Page 132 - Introduction to Transfer Phenomena in PEM Fuel Cells

generally evaluated experimentally. These coefficients, difficult to evaluate,
largely determine the transport of water in the membrane.
3.6.5. Parametric laws Mass Transfer Phenomena 121
3.6.5.1. Water content

The diffusion coefficient of water in the membrane ( D m ) strongly
H 2 O
depends on the local water content, which is defined as the ratio between the
number of water molecules and the number of sulfonic sites (SO 3) available
in the polymer. The following descriptions involve the water content of the
membrane (λ). This variable represents the number of water molecules per
active site (SO 3):

n
λ= HO [3.80]
2
n −
SO 3
In addition, electroneutrality imposes an equal number of positive
charges (protons) and negative charges (active sites). The ratio of water
molecules to active sites then reflects the potential number of water
molecules in the vicinity of each proton. The water content can also be
1
defined according to the equivalent mass (EW) in (g mol SO 3), the density of
–3
the dry membrane ( dry) expressed in (g.m ), and the water concentration in
the membrane ( c ):
H 2 O
EW
λ= c ⋅ [3.81]
ρ dry HO
2

In practice, the value of (λ) varies between 2 and 22.

In this relation, we neglect the variation of volume related to the variation
of concentration in water. The variable (λ) is commonly used in the literature
because it makes it possible to determine the hydration state of the
membrane with respect to a controlled parameter, the number of active sites.
The water content can also be expressed using the coefficient of water
activity as follows: