [email protected]; Tel.: +886-7-3814526 (ext. 15343)

Abstract: The performance of both air-breathing and air-feeding direct formic acid membraneless fuel cells (DFAMFCs) possessing different flow fields were numerically investigated in this study at given concentration and flow rate for both fuel and electrolyte. Single serpentine, stepwise broadening serpentine, multi-serpentine and parallel channel were tested as liquid flow field, while single serpentine, stepwise broadening serpentine, multi-serpentine and pin channel were tested as air flow field. The channel width was either 0.8 mm or 1.3 mm. The simulation results showed that the air-breathing DFAMFC having identical flow field for both fuel and electrolyte yielded highest cell output. The air-breathing DFAMFC having SBS liquid flow field yielded a maximum power density of 10.5 mW/cm2, while the air-breathing DFAMFC having S(1.3) liquid flow field produced an open circuit voltage of 1.0 V owing to few formic acid penetration into the cathode. Concerning the air-feeding DFAMFCs, the DFAMFC having SBS liquid flow field and MS(0.8) air flow field yielded highest peak power density, 12 mW/cm2, at an airflow rate of 500 sccm. Considering the power generated by the DFAMFCs together with the power consumed by the air pump, DFAMFC having SBS liquid flow field and Pin(0.8) air flow field could be the preferred design. Citation: Shyu, J.-C.; Hung, S.-H. Flow Field Effect on the Performance Keywords: membraneless; flow field; fuel cell; formic acid; simulation of Direct Formic Acid Membraneless Fuel Cells: A Numerical Study. Processes 2021, 9, 746. https:// doi.org/10.3390/pr9050746 1. Introduction

Academic Editor: Direct liquid fuel cells with polymer electrolyte membrane are becoming highly Tanja Vidakovic-Koch regarded worldwide because they are favorable to be power sources for portable electronics at room temperature. However, owing to the significant fuel crossover of the polymer Received: 28 March 2021 electrolyte membrane while feeding liquid fuel [1,2], one of the particular types of fuel cells Accepted: 20 April 2021 that generates electricity at room temperature by feeding liquid electrolyte between both Published: 23 April 2021 electrodes instead of installing a polymer electrolyte membrane have been developed for about a decade. Numerous studies on exploring the characteristics of membraneless fuel Publisher’s Note: MDPI stays neutral cells have been conducted based on both experimental test and numerical simulation [3–6]. with regard to jurisdictional claims in Those membraneless fuel cell usually featured a single, short and straight microchannel, published maps and institutional affil- and is also termed as microfluidic fuel cells. iations. Unlike the traditional DMFCs that possess a solid polymer membrane between two electrodes, a flowing electrolyte-direct methanol fuel cell (FE-DMFC) having a single serpentine, parallel serpentine, triple serpentine and a grid type cathode flow field were simulated by Ouellette et al. [7] to examine the cell performance. The three-dimensional Copyright: © 2021 by the authors. fuel cell model featured an electrolyte stream flowing between two polymer electrolyte Licensee MDPI, Basel, Switzerland. membranes, which individually assembled an electrode on one side, for eliminating the This article is an open access article fuel crossover. Results showed that the single serpentine flow field provided the best distributed under the terms and performance due to the better reactant distribution over the cathode catalyst layer. Similar conditions of the Creative Commons fuel cell configuration using a circulating liquid electrolyte between two MEAs of the Attribution (CC BY) license (https:// PEMFCs to tackle both water and thermal problems was also proposed and tested with creativecommons.org/licenses/by/ dry reactant gases [8]. 4.0/).

Processes 2021, 9, 746. https://doi.org/10.3390/pr9050746 https://www.mdpi.com/journal/processes Processes 2021, 9, 746 2 of 19

Besides the fuel crossover issue of the direct liquid fuel cells, flow field design for both electrodes of direct liquid fuel cell has also been considered as another crucial factor that affects the fuel cell performance. An optimal flow field design for fuel cells causes a uniform fuel and oxidant distribution on the electrode surface and ensures the products, H2O and CO2 for example, to be easily removed from the active surface area. Numerous studies have been conducted to investigate the effect of flow field designs on the DMFCs performance. Among those studies, single serpentine, parallel, and multiple serpentine flow fields are commonly employed as the anodic flow field [9–11]. In addition, a few particular anodic flow fields were also proposed. Wang et al. [12] numerically investigated the anodic flow velocity and temperature distributions of the DMFC with four different anodic flow fields, including double serpentine, parallel, helix and single serpentine, using 3-D simulation model. However, the helix anodic flow field yielded a non-uniform inner temperature distribution. Yuan et al. [13] tested an active liquid-feed DMFC with three different types of anodic flow fields, including traditional right-angle serpentine flow field, rounded-corner serpentine flow field, and stepwise broadening serpentine flow field, and investigated the effects of those flow fields on the cell performance, gas bubble behavior and pressure drop characteristics of the DMFC. The results show that the broadening serpentine flow field contributes to the CO2 emission and uniform distribution of reactants, respectively, thus yielding the highest power output. El-Zoheiry et al. [14] proposed new multi-path spiral flow field designs to improve the under-rib convection mass transport, and consequently the performance of direct methanol fuel cells. Their simulation results indicate a significant increase in fuel cell performance with the enhancement of convection mass transport. Besides the anodic flow field design, the serpentine, multiple serpentine, and parallel, as well as grid cathode flow fields were also studied for DMFCs in order to examine the cell performance over the past few years [15–19]. Jung et al. [15] found that the gas is well distributed within serpentine flow field because of the favorable mass transport and pressure drop while extremely non-uniform oxygen concentration distribution is observed within parallel flow field. The results obtained by Oliveira et al. [16] show that for the lower value of fuel cell temperature and lower value of methanol concentration, the use of multiple serpentine flow field for cathode leads to a better performance, because the pressure-driven mass flow in the channels ensures a good ability for water removal. Jung et al. [17] found that serpentine flow fields exhibited the highest cell output for low stoichiometric factor operation, while serpentine flow field and grid flow field revealed comparable cell performance for medium stoichiometric factor operation. Moreover, the performance of DMFCs having bio-inspired flow fields [20,21] was also numerically investigated, in order to achieve both a uniform reactant distribution on the electrode surface and a favorable pressure drop between the inlet and outlet of the reactant. The flow field effect on the direct liquid fuel cells performance that explored in the aforementioned literature are the fuel cells possessing a polymer electrolyte membrane or multiple polymer electrolyte membranes [8]. In order to eliminate the fuel crossover of direct liquid fuel cells as much as possible, designing direct liquid fuel cells with an electrolyte stream flowing between two gas diffusion electrodes is considered as an effective way. However, such design causes the fuel cells to possess an additional flow field for liquid electrolyte, resulting in more complicated fuel cell design to analyze. According to the literature survey in the previous paragraph, it has been confirmed that the flow fields for both anode and cathode of the direct liquid fuel cells play important roles in the fuel cell performance. Besides, an additional flow field for liquid electrolyte imposes an additional factor on the performance of the direct liquid membraneless fuel cells that has not yet been investigated using three-dimensional numerical simulation, this study aims to numerically investigate the performance of both air-breathing and air-feeding direct formic acid membraneless fuel cells (DFAMFCs) with different flow fields. Processes 2021, 9, x FOR PEER REVIEW 3 of 20

numerically investigate the performance of both air-breathing and air-feeding direct for- Processes 2021, 9, 746 mic acid membraneless fuel cells (DFAMFCs) with different flow fields. 3 of 19

2. Numerical Model

2.2.1. Numerical Computational Model Domain 2.1. ComputationalThe numerical Domain model of the two different types of DFAMFCs in Figure 1 accounts for the coupled transport of fluid, species and charge in conjunction with the electrochemical The numerical model of the two different types of DFAMFCs in Figure1 accounts for reactions. Similar model was also employed in the studies [22,23] using commercially the coupled transport of fluid, species and charge in conjunction with the electrochemical available CFD software. The detailed dimensions of the fuel cell geometry are summa- reactions.rized in Table Similar 1. The model following was assumptions also employed were in made the studies while performing [22,23] using the simulation. commercially available CFD software. The detailed dimensions of the fuel cell geometry are summarized in(1) Table The1. three-dimensional The following assumptions system is at were steady made state while and isothermal. performing the simulation. (2) Laminar, incompressible fluid flow and body force is negligible. (1) The three-dimensional system is at steady state and isothermal. (2)(3) Laminar,The physical incompressible properties of fluidthe electr flowodes and are body isotropic force is and negligible. homogeneous. (3)(4) TheThe physicalsolutions propertiesare dilute and of the uniformly electrodes mixed. are isotropic and homogeneous. (4)(5) TheProton solutions transport are from dilute anode and to uniformly cathode is mixed. by electromigration only. (5) Proton transport from anode to cathode is by electromigration only. (6) Electromigration of formate ions is negligible due to the high concentration of (6) Electromigration of formate ions is negligible due to the high concentration of sup- portingsupporting electrolyte. electrolyte. (7)(7) TheThe productproduct of carbon dioxide dioxide is is fully fully dissolved dissolved in inthe the solution. solution. (8)(8) OxygenOxygen transport in in the the porous porous gas gas diff diffusionusion electrode electrode is isby by diffusion diffusion only. only.

FigureFigure 1. 1.Schematic Schematic illustrations illustrations ofof thethe computationalcomputational domain of of the the present present direct direct formic formic acid acid membranless membranless fuel fuel cells cells (DFAMFCs),(DFAMFCs), (a) (a air-breathing) air-breathing and and (b ()b air-feeding.) air-feeding.

Table 1. Geometrical parameters of the present fuel cell model. Table 1. Geometrical parameters of the present fuel cell model. Fuel Cell Type The Exterior Dimensions of the Model Air-breathingFuel Cell Type The 26.8 Exterior mm × 24 Dimensions mm × 2.67 mm of the Model Air-feedingAir-breathing 26.8 26.8mm mm× 24 ×mm24 × mm 3.67× mm2.67 mm Parameters Symbol Value (mm) Source Air-feeding 26.8 mm × 24 mm × 3.67 mm Electrode Parameters Symbol Value (mm) Source Electrode width Wcl 20 – Electrode Electrode length Hcl 21.8 – Electrode width Wcl 20 – Electrode length δ H 21.8 – Anode catalyst layer thickness cl,a cl 0.1 – Anode catalyst layer thickness δcl,a 0.1 – CathodeCathode catalyst catalyst layer layer thickness thickness δ δ 0.1 0.1– – cl,c cl,c Thickness of anode carbon paper δgdl,a 0.28 [24] Thickness of cathode carbon paper δgdl,c 0.19 [24] Flow channel

Rib width Wrib 0.8 – Rib length Hch 21.8 – Channel depth δch 1 – Inlet and outlet radius r f low 1.5 – Processes 2021, 9, 746 4 of 19

Table 1. Cont.

Air-breathing holes Number 3 × 4 radius rh 2 – Transverse pitch dhor 6 – Longitudinal pitch dver 5 –

2.2. Fluid Flow The laminar, incompressible fluid flow in the fuel, liquid electrolyte and oxidant flow channels is governed by the continuity and Navier–Stokes equation as follows,

* ∇ · u = 0 (1)

→ → → ρ u · ∇ u = −∇p + µ∇2 u (2a)

→ where ρ, u , µ, and p are the fluid density, the velocity vector, the dynamic viscosity of fluid, and the static pressure, respectively. Within the porous media including the catalyst layer and gas diffusion layer, namely carbon paper, the fluid flow is governed by the continuity equation as Equation (1) and the Brinkman equation as follows,

" → # ρ → u µ → 2µ → µ → ( u · ∇) = −∇p + ∇2 u − ∇2 u − u (2b) ε p ε p ε p 3ε p κ

where ε p and κ denote the porosity and the permeability of the porous medium, respectively. An identical ﬂow rate of 2.0 mL/min is prescribed at both the fuel and electrolyte inlet boundaries, while the outlet of both the fuel and electrolyte is assumed to be at atmospheric pressure. No-slip and impermeable boundary conditions are applied to all channel walls and continuity is maintained at the interfaces between the ﬂow channel and the porous media.

2.3. Species Transport The species transport in both the ﬂow channel and porous gas diffusion layer by both diffusion and advection is governed as follows,

→ ∇ · (−Di,e f f ∇ci) + u · ∇ci = 0 (3a)

However, since both the formic acid and oxygen are consumed within the catalyst layer, the species transport in the porous catalyst layer should be:

→ ∇ · (−Di,e f f ∇ci) + u · ∇ci = Si (3b)

where Di,eff and ci denote the effective diffusion coefﬁcient of each species within the porous medium and the local species concentration, and source term Si represents the consumption of reactant within the catalyst layer. The effective diffusion coefﬁcient of the species within the gas diffusion layer and the catalyst layer is, respectively expressed as

ε p D = D (4a) i,e f f τ i

3 2 Di,e f f = ε p Di (4b)

where τ is the tortuosity of the carbon paper and Di is the species diffusion coefﬁcient in a ﬂow channel. Processes 2021, 9, 746 5 of 19

A constant value of the fuel concentration is set at the inlet, and a convective boundary condition is imposed at the outlet. The continuity is maintained at the interfaces between the flow channels and the porous media. All other walls are set to be zero-flux boundaries. In addition, the oxygen concentration at the cathode/air interface is prescribed as a constant value and all other walls are set as zero-flux boundary condition. Table2 shows the velocity and concentration boundary conditions at all inlets of both types of fuel cells in the study. Besides, the physical and transport properties used in the simulation are listed in Table3.

Table 2. The ﬂow rate and concentration boundary conditions at all inlets for both types.

Fuel Fluid Oxygen Electrolyte Operating Concentration at (Fuel/Electrolyte) Concentration at Inlet Air Flow Rate at Concentration at Conditions Inlet, HCOOH Flow Rate at Inlet and Breathing Holes Inlet (sccm) Inlet, H2SO4 (M) (M) + H2SO4 (M) (mL/min) (M) Air-breathing – 3 + 1.5 1.5 2.0 8.6 × 10−3 Air-feeding 200, 500

Table 3. The physical and transport used in the simulation.

Parameters Symbol Value (mm) Source Parameters Liquid 3 Density ρl 997.6 kg/m −4 Dynamic viscosity µl 8.52 × 10 Pa·s −9 2 Diffusion coefficient of formic acid DHCOOH 2.546 × 10 m /s [25] Conductivity of the electrolyte σl 59.900996 S/m Gas 3 Density ρg 1.1762 kg/m −5 Dynamic viscosity µg 1.8483 × 10 Pa·s Diffusion coefficient of oxygen D 2.1 × 10−9 m2/s [25] within catalyst layer O2,cl Diffusion coefficient of oxygen D 2.1 × 10−5 m2/s [3] within gas diffusion layer O2,gdl Catalyst layer of the anode

Porosity ε p_cl,a 0.28 – −13 2 Permeability κcl 3.62 × 10 m 4 Conductivity σcl,a 1.4 × 10 S/m [24] Volume fraction of the electrolyte εl,cl 0.024 – Gas diffusion layer of the anode (GDL)

Porosity ε p_gdl,a 0.672 – [24] −12 2 Permeability κgdl 4.53 × 10 m [24] Tortuosity τa 2.55 – [24] 4 Conductivity σgdl,a 1.4 × 10 S/m [24] Volume fraction of the electrolyte εl,gdl 0.035 – Catalyst layer of the cathode

Porosity ε p_cl,c 0.3 – −13 2 Permeability κcl 3.62 × 10 m 2 Conductivity σcl,c 5.2 × 10 S/m [24] Volume fraction of the electrolyte εl,cl 0.024 – Gas diffusion layer of the cathode (GDL)

Porosity ε p_gdl,c 0.739 – [24] −11 2 Permeability κgdl,c 3.67 × 10 m [24] Tortuosity τc 1.4 – [24] 2 Conductivity σgdl,c 5.2 × 10 S/m [24] Processes 2021, 9, 746 6 of 19

2.4. Electrochemical Reaction Kinetics The following two electrochemical reactions indicating the formic acid oxidation at the anode and the oxygen reduction at the cathode are considered here.

+ − HCOOH → CO2 + 2H + 2e → E0 = −0.22 V (5a)

+ − O2 + 4H + 4e → 2H2O → E0 = 1.23 V (5b) In brief, the liquid fuel, HCOOH, is oxidized to produce electrons and protons on the anode following Equation (5a). The former travel along the external circuit of the system through the load and generate the electricity, while the latter move to the cathode through the liquid electrolyte, H2SO4 in the study. Subsequently, the protons, electrons and the oxygen molecules in the cathode react to achieve the reduction reaction indicate as Equation (5b). The source term in Equation (3b) for anode, Sf, and cathode, So, can be expressed in terms of both the active speciﬁc area of the catalyst layer on both electrodes (av,a and av,c), and the local current density of the catalyst layer in both electrodes (iloc,a and iloc,c), respectively as follows, i S = −a loc,a (6a) f v,a 2F

i S = −a loc,c (6b) o v,c 4F

where iloc is estimated with both the limiting current density, ilim, depending on the maximum reactant transport rate, and the current density generated on the electrode surface, iexp r, as follows, ilimiexpr iloc = (7) ilim + kiexprk c i = nFD i,o (8) lim i,e f f δ where d is the diffusion distance, n is the number of electrons transported on the electrode, and Di,eff is the effective diffusion coefﬁcient of the reactant within the porous medium. The iexpr in Equation (7) is determined by the concentration-dependent Butler–Volmer eqauation for both anode and cathode, respectivley, as follows,

!β c f αaF αcF iexpr,a = i0,a exp η − exp η (9a) c f ,re f RT RT

!β co αaF αcF iexpr,c = i0,c exp η − exp η − nFMcross (9b) co,re f RT RT

where io,a and io,c are the exchange current density on the anode and cathode, respectively, c f and co are the local fuel and oxygen concentrations, respectively, c f ,re f and co,re f are the reference fuel and oxygen concentrations, respectively, β is the reaction order (β = 1), αa and αc are the charge transfer coefﬁcients, and η is the activation overpotential, which can be estimated by η = φs − φl − Eeq (10)

where Eeq, φl and φs are the equilibrium potential, the local electrolyte and electric potential, respectively. Note that Mcross in Equation (9b) denotes the effective fuel crossover ﬂux at the electrolyte/cathode catalyst layer interface. The reaction kinetics used in the abovementioned equations are listed in Table4. Processes 2021, 9, 746 7 of 19

Table 4. The reaction kinetics in the study.

Parameter Symbol Value Units 2 Exchange current density of anode i0,a 0.8 A/m 2 Exchange current density of cathode i0,c 0.00018 A/m 2 Active specific area of the anode av,a 1.0618 × 106 1/m 2 Active specific area of the cathode av,c 2.331 × 105 1/m Charge transfer coefficeint of anode αa 0.5 – Charge transfer coefficeint of cathode αc 0.5 – 3 Reference fuel concentration c f ,re f 1000 mol/m 3 Reference oxygen concentration co,re f 8.5 mol/m Faraday constant F 96,485 C/mol Universal gas constant R 8.3145 J/mol·K Ambient temperature T 300.15 K

2.5. Electric Current Flow Both the local electrolyte potential and local electric potential in Equation (10) can be determined by: σl∇ · ∇φl = 0 (11a)

σs∇ · ∇φs = 0 (11b)

where σl and σs are the conductivity of the liquid electrolyte and effective conductivity of the electrode that is determined by the following equations

3/2 σl,e f f = εl σl (12)

where ε denotes the porosity of either the catalyst layer or the gas diffusion layer. Once the → local electric potential is determined, the electric current ﬂows through the electrolyte, i l, → and the electrode, i s, is expressed as follows,

→ i l = −σl∇φl (13a) → i s = −σs∇φs (13b) The anode side wall is set to zero potential and the cathode end face is set to the cell voltage. All other boundaries are zero-ﬂux boundaries.

2.6. Solution Procedure → All unknowns including u, p, c f , co, φl and φs are solved by means of coupling the continuity equation, momentum equation, species transport equation and the electrochemical reactions, as well as charge transfer mentioned above using the commercial software, COMSOL Multiphysics 5.2. Structured grids were established to discretize the flow field, while unstructured grids were established to discretize the rest of the computational domain. Some of the structured grids were converted in order to join the structured grids and unstructured grids at the interface. Grid independence was ensured by testing numerous sets of meshes for the computational domain. Once the differences in both the current density and the average formic acid concentration within the catalyst layer at 0.4 V between two successive sets of meshes was less than 1%, the grid independence was considered to be achieved. According to the test result revealed in Figure2, the final solutions were obtained with mesh elements of about 100,000 and 240,000 for air-breathing and air-feeding DFAMFCs in this study. Parametric sweep and a direct solution procedure with PARDISO and MUMPS solvers are employed to calculate the current density at different voltages Processes 2021, 9, 746 8 of 19

with the convergence criteria for the residual of 10−4. Finally, the current density, j, of the fuel cells is calculated using the following equation,

1 Z j = is,ndA (14) AR AR Processes 2021, 9, x FOR PEER REVIEW 9 of 20 where AR is the entire electrode surface, 20 mm × 21.8 mm, and is,n is the component of the electric current normal to the surface of the catalyst layer.

(a) (b)

FigureFigure 2.2. ResultsResults ofof ((aa)) gridgrid independenceindependence test,test, andand ((bb)) thethe comparisoncomparison ofof VV-I-I curvescurves betweenbetween measuredmeasured datadata andand thethe numericalnumerical SchemeScheme 0.0. AsAs bothboth fuelfuel andand electrolyteelectrolyte ﬂowflow ﬁelds. fields.

InIn orderorder toto validatevalidate thethe simulationsimulation results,results, thethe polarizationpolarization curvescurves ofof thethe air-breathingair-breathing DFAMFCsDFAMFCs having having S(0.8) S(0.8) as as both both fuel fuel and and electrolyte electrolyte flow flow fields fields obtained obtained by simulation by simulation were comparedwere compared with thewith measured the measured values values in the in experiment the experiment [26]. Note [26]. thatNote the that configuration the configu- andration dimensions and dimensions of the air-breathingof the air-breathing DFAMFCs DFAMFCs in that in experiment that experiment [26] were [26] identical were iden- to thetical model to the depictedmodel depicted in Figure in1 Figurea andthe 1a and Nafion the contentNafion content in the anode in the catalyst anode catalyst layer of layer the DFAMFCof the DFAMFC was 3.73 was mg/cm 3.73 mg/cm2 with2 catalystwith catalyst loading loading of 2 mg-Pd/cm of 2 mg-Pd/cm2 and2 2and mg-Pt/cm 2 mg-Pt/cm2 on2 theon the anode anode and and cathode, cathode, respectively. respectively. Figure Figure2b 2b shows shows that that both both data data are are in in fairly fairly good good agreementagreement especiallyespecially at at both both high high fluid fluid flow flow rate rate and and concentration, concentration, for example,for example, the resultsthe re- presentedsults presented by purple by purple dashed dashed curve curve and purple and purp hollowle hollow circles circles in Figure in Figure2b with 2b fluid with flow fluid rateflow of rate 2.0 of mL/min 2.0 mL/min and reactant and reactant concentration concentration of 3.0 M,of 3.0 because M, because of the minorof the effectminor of effect gas bubbleof gas bubble produced produced on the catalyston the catalyst layer on layer the cellon the performance cell performance that was that not was considered not consid- in theered simulation in the simulation model. model.

3.3. ResultsResults Results and Discussion Results and Discussion Various configurations of the liquid flow fields for transporting the fuel and electrolyte Various configurations of the liquid flow fields for transporting the fuel and electro- and the gas flow fields for air distribution shown in Table5 were numerically investigated lyte and the gas flow fields for air distribution shown in Table 5 were numerically inves- here. Table6 shows the channel width, channel depth and rib width of each flow field tigated here. Table 6 shows the channel width, channel depth and rib width of each flow design. Note that the rib width between two adjacent channels, and the depth of both field design. Note that the rib width between two adjacent channels, and the depth of both channel and rib are 0.8 mm and 1.0 mm, respectively, for each flow field. channel and rib are 0.8 mm and 1.0 mm, respectively, for each flow field.

Table 5. The flow fields of the DFAMFCs simulated in this study with the inlet indicated with a pink circle.

Liquid Flow Field Gas Flow Field

Single Serpentine (S) Single Serpentine (S)

ProcessesProcesses 2021, 92021, x FOR, 9, x PEER FOR REVIEWPEER REVIEW 9 of 209 of 20

(a) (a) (b) (b) FigureFigure 2. Results 2. Results of (a) ofgrid (a) independencegrid independence test, andtest, ( band) the (b comparison) the comparison of V-I of curves V-I curves between between measured measured data anddata the and the numericalnumerical Scheme Scheme 0. As 0.both As fuelboth and fuel electrolyte and electrolyte flow fields.flow fields.

In orderIn order to validate to validate the simulation the simulation results, results, the polarization the polarization curves curves of the of air-breathing the air-breathing DFAMFCsDFAMFCs having having S(0.8) S(0.8) as both as bothfuel andfuel elecandtrolyte electrolyte flow flowfields fields obtained obtained by simulation by simulation were werecompared compared with withthe measured the measured values values in the in experiment the experiment [26]. [26].Note Nothatte thethat configu- the configu- rationration and dimensionsand dimensions of the of air-breathing the air-breathing DFAMFCs DFAMFCs in that in experimentthat experiment [26] were[26] wereiden- iden- tical totical the to model the model depicted depicted in Figure in Figure 1a and 1a th ande Nafion the Nafion content content in the in anode the anode catalyst catalyst layer layer of theof DFAMFC the DFAMFC was 3.73was mg/cm3.73 mg/cm2 with2 withcatalyst catalyst loading loading of 2 mg-Pd/cmof 2 mg-Pd/cm2 and2 2and mg-Pt/cm 2 mg-Pt/cm2 2 on theon anode the anode and cathode,and cathode, respectively. respectively. Figure Figure 2b shows 2b shows that boththat bothdata aredata in are fairly in fairly good good agreementagreement especially especially at both at bothhigh highfluid fluidflow flowrate andrate concentration,and concentration, for example, for example, the re- the results sultspresented presented by purple by purple dashed dashed curve curve and purpand purple hollowle hollow circles circles in Figure in Figure 2b with 2b withfluid fluid flow flowrate ofrate 2.0 of mL/min 2.0 mL/min and reactantand reactant concentration concentration of 3.0 of M, 3.0 because M, because of the of minor the minor effect effect of gasof bubble gas bubble produced produced on the on catalyst the catalyst layer layer on the on cell the performance cell performance that wasthat notwas consid- not considered eredin the in simulation the simulation model. model.

3. Results3. Results ResultsResults and Discussion and Discussion VariousVarious configurations configurations of the of liquid the liquid flow flowfields fi forelds transporting for transporting the fuel the andfuel electro-and electrolyte andlyte theand gas the flow gas flowfields fields for air for distribution air distribution shown shown in Table in Table 5 were 5 werenumerically numerically inves- inves- Processes 2021, 9, 746 tigatedtigated here. here.Table Table 6 shows 6 shows the channel the channel width, width, channel channel depth depth and riband width rib width of each of eachflow flow9 of 19 field fielddesign. design. Note Notethat the that rib the width rib width between between two adjacent two adjacent channels, channels, and the and depth the depth of both of both channelchannel and riband are rib 0.8 are mm 0.8 andmm 1.0and mm, 1.0 mm,respectively, respectively, for each for eachflow flowfield. field.

Table 5. TableTable 5. The 5. flow TheThe fieldsflow ﬂow fieldsof ﬁeldsthe of DFAMFCs ofthe the DFAMFCs DFAMFCs simulated simulated simulated in this in study this in this study with study thewith inlet with the indicatedinlet the inlet indicated indicatedwith awith witha a pink circle.pinkpink circle. circle.

LiquidLiquidLiquid Flow Flow FlowField Field Field Gas Flow Gas Gas Flow FlowField Field Field

Single Serpentine (S) Single Serpentine (S) ProcessesProcesses 2021, 920212021, x FOR,, 99,, xx PEER FORFOR PEERPEERREVIEW REVIEWREVIEW Single Single Serpentine Serpentine (S) (S) SingleSingle Serpentine Serpentine (S) (S) 10 of 201010 ofof 2020 ProcessesProcesses 2021, 20219, x FOR, 9, x PEERFOR PEER REVIEW REVIEW 10 of 2010 of 20

StepwiseStepwise Broadening Broadening Serpentine Serpentine StepwiseStepwise Broadening Broadening StepwiseStepwiseStepwise StepwiseBroadening BroadeningBroadening Broadening Serpentine SerpentineSerpentine StepwiseStepwiseStepwiseStepwise Broadening Broadening BroadeningBroadening (SBS)(SBS) SerpentineSerpentine (SBS) (SBS) Serpentine(SBS)(SBS) (SBS) (SBS) SerpentineSerpentineSerpentineSerpentine (SBS) (SBS) (SBS) (SBS)

Multi-SerpentineMulti-Serpentine Multi-SerpentineMulti-Serpentine (MS) (MS) Multi-SerpentineMulti-SerpentineMulti-Serpentine Multi-SerpentineMulti-SerpentineMulti-SerpentineMulti-Serpentine (MS) (MS) (MS)(MS) Multi-Serpentine(MS) (MS) (MS) (MS) (MS)(MS)

ParallelParallelParallel (P) (P) (P) PinPin (Pin)Pin (Pin) (Pin) ParallelParallelParallel (P) (P)(P) Pin (Pin)PinPin (Pin)(Pin)

TableTable 6. The 6. dimensions The dimensions of the of fuel, the electrolytfuel, electrolyte ande air and flow air fieldsflow fields in the in study. the study. TableTableTableTable 6. 6. TheThe 6.6. dimensions ThedimensionsThe dimensionsdimensions of of the the ofof fuel, fuel, thethe fuel,electrolytfuel, electrolyte electrolytelectrolyte and andee air airandand flow flow airair flowfieldsflow fields fieldsfields in in the the inin study. study. thethe study.study. Rib Width,Rib Width, Channel Channel and and FlowField Configuration Flow FlowField Field Configuration Configuration Channel Channel Width, Channel mm Width, Width, mm Rib mm Width,Rib Width,Rib mm Width, ChannelChannel Channel and and and Rib Flow Flow FlowField Field FieldConfiguration ConfigurationConfiguration Channel Channel Channel Width, Width,Width, mm mmmm mm mmRib Depth,RibDepth, Depth, mm mm mm mm mmmm Rib Depth,RibRib Depth,Depth, mm mmmm 0.8 0.8 0.8 Single SerpentineSingleSingle (S) Serpentine Serpentine (S) (S) 0.8 0.8 ElectrolyteElectrolyte Single Single Serpentine Serpentine (S) (S)1.3 1.3 1.3 Electrolyte ElectrolyteElectrolyteElectrolyte 1.3 1.31.3 (H SO ) 2 (H4 2SO4) Stepwise Broadening 2 4 Stepwise(H2SO(H4) 2 BroadeningSOStepwise4) Stepwise Broadening Broadening (H2SO(H4)2 SOStepwise4) Stepwise Broadening Broadening 0.8~1.3 0.8~1.30.8~1.3 Serpentine (SBS)SerpentineSerpentine (SBS) (SBS) 0.8~1.30.8~1.30.8~1.3 SerpentineSerpentineSerpentine (SBS) (SBS) (SBS) 0.8 0.8 0.8 Liquid LiquidLiquid Single SerpentineSingleSingle (S) Serpentine Serpentine (S) (S) 0.8 0.8 LiquidLiquid SingleSingle Serpentine Serpentine (S) (S)1.3 1.3 1.3 Fuel Fuel 1.3 1.3 Fuel (HCOOH + StepwiseFuel Fuel Broadening StepwiseStepwise Broadening Broadening H SO ) (HCOOH(HCOOH(HCOOH + Stepwise ++ Stepwise Broadening Broadening 0.8~1.3 0.8~1.30.8~1.3 2 4 (HCOOHSerpentine(HCOOH + (SBS) +Serpentine Serpentine (SBS) (SBS) 0.8~1.30.8~1.3 2 H4 2SO4) Serpentine (SBS) H2SOH4) 2SO4) Serpentine (SBS) 0.8 0.8 0.8 1 1 1 Multi-SerpentineH2SOH4)2 SOMulti-Serpentine4) (MS)Multi-Serpentine (MS) (MS)0.8 0.8 0.8 0.8 0.8 1 1 Multi-SerpentineMulti-SerpentineMulti-Serpentine (MS) (MS)(MS) 0.8 0.80.8 Parallel (P) ParallelParallel (P) (P) 0.8 0.8 0.8 ParallelParallelParallel (P) (P)(P) 0.8 0.80.8 0.8 0.8 0.8 Single SerpentineSingleSingle (S) Serpentine Serpentine (S) (S) 0.8 0.8 SingleSingleSingle Serpentine SerpentineSerpentine (S) (S)(S) 1.3 1.3 1.3 1.3 1.31.3 Stepwise BroadeningStepwiseStepwise Broadening Broadening Gas Air Gas Gas Air Air StepwiseStepwise Broadening Broadening 0.8~1.3 0.8~1.30.8~1.3 Gas GasGas SerpentineAir AirAir (SBS)SerpentineSerpentine (SBS) (SBS) 0.8~1.30.8~1.30.8~1.3 SerpentineSerpentineSerpentine (SBS) (SBS) (SBS) Multi-SerpentineMulti-Serpentine (MS)Multi-Serpentine (MS) (MS)0.8 0.8 0.8 Multi-SerpentineMulti-SerpentineMulti-Serpentine (MS) (MS)(MS) 0.8 0.80.8 Pin (Pin) Pin (Pin)Pin (Pin) 0.8 0.8 0.8 Pin (Pin)PinPin (Pin)(Pin) 0.8 0.80.8 FigureFigure 3 shows 3 shows the V the-I curves V-I curves (solid (solid ones) ones) and Pand-I curves P-I curves (dashed (dashed ones) ones) of the of air- the air- FigureFigureFigure 3 shows 33 showsshows the V thethe-I curves VV--II curvescurves (solid (solid(solid ones) ones)ones) and andPand-I curves PP--II curvescurves (dashed (dashed(dashed ones) ones)ones) of the ofof air- thethe air-air- breathingbreathing membraneless membraneless fuel cellsfuel cellshaving having three three different different flow flowfield fieldconfigurations, configurations, includ- includ- breathingbreathingbreathing membraneless membranelessmembraneless fuel cells fuelfuel cellshavingcells havinghaving three threethree different differentdifferent flow flowflowfield fieldfieldconfigurations, configurations,configurations, includ- includ-including theing 0.8-mm-wide the 0.8-mm-wide serpentine serpentine flow flowfield fieldfor bo forth bofuelth andfuel electrolyte,and electrolyte, denoted denoted as S(0.8) as S(0.8) ing theinging 0.8-mm-wide thethe 0.8-mm-wide0.8-mm-wide serpentine serpentineserpentine flow flow flowfield field fieldfor bo forforth bo bofuelthth fuelandfuel electrolyte,andand electrolyte,electrolyte, denoted denoteddenoted as S(0.8) asas S(0.8)S(0.8) × S(0.8),× S(0.8), the 0.8-mm-wide the 0.8-mm-wide multiple multiple serpentine serpentine fuel flowfuel flowfield fieldand 0.8-mm-wideand 0.8-mm-wide serpentine serpentine × S(0.8),×× S(0.8),S(0.8), the 0.8-mm-wide thethe 0.8-mm-wide0.8-mm-wide multiple multiplemultiple serpentine serpentineserpentine fuel flow fuelfuel flowflowfield fieldfieldand 0.8-mm-wide andand 0.8-mm-wide0.8-mm-wide serpentine serpentineserpentine electrolyteelectrolyte flow flowfield, field, denoted denoted as MS(0.8) as MS(0.8) × S(0.8), × S( and0.8), theand 0.8-mm-wide the 0.8-mm-wide parallel parallel fuel flowfuel flow electrolyteelectrolyteelectrolyte flow flowflowfield, field,field, denoted denoteddenoted as MS(0.8) asas MS(0.8)MS(0.8) × S(0.8), ×× S(S( 0.8),and0.8), theandand 0.8-mm-wide thethe 0.8-mm-wide0.8-mm-wide parallel parallelparallel fuel flowfuelfuel flow flow field fieldand 0.8-mm-wideand 0.8-mm-wide serpentine serpentine electrolyte electrolyte flow flowfield, field, denoted denoted as P(0.8) as P(0.8) × S(0.8). × S(0.8). It can It can fieldfield fieldand and0.8-mm-wideand 0.8-mm-wide0.8-mm-wide serpentine serpentineserpentine electrolyte electrolyteelectrolyte flow flow flowfield, field,field, denoted denoteddenoted as P(0.8) asas P(0.8)P(0.8) × S(0.8). ×× S(0.8).S(0.8). It can ItIt cancan be foundbe found in Figure in Figure 3 that 3 thethat air-breathing the air-breathing DFAMFC DFAMFC having having P(0.8) P(0.8) fuel flowfuel flowfield fieldreveals reveals be foundbebe foundfound in Figure inin FigureFigure 3 that 33 thatthethat air-breathing thethe air-breathingair-breathing DFAMFC DFDFAMFCAMFC having havinghaving P(0.8) P(0.8)P(0.8) fuel fuflowfuelel flow flowfield field fieldreveals revealsreveals the highestthe highest open open circuit circuit voltage, voltage, while while the fuel the cellfuel having cell having S(0.8) S(0.8) fuel flowfuel flowfield fieldshows shows the the the highestthethe highesthighest open openopen circuit circuitcircuit voltage, voltage,voltage, while whilewhile the fuel thethe cellfuelfuel having cellcell havinghaving S(0.8) S(0.8)S(0.8) fuel flowfuelfuel flow flowfield field fieldshows showsshows the thethe lowestlowest open open circuit circuit voltage. voltage. However, However, in spit ine spit of thee of highest the highest open open circuit circuit voltage voltage of the of the lowestlowestlowest open openopen circuit circuitcircuit voltage. voltage.voltage. However, However,However, in spit inine spit spitof ethee ofof highest thethe highesthighest open openopen circuit circuitcircuit voltage voltagevoltage of the ofof thethe fuel cellfuel having cell having P(0.8) P(0.8) fuel flowfuel flowfield, field, its maximum its maximum power power density density was thewas lowest the lowest among among fuel fuelcellfuel having cellcell havinghaving P(0.8) P(0.8)P(0.8) fuel fuelflowfuel flow flowfield, field,field, its maximum itsits maximummaximum power powerpower density densitydensity was wasthewas lowest thethe lowestlowest among amongamong

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Figure3 shows the V-I curves (solid ones) and P-I curves (dashed ones) of the air- breathing membraneless fuel cells having three different flow field configurations, including the 0.8-mm-wide serpentine flow field for both fuel and electrolyte, denoted as S(0.8) × S(0.8), the 0.8-mm-wide multiple serpentine fuel flow field and 0.8-mm-wide serpentine electrolyte flow field, denoted as MS(0.8) × S(0.8), and the 0.8-mm-wide parallel fuel flow field and 0.8-mm-wide serpentine electrolyte flow field, denoted as P(0.8) × S(0.8). It can Processes 2021, 9, x FOR PEER REVIEW 11 of 20 be found in Figure3 that the air-breathing DFAMFC having P(0.8) fuel flow field reveals the highest open circuit voltage, while the fuel cell having S(0.8) fuel flow field shows the lowest open circuit voltage. However, in spite of the highest open circuit voltage of the fuelall cellbecause having of P(0.8) the significant fuel flow field, ohmic its maximumloss as shown power in density Figure was 3. In the addition, lowest among it is observed allin because Figure of3 that the significantthe DFAMFC ohmic having loss as identical shown in flow Figure field3. In for addition, both fuel it is and observed electrolyte has in Figure3 that the DFAMFC having identical flow field for both fuel and electrolyte has highest maximum power density. highest maximum power density.

FigureFigure 3. 3.The TheV- IVcurves-I curves (solid (solid ones) ones) and andP-I curves P-I curves (dashed (dashed ones) ofones) the air-breathingof the air-breathing DFAMFCs DFAMFCs havinghaving different different combinations combinations of the of liquid the liquid ﬂow ﬁelds flow (fuelfields channel (fuel channel× electrolyte × electrolyte channel). channel).

FigureFigure4a–c 4a–c show show the velocitythe velocity distribution distribution along S(0.8),along MS(0.8)S(0.8), MS(0.8) and P(0.8) and fuel P(0.8) chan- fuel channels,nels, respectively, respectively, while while Figure Figure4d–f show4d–f show the pressure the pressure distribution distribution along S(0.8), along MS(0.8) S(0.8), MS(0.8) and P(0.8) fuel channels, respectively, in the air-breathing membraneless fuel cells. It can be and P(0.8) fuel channels, respectively, in the air-breathing membraneless fuel cells. It can found that the fuel velocity in S(0.8) flow field in Figure4a is not only significantly higher thanbe found that in that both the MS(0.8) fuel andvelocity P(0.8) in flow S(0.8) fields, flow but field also morein Figure uniform 4a is along not theonly entire significantly channel,higher resultingthan that in in a both highest MS(0.8) pressure and drop P(0.8) between flow thefields, inlet but and also the more outlet uniform of fuel as along the shownentire in channel, Figure4 d.resulting Besides, in the a fuelhighest stream pressure of extremely drop between low velocity the isinlet observed and the in theoutlet of fuel parallelas shown channel in Figure of P(0.8) 4d. flow Besides, field in the Figure fuel4c. stream of extremely low velocity is observed in the parallel channel of P(0.8) flow field in Figure 4c.

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FigureFigure 4. 4.With With electrolyte electrolyte flow flow field field of of S(0.8), S(0.8), the the velocity velocity distribution distribution at at the the midplane midplane of of the the fuel fuel flowflow field field of of (a) ( S(0.8),a) S(0.8), (b) ( MS(0.8),b) MS(0.8), and and (c) P(0.8), (c) P(0.8), and and the pressure the pressure distribution distribution at the at midplane the midplane of the of fuelthe flow fuel fieldflow of field (d) S(0.8),of (d) S(0.8), (e) MS(0.8), (e) MS(0.8), and (f) and P(0.8), (f) ofP(0.8), the air-breathing of the air-breathing DFAMFCs. DFAMFCs.

FigureFigure5a–c 5a–c show show the formicthe formic acid concentrationacid concentration distribution distribution on three on different three different sections sec- withintions within the anode the catalystanode catalyst layer, while layer, Figure while5 Figured–f show 5d–f the show local the current local current distribution distribution on theon top the surfacetop surface of cathode of cathode gas diffusiongas diffusion layer, layer, of the of membranelessthe membraneless fuel fuel cells cells possessing possessing differentdifferent types types of of fuel fuel flow flow field field and and S(0.8) S(0.8) electrolyte electrolyte flow flow field field at 0.4 at V.0.4 The V. The front-most front-most sectionsection in in Figure Figure5 is 5 the is topthe surfacetop surface of the of anode the anode catalyst catalyst layer which layer contacts which thecontacts fuel flow the fuel field,flow while field, the while backmost the backmost section issection the bottom is the surface bottom of surface the anode of the catalyst anode layer catalyst which layer attaches to the gas diffusion layer. It can be seen in Figure5a that the uniformity of the which attaches to the gas diffusion layer. It can be seen in Figure 5a that the uniformity of formic acid concentration distribution on the top surface of the anode catalyst layer is the the formic acid concentration distribution on the top surface of the anode catalyst layer is best in S(0.8) fuel flow field in Figure5a, followed by MS(0.8) fuel flow field in Figure5b, the best in S(0.8) fuel flow field in Figure 5a, followed by MS(0.8) fuel flow field in Figure and is the worst in P(0.8) fuel flow field in Figure5c. 5b, and is the worst in P(0.8) fuel flow field in Figure 5c.

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Figure 5.5. With electrolyteelectrolyte flowflow field field of of S(0.8) S(0.8) at at 0.4 0.4 V, V, the the formic formic acid acid concentration concentration distribution distribution on on the plane in contact with fuel flow field, midplane, and the plane in contact with GDL (from right the plane in contact with fuel flow field, midplane, and the plane in contact with GDL (from right to left) of the anode catalyst layer of the air-breathing DFAMFCs having (a) S(0.8), (b) MS(0.8) and to left) of the anode catalyst layer of the air-breathing DFAMFCs having (a) S(0.8), (b) MS(0.8) and (c) P(0.8) fuel flow field, and the distribution of the normal component of the current density with c (respect) P(0.8) to fuel the flowcathodic field, gas and diffusion the distribution layer of ofthe the air-breathing normal component DFAMFCs of the having current (d) density S(0.8), ( withe) respectMS(0.8) to and the ( cathodicf) P(0.8) gasfuel diffusion flow field. layer of the air-breathing DFAMFCs having (d) S(0.8), (e) MS(0.8) and (f) P(0.8) fuel flow field.

Figure6 6 shows shows the theV V-I-Iand andP P-I-Icurves curves of of the the air-breathing air-breathing membraneless membraneless fuel fuel cells cells (DFAMFC) possessingpossessing various various fuel fuel and and electrolyte electrolyte flow flow field field combinations. combinations. It showsIt shows that that air-breathing DFMFC possessing possessing S(1.3) S(1.3) fluid fluid flow flow field field yields yields the the highest highest open open circuit circuit volt- voltageage among among all, all,1.0 V, 1.0 which V, which is approximately is approximately 0.1 0.1V higher V higher than than that that of ofthe the DFMFC DFMFC pos- possessingsessing S(0.8) S(0.8) fluid fluid flow flow field. field. In order In order to qu to quantitativelyantitatively indicate indicate the the measure measure of ofthe the fuel fuelcrossover, crossover, the theformic formic acid acid concentration concentration dist distributionribution along thethe centerlinecenterline of of the the contact contact plane as schematically schematically shown shown in in Figure Figure 7a7a be betweentween the the cathode cathode catalyst catalyst layer layer and and the the elec- electrolytetrolyte flow flow field field is plotted is plotted in Figure in Figure 7b. Due7b. Dueto the to lack the of lack the of polymer the polymer membrane membrane between betweentwo GDEs, two the GDEs, formic the acid formic indeed acid invades indeed the invades cathode the catalyst cathode layer, catalyst and layer, the formic and the acid formicconcentration acid concentration becomes increased becomes from increased the first from channel the first to channel the lower to the reach lower for reach each forfluid eachflow fluidfield flowcombination field combination as revealed as in revealed Figurein 7b. Figure Each7 b.peak Each of peakthose of curves those curvesin Figure in 7b Figurecorresponds7b corresponds to the boundary to the boundary of the fluid of channel. the fluid Note channel. that the Note illustrations that the illustrations above Figure above7b denote Figure the7b position denote theof the position fluid ofchannel the fluid depicted channel as depicted blue region as blue and region the rib and marked the with slashes for the three fuel and electrolyte flow field combinations along the centerline in Figure 7a. As observed in Figure 5, as the channel width of the flow field is increased,

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rib marked with slashes for the three fuel and electrolyte flow field combinations along the Processes 2021, 9, x FOR PEER REVIEW 14 of 20 centerline in Figure7a. As observed in Figure5, as the channel width of the flow field is increased,the pressure the pressure established established in the in flow the flow field field redu reducesces at at a givengiven flow flow rate, rate, resulting resulting in in less lessdriving driving force force of of the the fuelfuel crossovercrossover to to the the cathode cathode catalyst catalyst layer andlayer higher and openhigher circuit open circuit voltage.thevoltage. pressure Therefore, Therefore, established as SBSas inSBS flowthe flowflow field field was redu employed,wasces employed, at a whose given whose channelflow rate, channel width resulting is width stepwise in lessis stepwise broadeneddrivingbroadened force from fromof the 0.8 0.8 mmfuel mm tocrossover 1.3 to mm,1.3 mm,to the the formic the cathode formic acid catalyst concentration acid concentration layer and in Figurehigher in7 bopenFigure is second circuit 7b is second highest,voltage.highest, correspondingTherefore, corresponding as SBS to second toflow second field highest higheswas open employed,t open circuit circuit voltage whose voltage inchannel Figure in 6width .Figure is 6.stepwise broadened from 0.8 mm to 1.3 mm, the formic acid concentration in Figure 7b is second highest, corresponding to second highest open circuit voltage in Figure 6.

FigureFigureFigure 6.6. 6.The The V-- IIV curvescurves-I curves (solid (solid (solid ones) ones) ones) and and PandP--II curvescurves P-I curves (dashed (dashed (dashed ones) ones) of ones) of the the air-breathing of air-breathing the air-breathing DFAMFCs DFAMFCs DFAMFCs possessingpossessingpossessing differentdifferent different combinationscombinations combinations of the of fuel the andfuel electrolyteel andectrolyte electrolyte ﬂowflow ﬁeldsfields flow (fuel fields channel (fuel channel× electrolyteelectrolyte × electrolyte channel). channel).channel).

(a) (b)

FigureFigure 7.7. ((aa)) TheThe schematic schematic diagram diagram(a) of of a centerlinea centerlin (blue)e (blue) on on the the contact contact surface surface between between the the electrolyte electrolyte ﬂow(b) flow ﬁeld field plate plate and theand cathodic the cathodic catalyst catalyst layer oflayer the of air-breathing the air-breathing DFAMFCs, DFAMFCs, and (b) and the formic(b) the acid formic concentration acid concentration variation variation along the along blue line the Figureline plotted 7. (a )in. The schematic diagram of a centerline (blue) on the contact surface between the electrolyte flow field plate plotted in (a). and the cathodic catalyst layer of the air-breathing DFAMFCs, and (b) the formic acid concentration variation along the line plotted in. As the upstream channel width of SBS fluid flow field is narrower than that of S(1.3) flow field, the pressure of the fuel flow in SBS is higher than that in S(1.3), causing a fa- vorableAs condition the upstream for formic channel acid to width penetrate of SBS into fluid the anodeflow field catalyst is narrower layer. In addition than that to of S(1.3) theflow slight field, fuel the crossover pressure of the of DFAMFCthe fuel flow posse inssing SBS SBS is higher fluid flow than field, that the in air-breathing S(1.3), causing a fa- DFAMFCvorable conditionpossessing for SBS formic fluid flow acid field to penetrate generates inhighestto the peak anode power catalyst density layer. in Figure In addition to 6. the slight fuel crossover of the DFAMFC possessing SBS fluid flow field, the air-breathing DFAMFC possessing SBS fluid flow field generates highest peak power density in Figure 6.

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Processes 2021, 9, x FOR PEER REVIEW As the upstream channel width of SBS fluid flow field is narrower than that of S(1.3) 15 of 20

flow field, the pressure of the fuel flow in SBS is higher than that in S(1.3), causing a favorable condition for formic acid to penetrate into the anode catalyst layer. In addition to the slight fuel crossover of the DFAMFC possessing SBS fluid flow field, the air-breathing DFAMFCFollowing possessing the SBSoptimal fluid flowfluid field flow generates field configuration highest peak powerpresented density in inFigure Figure 6,6 .the nu- mericalFollowing simulation the optimal was further fluid flow performed field configuration for air-feeding presented DFAMFCs in Figure 6with, the SBS numer- flow field icalfor simulationboth fuel and was electrolyte further performed incorporating for air-feeding various DFAMFCs air flow fields with SBS at airflow flow field rates for of 200 bothsccm fuel and and 500 electrolyte sccm to investigate incorporating the various fuel cell air performance. flow fields at Firstly, airflow ratesboth ofV-I 200 and sccm P-I curves andof the 500 air-feeding sccm to investigate DFAMFCs the fuelwith cell various performance. air flow Firstly, fields bothwereV -plottedI and P -inI curves Figure of 8 along thewith air-feeding the V-I and DFAMFCs P-I curves with of various the air-breathing air flow fields DFAMFC were plotted for in comparison. Figure8 along It with can be ob- theservedV-I and in FigureP-I curves 8 that, of the compared air-breathing with DFAMFC the performance for comparison. of the Itair-breathing can be observed DFAMFC, inthe Figure maximum8 that, comparedpower density with the was performance enhanced ofwhatever the air-breathing air flow DFAMFC, field was the employed. maxi- The mumfairly power high pressure density was established enhanced in whatever the air airflow flow field field as was shown employed. in Figure The 9d–f fairly might high possi- pressure established in the air flow field as shown in Figure9d–f might possibly not only bly not only resist the fuel invasion to the cathode catalyst layer, but also cause the liquid resist the fuel invasion to the cathode catalyst layer, but also cause the liquid electrolyte toelectrolyte diffuse in to a more diffuse uniform in a more way withinuniform the way GDEs within because the of GDEs the counterpart because of in the pressure counterpart distributionin pressure on distribution both sides of on the both electrolyte sides of flow thefield. electrolyte Therefore, flow the field. air-feeding Therefore, DFAMFCs the air-feed- yieldeding DFAMFCs higher open yielded circuit higher voltage open and lowercircuit ohmic voltage overpotential and lower than ohmic the air-breathingoverpotential than one.the air-breathing In addition, the one. effective In addition, supply of oxygenthe effe toctive the cathodesupply ofof the oxygen DFAMFCs to the is responsi-cathode of the bleDFAMFCs for the higher is responsible maximum for current the higher density. maximu Besides,m the current slight density. effect of theBesides, airflow the rate slight ef- onfect the of performancethe airflow rate of the onDFAMFCs the performance having of pin the type DFAMFCs air flow field having can pi ben observedtype air flow in field Figurecan be8 .observed The DFAMFC in Figure having 8. The MS(0.8) DFAMFC air flow havi fieldng fed MS(0.8) at an airflowair flow rate field of fed 500 at sccm an airflow 2 yieldedrate of the500 highest sccm yielded peak power the densityhighest than peak other power cells density in Figure than8, 12 mW/cmother cells, while in Figure the 8, 12 air-breathing one produced the peak power density of 10.5 mW/cm2. mW/cm2, while the air-breathing one produced the peak power density of 10.5 mW/cm2.

FigureFigure 8. 8.Comparison Comparison of ofV- IV-Icurves curves (solid (solid ones) ones) and Pand-I curves P-I curves (dashed (dashed ones) between ones) between air-breathing air-breath- anding air-feedingand air-feeding DFAMFCs DFAMFCs possessing possessing different different air flow ai fieldsr flow with fields airflow with ratesairflow of 200 rates sccm of 200 and sccm 500and sccm. 500 sccm.

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FigureFigure 9. 9.The The velocity velocity distribution distribution at the at midplanethe midplane of the of (a )the SBS, (a ()b SBS,) Pin(0.8), (b) Pin(0.8), and (c) MS(0.8)and (c) airMS(0.8) flow air fieldflow plate, field and plate, the and pressure the pressure distribution distribution at the midplane at the midplane of the (d) SBS,of the (e )(d Pin(0.8),) SBS, (e and) Pin(0.8), (f) MS(0.8) and (f) airMS(0.8) flow field air plateflow offield the plate air-feeding of the DFAMFCsair-feeding at DFAMFCs airflow rate at of airflow 200 sccm. rate of 200 sccm.

InIn order order to to exhibit exhibit the the air air flow flow field field effect effe onct theon performancethe performance of the of air-feeding the air-feeding DFAMFCs,DFAMFCs, the the oxygen oxygen concentration concentration distribution distribution within within the cathodethe cathode catalyst catalyst layer withlayer with airair various various flow flow fields, fields, including including SBS, SBS, Pin(0.8), Pin(0.8), and and MS(0.8), MS(0.8), at 0.4 at V 0.4 with V with airflow airflow rates ofrates of 200200 sccm sccm and and 500 500 sccm sccm is plottedis plotted in Figure in Figure 10. It10. can It can be seen be seen in Figure in Figure 10 that 10 as that the as airflow the airflow raterate was was increased, increased, the the oxygen oxygen concentration concentration within within the catalystthe catalyst layer layer of each of DFAMFCeach DFAMFC becomebecome high. high. This This phenomenon phenomenon is especially is especially obvious obvious on the on planethe plane of the of catalyst the catalyst layer inlayer in contact with the electrolyte flow field of the DFAMFCs. However, even though the airflow contact with the electrolyte flow field of the DFAMFCs. However, even though the airflow rate is increased, both oxygen and electrolyte seems to maintain uniform distribution rate is increased, both oxygen and electrolyte seems to maintain uniform distribution within the entire cathode catalyst layer of the DFAMFC having Pin(0.8) air flow field, whichwithin could the beentire one ofcathode the possible catalyst reasons layer causing of the theDFAMFC slight increase having inPin(0.8) the peak air power flow field, densitywhich ofcould the DFAMFC be one of having the possible Pin(0.8) reasons air flow caus fielding as observedthe slight in increase Figure8 in. the peak power density of the DFAMFC having Pin(0.8) air flow field as observed in Figure 8.

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Figure 10. With SBSFigure as both10. With fuel SBS and as electrolyte both fuel flowand electrolyte fields at 0.4 flow V, the fields oxygen at 0.4 concentration V, the oxygen distribution concentration on dis- the plane in contact with electrolytetribution on flow the field, plane midplane, in contact and with the electrolyt plane ine contactflow field, with midplane, GDL (from and right the plane to left) in of contact the air-feeding with GDL (from right to left) of the air-feeding DFAMFCs having SBS, Pin(0.8) and MS(0.8) air DFAMFCs having SBS, Pin(0.8) and MS(0.8) air flow field (top-to-bottom) at 0.4 V with airflow rate of 200 sccm (a–c) and flow field (top-to-bottom) at 0.4 V with airflow rate of 200 sccm (a–c) and 500 sccm (d–f). 500 sccm (d–f).

Since an airSince pump an airhas pump to be hasused to to be delive usedr to the deliver specific the airflow specific rate airflow in the rate air inflow the air flow field for anfield air-feeding for an air-feeding DFAMFC, DFAMFC, the air pu themp air consumes pump consumes additional additional power. The power. power The power consumption of the air pump, Wp,air, can be estimated using the following equation, consumption of the air pump, Wp,air, can be estimated using the following equation, Δ = pQa Wp,air ∆pQa (15) WpA,Rair = (15) AR Δ where pwhere (Pa) ∆isp the(Pa) air is pressure the air pressure drop between drop betweenthe inlet theand inletoutlet and of outletthe air offlow the field, air flow field, 3 3 2 2 Qa (m /s) Qisa the(m volumetric/s) is the volumetric flow rate of flow therate air, ofand the A air,R (cm and) isA Rthe(cm electrode) is the surface electrode area. surface area. In order toIn evaluate order to evaluatethe performance the performance of the DFAMFCs of the DFAMFCs having having different different air flow air field flow de- field designs signs in termsin terms of the of the net net power power output, output, the the net net power power density outputoutput ofof the the air-feeding air-feeding DFAMFCs DFAMFCsis is shown shown in in Figure Figure 11 .11. The The net net power powe densityr density output output is definedis defined as theas the difference differ- between ence betweenthe power the power density density produced produced by the by air-feeding the air-feeding DFAMFCs DFAMFCs and the and power the power consumption of consumptionthe airof the pump air aspump follows, as follows, Wnet = Wcell − Wp,air (16) W =W −W (16) net cell p,air

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Figure 11. TheThe maximum maximum power power density density and and the therelative relative net netpower power density density of the of air-feeding the air-feeding DFAMFCs havinghaving variousvarious airair flowflow fieldsfields atat airair flowflow ratesrates ofof 200200 andand 500500 sccm.sccm.

Note that the maximum net power density produced by the air-breathing DFAMFC was 10.5 mW/cmmW/cm22 asas shown shown in in Figure Figure 88.. It cancan bebe seenseen inin FigureFigure 1111 thatthat thethe DFAMFCDFAMFC having Pin(0.8) air flowflow fieldfield produced highest net power density at bothboth airflowairflow ratesrates because of its lowest pressure drop between inletinlet and outlet of the air flowflow fieldfield thanthan thethe other two DFAMFCs havinghaving SBSSBS andand MS(0.8)MS(0.8) airair flowflow fields.fields.

4. Conclusions In this study, thethe performanceperformance of both air-breathing and air-feeding DFAMFCs were numerically investigated possessing various flowflow fieldfield designs at fixedfixed concentration andand fixedfixed volumetricvolumetric flow flow rate rate of of both both fuel fuel and and electrolyte. electrolyte. The The tested tested liquid liquid flow fieldsflow fields included in- singlecluded serpentine, single serpentine, stepwise step broadeningwise broadening serpentine, serpentine, multi-serpentine multi-serpentine and parallel and flow parallel fields, whileflow fields, the tested while air the flow tested fields air comprised flow fields single comprised serpentine, single stepwise serpentine, broadening stepwise serpentine, broad- multi-serpentineening serpentine, and multi-serpentine pin flow fields and with pin channel flow fields width with of 0.8 channel mm and width 1.3 mm. of 0.8 The mm results and of this study are listed below. 1.3 mm. The results of this study are listed below. 1. TheThe air-breathing air-breathing DFAMFC DFAMFC having identica identicall flow flow fieldfield for both fuel andand electrolyteelectrolyte yieldedyielded optimal optimal cell cell output because the similar liquid flowflow condition on bothboth sidessides ofof the the anode GDE attributed to uniform formic acid distributiondistribution within thethe anodeanode catalystcatalyst layer. layer. 2. TheThe air-breathing air-breathing DFAMFC DFAMFC having having SBS SBS flow flow field field for both fuel and electrolyte pro- 2 ducedduced a a maximum maximum power density of 10.5 mW/cm2,, while while the the air-breathing air-breathing DFAMFC DFAMFC havinghaving S(1.3) S(1.3) flow flow field field for both both fuel fuel and and electrolyte electrolyte produced an open circuit voltage ofof about about 1.0 1.0 V V owing owing to to few few formic formic acid penetration into the cathode catalyst layer. 3. TheThe simulationsimulation results results concerning concerning the air-feedingthe air-feeding DFAMFCs DFAMFCs showed showed that the DFAMFCthat the DFAMFChaving SBS having liquid SBS flow liquid field flow and field MS(0.8) and airMS(0.8) flow air field flow yielded field yielded highest highest peak power peak density of about 12 mW/cm2 at an airflow rate of 500 sccm. power density of about 12 mW/cm2 at an airflow rate of 500 sccm. 4. Considering the power generated by the DFAMFC together with the power consumed 4. Considering the power generated by the DFAMFC together with the power con- by the air pump, the simulation results suggested that the DFAMFC having Pin(0.8) sumed by the air pump, the simulation results suggested that the DFAMFC having air flow field could be the optimal design, yielding a highest maximum net power Pin(0.8) air flow field could be the optimal design, yielding a highest maximum net density of about 11.9 mW/cm2 and 11.5 mW/cm2 at air flow rates of 200 sccm and power density of about 11.9 mW/cm2 and 11.5 mW/cm2 at air flow rates of 200 sccm 500 sccm, respectively, in the study. and 500 sccm, respectively, in the study.

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Author Contributions: Software, S.-H.H.; validation, S.-H.H.; formal analysis, J.-C.S. and S.-H.H.; investigation, J.-C.S.; writing—original draft preparation, J.-C.S. and S.-H.H.; writing—review and editing, J.-C.S.; supervision, J.-C.S.; project administration, J.-C.S. Both authors have read and agreed to the published version of the manuscript. Funding: This research was funded by Ministry of Science and Technology of Taiwan, grant number MOST 108-2628-E-992-001-MY3. Data Availability Statement: Data available on request due to restrictions. Acknowledgments: The authors are indebted to Ministry of Science and Technology of Taiwan for the financial support to the study under contract of MOST 108-2628-E-992-001-MY3. Conflicts of Interest: The authors declare no conflict of interest.

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