Page 106 - Introduction to Transfer Phenomena in PEM Fuel Cells

In the term source of water, it is assumed that the produced water is in the
liquid state, and then it becomes vapor if the medium (airflow channel or O 2)
is not saturated [BAR 05]. Mass Transfer Phenomena 95
A bibliographic synthesis from [BER 91, COS 01, DJI 02, FUL 93, GUR
98, SPR 91] allows us to see how these authors have described the diffusion of
gases (binary H 2 and H 2O at the anode and ternary of O 2, N 2 and H 2O at the
cathode) in the diffusion layers (anode and cathode) using the Stefan–Maxwell
model which is a generalization of Fick’s law for two or more constituents
[SPR 91], and that takes into account the collisions between the gas molecules
[RAM 05]. This model makes it possible to express the variations in molar
concentrations (C i) of the constituents of the gas mixture as a function of their
molar flux densities (N i) with (i = 1…n), it is still defined as the gradient of the
molar fraction for each species [AMU 03, BIR 02, CUR 99]:

  N  1   
i 
∇ x =  ( i ⋅ j − x j ) i N 
x N
⋅
 j1,j i ≠  =  cD eff  

ij
 [3.23]
 N
 x = 1
i
  i1 =
where:
– N is the number of species (N = 2 for the anode and N = 3 for the
cathode);

–2
–1
– N is the molar flow density of the gas (i) in [mol.m .s ];
i
– x is the molar fraction of the gas (i), with (x i = c i/C);
i
–3
– c is the total concentration of the mixture in [mol.m ] with
( =c  n i =1 c i );

– D eff is the binary diffusion coefficient of the gaseous mixture in a
ij
–1
porous medium of species (i) in species (j), in [m² .s ].