Department of Hydrogen Energy Systems, Kyushu University1

Department of Mechanical Engineering, Kyushu University2

744 Motooka, Nishi-ku, Fukuoka 819-0395, JAPAN

Hironori NAKAJIMA1, 2

Shintaro IWASAKI1

Tatsumi KITAHARA1, 2

I01A-1033:

Mass Transfer in Microporous Layers for

Polymer Electrolyte Fuel Cells Analyzed

with Pore Network Modeling240th ECS Meeting (October 10-14, 2021)

2

H2 2H+ + 2e-

1/2O2 + 2H+ + 2e- H2O

Concentration overpotential

by oxygen transport

limitation (voltage drop)

Flooding by excess liquid

product water

Water management by the

gas diffusion layer

(microporous layer)

Background

Polymer Electrolyte Fuel Cells

3Background

50 μm

Substrate

MPL

60

μm

16

0 μm

Microporous Layer (MPL)

MPL has been known to improve

water management characteristics by

mitigating flooding and dehydration.*

Optimized MPL structure and wettabilityVapor-liquid two phase transport model verified by experiment

Gas diffusion layer coated with MPL

5 μm

T. Kitahara, T. Konomi, and H. Nakajima, J. Power Sources, 195, 2202-2211

(2010).

*Z. Qi, A. Kaufman, J. Power Sources 109 (2002) 38-46

Background

4

Pore Network Model (PNM)*

Modeling porous media by pores and throats.

Transport is modeled by convection and diffusion.

Pore diameter distribution by cross-sectional

observation of the MPL (FIB-SEM)

Vapor-liquid two phase transport in the MPL

*Gostick, J. T., Ioannidis, M. A., Fowler, M. W., Pritzker, M. D. J. Power Sources, 173(1), 277-290 (2007).

Construction of PNM of hydrophobic MPL(4)

⑥Pore diameter distribution

(Weibull distribution)

⑤Fitting

Validation

k = 𝑄

𝐴∆𝑃

R = ℎ

𝐷

d = 𝑅dry

𝑅wet

①Preparation of GDL with in-house hydrophobic MPL

(FIB scanning electron microscope)

Flow of research

④PNM3D-Porous Structure Analysis

FIB-SEM②FIB-SEM

(4) D. CHEN, K. HARANO, Y. MONDE, H. NAKAJIMA, T. KITAHARA, K. ITO, The Proceedings of the National

Symposium on Power and Energy Systems, C114, The Japan Society of Mechanical Engineers (2018)

Permeance : k

Oxygen diffusion resistance : R

③Mass transfer

measurements

Relative oxygen diffusion resistance : d

5

①Preparation of GDL with hydrophobic MPL

6

2. Apply to a GDL substrate1. Slurry production

Drying : 130℃ 5 min

Firing : 350℃ 30 min

3. Drying and firing of GDL

①Pore structure changes with distilled water amount added

(Control of pore diameter distribution)

②Adjust MPL thickness by the number of applications

Carbon black 14-15 wt%

PTFE 4-5 wt%

Distilled water 80-82 wt%

Surfactant 1 wt%

Carbon black (80 wt%)

PTFE (20 wt%)

Stir：2000 rpm 60 min Number of applications

：2 - 4 times

Coating thickness

：10 - 20 μm

Slurry Doctor-blade coating Drying and firing

In-house MPL

6

Maximum pore size measurement with wetting liquid

d

cos

PPP

θd

4cos4

max 0

( γ = 0.015 (N/m) )

Galwick(5)：Non-volatile wetting

liquid with contact

angle of θ ≈ 0°

(5) Galwick: Porous Materials Inc.

Wetting liquid

Measurement of bubble point pressure

Sample A Sample B Sample C

dmax(µm) 2 5 15

CB (wt%) 80 80 80

PTFE (wt%) 20 20 20

MPL thickness (µm) 60 60 60

Substrate thickness (µm)

(Toray, TGP-H-030)100 100 100

Table1. Specifications of the MPL samples

60

μm

5 μm

50 μm

In-house MPL

Illustration of GDL1

60

μm

①Preparation of GDL with hydrophobic MPL

Wetting liquid

impregnated under

vacuum beforhand

7

②FIB-SEM

(6) Amira 6.3: Thermo Fisher Scientific Inc.

(7) D. CHEN, K. HARANO, Y. MONDE, H. NAKAJIMA, T. KITAHARA, K. ITO, The Proceedings of the National Symposium

on Power and Energy Systems, C114, The Japan Society of Mechanical Engineers (2018)

Cross-sectional observation with FIB-SEM (FIB scanning electron microscope)

0

200

400

600

800

1000

0 1 2 3 4 5F

requ

en

cy

Pore diameter(µm)

sample B(max 5)

Approximate with Weibull distribution

and use for PNM

FIB-SEM cross-section

observationBinarization of cross-

sectional imagesAnalyzing 3D structure

Pore diameter distribution by watershed analysis

method

Amira

Watershed

Flow of porous Structure Analysis

8

𝑘 =𝑄

𝐴 × ∆𝑃

k : Air permeance (µm/(Pa･s))

Q: Flow rate (cm3/s)

A : Air permeable area (=19.6 cm2)

ΔP : Gauge Pressure (=1.23 kPa)

1. Air permeation measurement

2. Oxygen diffusion measurement

Permeance

A

CQJ 44

)(

)(ln

)()(

43

21

4321

CC

CC

CCCCC

J

CR

Oxygen diffusion resistance

J: Oxygen flux

𝐶: Oxygen concentration

R: Oxygen diffusion

resistance (s/m)

③Mass transfer measurements

Schematic of the air permeability measurement

Experimental apparatus of oxygen diffusivity

9

10

Oxygen diffusivity measurementAnalysis of the concentration boundary layer

Air

N2

Sample

Multilayered GDL measurements for

diffusion resistance of the concentration boundary layer

(In analogy with temperature boundary layer)

Boundary layer

③Mass transfer measurements

11

Diffusion resistance of the concentration boundary layer

RTorayH030= 16.9𝑛 + 26.5

R = 𝑅Subn + 𝑅BL

RBL = 26.5 s/m (intercept)

RBL

RBL：R of boundary layer

RSub

①Air: 2.8 m/s

N2: 2.8 m/s

② ③Air

N2

Air

N2

43.4

60.377.2

R = 16.9n + 26.5

0

10

20

30

40

1 2 3

R (

s/m

)

Numbers of Substrate

R of Toray H030

RBL

③Mass transfer measurements

12

Diffusion resistance of the microporous layer

Substrate(TGP-H-030)

MPL

60

µm

16

0µ

m

Substrate(TGP-H-030)1

00

µm MPL

60

µm

Boundary layer

RMPL = 14.8 s/mMPL:

dmax = 5 µm

Porosity = 0.37

RMPL = RGDL - Rsub

③Mass transfer measurements

(5) Galwick：Porous Materials Inc.

Galwick (5) ： Non-volatile wetting liquid with a contact angle of θ ≈ 0 °Penetrating into both hydrophilic and hydrophobic pores

① Install GDL impregnated

with the wetting liquid into

the apparatus

② Discharge the wetting

liquid with increasing air

pressure

③ Gas chromatography

analysis under

atmospheric pressure.

𝑑 =𝑅dry

𝑅wet

Liquid saturation

with pressure

control

(intrusion volume

fraction)

Schematic of oxygen diffusivity test with GDL impregnated with the wetting liquid

Fig.5 Wetting liquid

3. Relative oxygen diffusion resistance with wetting liquid

③Mass transfer measurements

13

14

O2 diffusion resistance under wet condition

𝑃in >4𝛾cos𝜃

𝑑𝑃in <

4𝛾cos𝜃

𝑑

MPL saturated with the wetting liquid

Pressure difference, Pin

The wetting liquid is discharged to a

saturation level depending on Pin

and capillary pressure of each throat

Vacant throats (gas pathway)

Pin

Wetting liquid

(Galwick)

θ ≈ 0°

③Mass transfer measurements

15

O2 diffusion resistance under wet condition

Larger pressure gives larger r - Wetting liquid is discharged

(Smaller liquid saturation, larger effective O2 diffusivity)

PNM reproduces the tendency of the effective O2 diffusivity

Comparison of 𝑟 =𝑅dry

𝑅wet(0 ≤ r ≤ 1) between the PNM and experiment

Sample B (dmax = 5 µm)

Results and discussion

16

Comparison with the Leverett function

PNM appears to be more reliable for the MPL

analysis than the Leverett approach proposed for fluid flow

through packed soil beds

Sample B (dmax = 5 µm)

Leverett function : Pc = γ cosθ𝜀

𝑘

0.5J(sl)

Results and discussion

17

Air and liquid water relative permeability

Empirical fits for the relative permeabilities exhibit high-order power-law

dependence, indicating a wide pore diameter distribution

Asymmetric behavior of the permeability of liquid water and air suggests a

difference in their percolation structures in the pore network.

Sample B (dmax = 5 µm)

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0

Re

lative

pe

rme

ab

ility

Liquid water saturation

Water

Air

kr,water=s^2.5

kr,air=(1-s)^9

Results and discussion

18

Air permeability and oxygen diffusion resistances for the dry and wet

conditions of the MPL agree well between the PNM and experiment.

PNM is validated and useful to model oxygen and water transports in MPLs

with employing wettability (contact angle) of water in the pores.

Numerical models with the PNM for optimized designs of MPLs are feasible.

Conclusion