Page 107 - Introduction to Transfer Phenomena in PEM Fuel Cells

96 Introduction to Transfer Phenomena in PEM Fuel Cells
From the ideal gas law, the total pressure is related to the concentration of
the mixture:
=⋅
⋅
pc R T [3.24]
Due to the porous structure of the electrodes, the binary diffusivity
calculation needs to be corrected by the porosity (ε ) of the medium
s
[BER 92]:
D eff = D ⋅ε τ s [3.25]
ij
ij
eff
The effective diffusion coefficient (D ij ), which is generally weaker than
the intrinsic diffusion coefficient in an exclusively fluid phase (D ij), is not only
a function of the porosity (ε s) of the medium, but also a function of the
tortuosity given by the Bruggeman correlation (τ=1.5) [AMA 03]. The porous
and tortuous structure is responsible for lengthening the particle path and
causes a decrease in the diffusion coefficient [BER 92]. It should also be noted
that the diffusion coefficients of gases (i) and (j) are linked by a reciprocal
relationship, here known as the Onsager reciprocal relation [MAZ 03]:

D eff = D eff [3.26]
ij
ji
The transport of species in the diffusion layers (GDL) includes the
Stefan–Maxwell binary diffusion and convection by Curtis and Bird
[CUR 99]. It is expressed as a mass conservation equation of each of the
components of the gas mixture [NGU 10]:



 
∂ (ρ⋅ε⋅ w + ∇⋅ −ρ⋅ w ⋅ N D . ∇ x + x − w ⋅ ∇ p   + ρ⋅ w u ⋅    = 0 [3.27]
i 

t ∂ ) i  ij   j ( j ) j p   i 
 j1,j i ≠ 
=
with i = H 2 or H 2O for the anode, and i = N 2, O 2 or H 2O for the cathode. The
density of the gas mixture is determined by:
p
(RT )
ρ= N [3.28]
 w i
i1 = M i