Permeability of Catalyst Layers 55

3.4.1 Principle of Permeability Measurement

The gas permeability of the porous electrode is determined by using Darcy’s law. It should be noted that Darcy’s law is valid only for a slow flow, while a modified version of Darcy’s law (i.e., Forchheimer Equation) must be considered for high-

N2 N2 O2 N2 O2 Sample Sample N2 O2 (c) Experimental Process (a) Calibration Process (b) Purge & fill Process

velocity flows with high Reynolds numbers greater than 1-100 [5,105]. This is because the inertial effect becomes significant [93,106]. However, the pore Reynolds number for air in the PEM fuel cell electrodes is in the order of 10-4 [107], and it is also true in the current experimental setup. The small pore Reynold number indicates that the inertial effect is negligible and Darcy’s law is valid for this study.

The general form of Darcy’s law is,

𝑢 𝐾

𝜇∇𝑝 (3.33)

where u is the superficial velocity in mꞏs-1, K is the permeability in m2, μ is the gas viscosity in Paꞏs, and p is the pressure in Pa.

The superficial velocity is defined as follows:

𝑢 𝑄

𝐴

𝑚𝑅u𝑇

𝐴𝑀𝑝 (3.34)

where Q is the volumetric flow rate in m3_ꞏs-1_{, ṁ is the mass flow rate in kgꞏs}-1_{, R} u is

the universal gas constant in Jꞏkmol-1ꞏK-1, T is the temperature in K, A is the cross- sectional area of the samples in m2, and M is the molecular weight of the gas in in kgꞏkmol-1.

By substituting Eq. (3.34) into Eq. (3.33) and then integrating Eq. (3.33) from the inlet pressure, pin, in Pa to the outlet pressure, pout, in Pa across the thickness, δ, in

m of the test porous sample, Darcy’s law yields [20,107]:

𝐾 2𝜇𝛿𝑅𝑇𝑚

𝐴𝑀 𝑝_in 𝑝_out (3.35)

The permeability tests are repeated five times under each condition, and the standard deviation is typically within 1-2% for the GDLs with and without the CLs, and still within 5% for the worst case when the CL permeability is determined.

3.4.2 Experimental Setup

Fig. 21 shows the experimental setup used to measure the permeability of the electrode. The electrode samples are placed between two gas chambers. The interior length and diameter of the two chambers are 42.5 cm and 3.8 cm, respectively. The cross-sectional area of the tested samples is 11.3 cm2. The nitrogen and oxygen gases with a purity level of 99.99% and the dried air are used as the test gas, respectively; and they are supplied by gas tanks separately. These gases are introduced into the top chamber through valve #1, forced to pass through the samples, and expelled to the

ambient atmosphere through valve #2. Two pressure sensors and thermocouples are installed in both chambers to measure the pressure and temperature of the gases, respectively. The flow meter is employed at the inlet in order to control the mass flow rates of the supplied gases.

In this study, the temperature at which the permeability is measured is controlled by a water loop as shown in Fig. 21. A thermal bath (Thermo Fisher Scientific) is used to maintain the desired temperature with an accuracy of 0.2 oC. Thermocouples located in both chambers in order to ensure the temperature uniformity throughout during the test periods. In order to simulate the PEM fuel cell environment, the measurements are conducted over a range of temperatures (25, 37.5, 50, 62.5, and 75 o_C).

Fig. 21. Experimental setup for the gas permeability measurement. Air, oxygen, and nitrogen are used as the test gas, respectively, in the present study.

3.4.3 Experimental Procedures

A leak-check is performed before each experiment, and the experiment is conducted under predetermined operating conditions. The measurement procedure for each sample can be generalized into the following steps:

1. The temperature of both chambers is set to the desired value, e.g., 25 oC. 2. The inlet valve is open and the entire chambers are filled with the gas, e.g., air. 3. The filling process lasts for more than 3 minutes with a flow rate of 500 SCCM.

4. After the flow is stabilized, the pressure and temperature of both the top and bottom chambers are recorded.

5. Change the flow rate to 400, 300, 200, and 100 SCCM, and repeat step 4 for each flow rate.

6. Change the gas species, e.g., oxygen and nitrogen, and repeat step 2-5.

7. Change the temperature to 37.5, 50, 62.5, and 75 oC respectively, and repeat step 1- 6 for each temperature.

The experimental procedure is continued with either the uncatalyzed GDL or the catalyzed GDLs (nine samples in total) being placed in the middle of the two connected chambers. Since in the PEM fuel cells, the mass transport of air or oxygen in the cathode is much slower than that of hydrogen in the anode, and cathode process is far more important in affecting the PEM fuel cell performance, only the permeability for air, oxygen, and nitrogen are measured in this study.

3.3.4 Uncertainty Analysis

The permeability, K, is a multiple-variable function. The uncertainty in a multi- variable function K = func(x1, x2, … xN) due to uncertainties in variables x1, x2, …, xN

are evaluated by the root sum square product of the individual uncertainties computed to the first-order accuracy as [107]:

𝑈 𝜕𝐾

𝜕𝑥 𝑈 (3.36)

where the partial derivative represents the sensitivity of K to the ith variable xi. xi

represents the temperature, pressure, thickness, cross-sectional area, viscosity, and mass flow rate as indicated in Eq. (3.35). The uncertainties in independent variables are obtained either from the manufacturer’s specifications for the instrument or from the measurement taken in the laboratory. In order to ensure the repeatability, each test is repeated three times on separate days.

It should be pointed out that for ultra-thin CLs (much thinner than 10 μm), the permeability measurement should be carefully improved for the reduction of measurement uncertainty. A high accuracy pressure sensor and a large-range flow rate controller can be employed for the experiment improvement.