Page 104 - Introduction to Transfer Phenomena in PEM Fuel Cells

Mass Transfer Phenomena 93
Darcy’s law, which describes the convection of a gas mixture in a porous
medium (diffusion layers), is based on the homogenization of porous and
fluid media in a place where the detailed geometric description of the pore
structure is not necessary [GAL 05]. In this case, the volume of the medium
is considered relatively large in relation to the pore size; therefore, the speed
of the gas mixture is determined by the pressure gradient, the viscosity and
the structure of the porous medium [NGU 10]:
 k  
u =− P ∇ p [3.17]
μ

where:

–1
–1
– µ is the dynamic viscosity of the gas [kg.m .s ];
– K p is the permeability [m²];
– P is the pressure [Pa].

3.4.2. The conservation of species

The species conservation equation representing conservation of mass for
the gas phase of a single species is written as [BAR 05]:




( ∂ρ⋅ε⋅ w i ) +∇ ( ρ⋅ε⋅ wu = ∇ ρ⋅ D eff ⋅∇ w + S [3.18]

) (
⋅
t ∂ i i ) i s,i
where:
– w is the mass fraction of the species (i) in its gaseous phase (H 2, O 2,
i
H 2O and N 2);
– S s,i is the source term (or well) of the species (i);

– D eff is the diffusion coefficient of the species (i) in a porous
i
–1
environment in [m².s ];
( ∂ρ⋅ε⋅ w )
– i is the species accumulation term;
t ∂
 
– ( ρ⋅ε⋅ wu ) is the advection term;
∇
⋅
i