Page 129 - Introduction to Transfer Phenomena in PEM Fuel Cells

118 Introduction to Transfer Phenomena in PEM Fuel Cells
This formalism has also been taken up more recently by Janssen
[JAN 01] as well as Weber and Newman [WEB 04b]. However, Meyers
[MEY 98] remarks that it is not possible in this case to characterize the
transport in a membrane with a pressure gradient at its boundaries. In
general, the membrane can thus be assimilated to an electrolytic solution,
where the transport of water is governed by two contributions:
– a diffusive Fick’s flow generated by the water concentration gradients
in the membrane. This flow can be indifferently directed from the anode to
the cathode or vice versa depending on the humidification conditions of the
membrane;
– an electro-osmotic flow describes the procession of water molecules
carried by each proton when crossing the membrane. This flow, proportional
to the proton flow (i/F), is always directed from the anode to the cathode.

According to Okada, the transport by electro-osmosis is the result of two
simultaneous effects [OKA 98]:
+
– an electrostatic effect ensuring the solvation of the protons (H 2O) nH in
+
hydronium (H 3O );
– a volume effect due to the size of the solvated molecules that will push
the water molecules.

In the theory of dilute solutions, the transport of species results from
migration, diffusion and convection phenomena. The flow of the species (i)
is given by [BOU 07]:

D
N =− ⋅ i ⋅ F c ⋅∇ϕ − D c + ν [3.73]
∇
⋅
z
c
i
i
i
i
i
i
RT
where:
– z is the valency (electroneutrality) of species (i);
i
– v is the velocity of the solvent.
In this case, the solvent corresponds to the single phase of the membrane
and therefore (v = 0); convective transport is canceled out (unlike the
hydraulic model).