Page 100 - Introduction to Transfer Phenomena in PEM Fuel Cells

Mass Transfer Phenomena 89
By convention, flows are positive when they move from the anode to the
cathode; the location of the wells (and sources) of matter imposes the
densities of flows of matter that are written as follows:
– at the anode:
j
N = [3.8]
H
2 2F
– in the membrane:
N + = j [3.9]
H F

– at the cathode:

j
N O 2 =− 4F ; N N 2 = 0 [3.10]

It should be noted that the flow of nitrogen is considered zero because it
is not involved in the reactions, and it is also assumed that the membrane is
impervious to this gas.

In addition, the continuous flow of water at the interfaces
(membrane/diffusion layers) must be taken into account:
– at the anode (in x = L d), we have:

N m = N a [3.11]
HO HO
2
2
– at the cathode (in x = L d + L m), we have:

N c = N m + N Pr od [3.12]
H O HO HO
2
2
2
m
The water flow density (N H 2 O) is mainly imposed by the transfer
mechanisms in the membrane, whereas the other densities of material flow
are known as a function of the current density [RAM 05].