Fuel Cells for Automotive Applications - Hydrogen Fuel Cells for Road Vehicles - page 93

The linear and slower decrease of stack potential with current shown in Fig. 3.5
can be simply explained with the Ohm's law, then the voltage losses due to this
effect are described by the following equation:

V ohm ¼ i þ i in ð Þ R in ð 3 : 32 Þ

where i is the current density and R in is the total cell internal resistance, mainly
constituted by electric resistance of cell components and resistance to ionic flow
through the electrolyte membrane. Typical values of R in are comprised in the range
0.1-0.2 X cm 2 [ 34 ].
High conductivity of electrodes, GDL and bipolar plates, and membrane thin-
ness are the obvious ways to reduce the effect of resistive losses.

3.3.1.4 Losses Due to Mass Transport Resistance

The polarization curve in Fig. 3.5 stops when the stack power is close to its
maximum nominal value (480 W at 30 A), because other sources of voltage losses
would become predominant for higher values of current, whose effect could
seriously damage the stack. These losses derive from resistance to the mass
transport of gaseous reactants toward the catalytic sites, and of products water out
of the cell. The mass transport resistance becomes predominant at high current
density, when the rate of reactant consumption is higher than its supply flow rate,
and water accumulation inside the cell is faster than its removal. The consequence
of this phenomenon is that for a particular current density value (called limiting
current, i L ), the concentration of reactants on electrode surface, and then the stack
voltage, would rapidly decrease down to zero. The voltage drop associated with
the effect of mass transport resistance can be described by applying the Nernst
equation ( 3.15 ) to the hydrogen partial pressure gradient density between gas bulk
and electrode surface at high current:

V tr ¼ RT

p b
p s

2F ln

ð 3 : 33 Þ

where V tr is the voltage change due to mass transport resistance, and p b and p s are
the hydrogen partial pressure in the bulk and at the electrode surface, respectively.
Assuming a linear diminution of hydrogen partial pressure when the current
density increases from i to i L , the variation of p s with current density results:
p s ¼ p b p b i
i L

ð 3 : 34 Þ

Equation 3.34 evidences that the hydrogen partial pressure on the electrode
surface is the same as in the bulk at zero current density, and becomes zero when
the current density reaches the limiting value i L . By combining Eqs. 3.33 and 3.34