Mench M.M. Fuel Cell Engines

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370 Polymer Electrolyte Fuel Cells

can be tailored by engineering the wettability and pore size distributions of the catalyst

layers, microporous layers, and DM on the cathode and anode. This approach of capillary

pressure management is also used on the DMFC to control water and methanol crossover.

The water ﬂux caused by a temperature gradient and heat ﬂux can be exploited during

shutdown to help purge the fuel cell.

The overall roles of the various fuel cell components in controlling the liquid- and

gas-phase water balance inside the fuel cell were discussed. In particular, the MPL, a thin,

highly hydrophobic layer between the DM and catalyst layer, is critical in the overall water

management. At the cathode, a MPL helps to push liquid water in the hydrophilic pores of

the catalyst layer back toward the anode. The MPL also acts as a barrier to prevent liquid

water ﬂow from the DM into the catalyst layer and provides a low saturation condition to

permit ﬂow of oxygen to the catalyst layer. At the anode, the MPL acts to restrict water vapor

transport away from the catalyst layer and reduce dryout, since water vapor diffusivity into

hydrogen is around four times higher than into air. Hydrogen access to the catalyst layer is

typically not limiting, and the additional restriction from the MPL is not critical. Although

an understanding of capillary ﬂow is important, condensation, evaporation, interfacial and

morphological factors also play important roles in ﬂooding, and need to be considered in

any comprehensive approach.

For DAFCs using a liquid feed, like the DMFC, the water balance and fuel crossover

problem are more acute than the hydrogen fuel cell. Dilute liquid solutions, thicker mem-

branes, and capillary pressure management are used to control these two issues. As a result

of the high methanol and water crossover in the DMFC, the open-circuit potential is very

low, and performance is also low compared to the H

PEFC. However, the use of diffusion

barriers in the anode and capillary pressure management eliminates the need for highly

dilute methanol solutions, and these systems may ultimately be more appropriate than their

PEFC counterparts for portable applications.

Various ﬂow ﬁeld designs and conﬁgurations have been designed and used in PEFCs.

There is no “optimal design,” and there are advantages and drawbacks of all different

design solutions. Most ﬂow designs are a mixed parallel–serpentine design, made to balance

pressure drop and slug holdup considerations. Unintentional crossover should be avoided in

the design stage. This bypass phenomenon occurs when ﬂow from one channel short circuits

underneath the land and into an adjoining channel because the pressure drop to continue

along the ﬂow path is similar or greater than the pressure drop to bypass the channel. Any

PEFC channel design needs to consider ﬂooding management, channel drainage by gravity,

humidity loss versus reactant availability and electrical contact.

Although beginning-of-life (BOL) performance is important, fuel durability and time-

dependent performance are just as critical. The lifetime of a fuel cell is expected to compete

with existing power systems it would replace. The automotive fuel cell must withstand load

cycling and freeze–thaw environmental swings with minimal degradation (3–5%) over a

lifetime of at least 5000 h. A stationary fuel cell must withstand over 40,000 h of steady

operation with minimal downtime. There are many phenomena that can result in gradual

degradation and performance loss in PEFC systems. These include assorted chemical and

mechanical degradation modes [81]. Many different modes of physicochemical degradation

are known to exist that can generally be grouped into categories of reversible and irreversible

physical and chemical damage. Almost every component in PEFC systems is susceptible to

lifetime degradation. In general, degradation is accelerated by operation at high-temperature

c06 JWPR067-Mench January 26, 2008 20:1 Char Count=

Problems 371

or low-humidity conditions, aggressive load cycling from low to high cell voltages, and

large temperature swings in the environment.

The ﬁnal section of the chapter dealt with multidimensional effects. While this topic

is sufﬁciently detailed that an entire book could be written about it, the goal here was to

reinforce the reality that almost nothing inside the PEFC is isotropic, and strong gradients

in species, temperature, and current commonly exist under normal operating conditions.

Under low-humidity environments, the anode moisture proﬁle tends to control the current

distribution proﬁle, since anode dryout is limiting performance. Under higher humidity and

ﬂooding conditions, however, the cathode oxygen content and ﬂooding condition controls

the current distribution. Gradients is nearly every parameter are normal in PEFC operation,

and many can be exploited to improve operating performance.

APPLICATION STUDY: DIRECT LIQUID FUEL CELL FOR

PORTABLE APPLICATIONS

Perhaps the ﬁrst real commercial PEFC system to reach mass production will be the portable

DMFC. Ultimately, the DMFC system must replace some existing power source. Take the

laptop computer system as an example for comparison purposes:

1. Find the expected time of operation, power density, and weight of a typical existing

battery system.

2. Using 0.1 W/cm

active area as a design point and a best estimate to account for

ﬂow manifolding (assume 15% of the total volume) estimate the volume of a DMFC

stack to provide equivalent power of the battery.

3. Estimate the methanol solution reservoir volume needed to compete with the existing

battery system assuming (a) a diluted 2 M methanol solution or (b) a neat methanol

solution feeds the anode.

4. What power density must the DMFC achieve to be able to compete favorably with

a modern battery?

5. Discuss the trade-offs (in as much engineering detail as possible) between the use

of stored hydrogen and methanol for this application.

6. How would you propose to maintain a thermal balance of the stack?

PROBLEMS

6.1 Determine the change in the mass transfer limiting

current density for the cathode of a PEFC between an un-

compressed and a 20% compressed DM. The fuel cell is

operating at 80

◦

C on fully humidiﬁed cathode air ﬂow at

1 atm pressure. The uncompressed DM is 300 µmthick

with a porosity of 70%. Assume there is no ﬂooding on the

catalyst layer or in the DM.

6.2 Discuss the various methods of ﬂow humidiﬁcation and

identify the strengths and weaknesses of each approach.

6.3 Do some reading and ﬁnd out how the relative humidity

of a ﬂow of gas can be measured in a fuel cell. Is there a

robust, inexpensive sensor that is readily available?

6.4 Calculate the net rate of water vapor uptake into an

air cathode ﬂow at the given conditions (see the table on

page 372) for a 250-cm

fuel cell operating at 1.2 A/cm

Compare the cathode uptake to the water generation. What

drying rate would the anode have to share to obtain a steady-

state global balance?

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372 Polymer Electrolyte Fuel Cells

Cathode Condition Inlet Outlet

RH 0.5 1.0

Temperature 80

◦

C80

◦

Pressure 3.2 atm 2.7 atm

Stoichiometry 2.0 —

6.5 Derive Eq. (6.16), assuming a transient buildup or dry-

out of water can occur.

6.6 For the fuel cell in problem 6.4, determine the inlet

relative humidity that would achieve a global balance, as-

suming all uptake occurs in the cathode and there are no

water slugs at this balanced condition.

6.7 For the fuel cell in problem 6.4, determine the exit tem-

perature that would achieve a global balance, assuming all

uptake occurs in the cathode and there are no water slugs

at this balanced condition. If the exit temperature is not

changed, what is the total volume of liquid water that must

exit a 100-fuel-cell stack in 1 h to maintain a balance at

these conditions?

6.8 Calculate the net rate of water vapor uptake into an air

cathode ﬂow at the given conditions for a 320 cm

fuel cell

that is operating at 1.0 A/cm

. If the net transport coefﬁcient

of water from the anode to the cathode is -0.2, calculate the

net rate of water storage in the fuel cell at this condition.

What would happen over time to the fuel cell performance

and operating parameters in the accompanying table?

Cathode/Anode Condition Inlet Outlet

RH 0.5/1.0 1.0/1.0

Temperature 80

◦

C80

◦

Pressure 3.2/3.2 atm 2.6/2.8 atm

Stoichiometry 2.0/1.5 —

6.9 For the fuel cell in problem 6.8, what exit temperature

of the fuel cell would be needed to achieve a water balance

in this condition, assuming all other parameters remain the

same?

6.10 For the fuel cell in problem 6.8, what inlet RH of the

fuel cell would be needed to achieve a water balance in this

condition, assuming all other parameters remain the same?

6.11 For a 100-cm

fuel cell at 1 A/cm

operation, with a

net drag coefﬁcient of 0.1, and the other conditions shown

in the accompanying table, solve for the cathode ﬂow rate

that must be used to achieve a water balance with no liquid

water ejection from the fuel cell

Cathode/Anode Condition Inlet Outlet

RH 0.5/1.0 1.0/1.0

Temperature 65

◦

C70

◦

Pressure 1.2/1.1 atm 1/1 atm

Stoichiometry 2.5/1.2 —

6.12 For the fuel cell in problem 6.11 and the conditions

shown in the table for problem 6.11, solve for the cath-

ode exit temperature that must be used to achieve a water

balance with no liquid water ejection from the fuel cell.

What would happen to the net drag coefﬁcient if the anode

humidity at the inlet were reduced?

6.13 The problem of unintentional crossover, or the by-

pass phenomenon, can be reduced in several ways. A few

ways we can design a ﬂow channel with reduced crossover

to an adjacent channel include increased compression, de-

creased DM porosity, and increased land width. Discuss the

trade-offs associated with these approaches.

6.14 For a net drag coefﬁcient of 4.0, no hydraulic perme-

ation effects, and an electro-osmotic drag coefﬁcient of 3.0,

calculate the water crossover and equivalent power lost per

day for a 10 M methanol solution at idle in the anode of a

10-cell, 10-cm

/cell DMFC stack.

6.15 Determine the ideal net water transfer coefﬁcient for

a hydrogen fuel cell so that external humidiﬁcation is not

needed. How would you design the electrode and diffusion

media structure to achieve this goal?

6.16 Determine the global anode oxidation and cath-

ode reduction reactions for trioxane, formaldehyde, and

ethanol.

6.17 Would the best possible diffusion media used in the

anode of the DMFC be hydrophobic or hydrophilic? Why?

6.18 Consider a typical DMFC operating system. On the

anode side, a 2 M solution of methanol (2 mol of methanol

per liter of solution) is circulated into the anode and then

pumped back into the fuel tank. Some of the methanol in the

solution is being consumed at the anode, and ∼100 mA/cm

equivalent is being consumed at the cathode via crossover.

The water generated at the cathode or transported to the

cathode by drag/diffusion is condensed and pumped back

into the anode tank, along with all efﬂuent from the anode.

Write a symbolic expression to solve for the required mass

ﬂow rate of pure methanol back into the anode mix to main-

tain molarity of the mixture as constant. (Hint: the water

produced at the cathode is being added to the mixture, and

some of the methanol is being consumed, so the mixture

c06 JWPR067-Mench January 26, 2008 20:1 Char Count=

Problems 373

will become more diluted with time unless a stream of pure

methanol is added to balance the mass loss.)

Anode

Cathode

Water, methanol in

= ?

Dry air in

Water, methanol out

Moist air out

Condenser and pump

All water in + generated + left over methanol back to anode

Dry air to ambient

Pure

MEOH

6.19 For an isothermal neat hydrogen fuel cell at moderate

current density with adequate cathode ﬂow stoichiometry,

sketch the current distribution from inlet to exit for the

following cases:

Ĺ 50% RH inlet anode, 50% RH inlet cathode, con-

current ﬂow

Ĺ 50% RH inlet cathode, 50% RH inlet anode, con-

current ﬂow

6.20 Determine the relationship between the required water

at the anode (water stoichiometry) and the fuel stoichiom-

etry for a dimethyl ether (DME) fuel cell in symbols. What

are the consequences on performance of so much water re-

quired at the anode inlet? What can be done to engineer this

situation?

6.21 Assume a 100-cm

fuel cell anode exit at 100% RH,

= 1.5 at 1 A/cm

and a cathode exit of 80%, λ

= 2.5 at

1 A/cm

, 363 K, 1 atm back pressure throughout. What is

the total combined relative humidity of the exit ﬂow? That

is, if the anode and cathode exit ﬂow were mixed, what

is the resulting RH? This concept of total humidity can

be useful when evaluating the expected performance and

ﬂooding criteria. That is, if total RH > 100%, then some

liquid buildup and slug ejection will occur.

6.22 Calculate the percent change in effective diffusivity

for a gas ﬂowing through an uncompressed DM and a DM

compressed to 10 and 20% strain, assuming the tortuosity

remains the same.

6.23 What is the effect of reactant dilution on water vapor

uptake? That is, will a 50% mixture of hydrogen and nitro-

gen at the anode pick up more, less, or the same moisture

as a pure hydrogen feed?

6.24 Compare hydraulic permeability to drag and diffu-

sion. Under what cases would each mode dominate water

transport?

6.25 For a direct methanol anode reaction, 1 mol of water

is reacted per mole of methanol. Determine the molarity

of a 1 : 1 molar ratio DMFC solution. This is the desired

design molarity of the solution at the anode electrode.

Open-Ended Problem

6.26 Can you think of a way to actually monitor the so-

lution molarity? That is, is there a way to make some sort

of gauge to measure the molarity of a methanol solution?

How would you do this in practice? (Hint: There are several

ways to achieve this, think of what property variation there

would be between different molarity solutions.)

Computer Problems

6.27 Program the gas-phase water balance for a H

PEFC

in Excel or other computer language or workbook soft-

ware you are comfortable with. Assume the net drag to the

cathode is zero (i.e., electro-osmotic drag = diffusion and

hydraulic drag is zero). Is this cell ﬂooding or drying? Hint:

This zero-net drag assumption is generally valid (globally,

at least) for thin membranes and means that all water gen-

erated must be removed by the cathode ﬂow, that is, you

can ignore the anode here. Complete the following:

(a) Calculate the mass ﬂow rate of water into an air

cathode at RH = 50%, 80

◦

C, 3.2 atm pressure,

and stoichiometry of 2.6 at 1 A/cm

for a 100-cm

cell. Check your computed solution with a hand

calculation.

(b) Calculate the mass ﬂow rate of water out of the

same air cathode at RH = 100%, 80

◦

C, 3.1 atm

exit pressure. Check your computed solution with

a hand calculation.

the heat generated by the cell to tailor the cooling

channels and provide a desired outlet temperature.

Calculate the exit temperature of the cathode re-

quired to balance the water with this cell, assuming

the exit RH is 1.

(d) Another way to balance the water in the cell is to

tailor the exit pressure of the cell. Calculate the exit

pressure required to balance the water with this

cell, assuming the exit RH is 1. If this is not pos-

sible with the given cathode stoichiometry, what

cathode stoichiometry will get the job done?

(e) Another way to balance the water is to tailor

the inlet RH. Calculate the inlet RH required to

balance the water with this cell, assuming the exit

RH is 1. If this is not possible with the given

c06 JWPR067-Mench January 26, 2008 20:1 Char Count=

374 Polymer Electrolyte Fuel Cells

cathode stoichiometry, what cathode stoichiome-

try will get the job done?

6.28 Expand your program in problem 6.27 to include a net

drag coefﬁcient and the effects of anode ﬂow. For the same

cathode conditions as problem 6.27, (a) and (b), determine

the anode/cathode (assume they are the same) exit temper-

ature needed to balance the water generated. The ﬂow of

humidiﬁed hydrogen into the anode is at RH =100%, 80

◦

3.2 atm pressure, and stoichiometry 1.5 at 1 A/cm

for a

100-cm

cell. The anode ﬂow leaves at 3.1 atm and 100%

RH at the chosen exit temperature. Plot the required exit

temperature as a function of net drag coefﬁcient.

6.29 Apply the program developed in problem 6.27 to a

direct methanol fuel cell. There will be no uptake by the

anode, and the cathode must remove all water to prevent

ﬂooding. The ﬂow of a 5 M methanol solution into the an-

ode is at 60

◦

C, 1 atm pressure, and stoichiometry 1.5 at

0.2 A/cm

for a 100-cm

cell. The anode ﬂow leaves at 1

atm. The cathode ﬂow enters at 0% RH and leaves at 100%

RH.

(a) Plot the required cathode ﬂow rate at 60

◦

Ctoavoid

slug formation in the cathode for a net drag coef-

ﬁcient of 3.0.

(b) Plot the required cathode ﬂow rate at 80

◦

Ctoavoid

slug formation in the cathode for a net drag coef-

ﬁcient of 3.0.

◦

Ctoavoid

slug formation in the cathode as a function of net

drag coefﬁcient.

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