Page 127 - Introduction to Transfer Phenomena in PEM Fuel Cells

116 Introduction to Transfer Phenomena in PEM Fuel Cells
where:
– K is the electrokinetic permeability, in Darcy (D);
– δ E + is the ionic conductivity of the membrane, in (S. m ).
–1
H
By associating the equations [3.62] and [3.66], we write:
K  K c + 
2
j =− F c + ⋅ p ⋅∇ P −  F c + E ⋅ C + D eff + F ⋅ 2 ⋅ H  ⋅∇ϕ [3.68]
H μ b   H μ f H O,H RT  
2
Ion conductivity is defined by the ratio (i ∇φ ):

K p c +
2
δ H + = F 2 c H + ⋅ C + D eff + ⋅ F ⋅ H [3.69]
f
μ
HO ,H
RT
2
  
Convective Term Diffusive Term
In the case of Nafion membranes, the fluid flowing in the pores contains
charged particles (protons). Their convective displacement also contributes
to the current density. The ionic conductivity is then the sum of a diffusive
term and a convective term; the convective term exists for this model,
because it is assumed that the protons are mainly present in the membrane,
–
with the OH being negligible. In the case of a symmetrical electrolytic
solution (with as many co-ions as of counter-ions), this convective term
vanishes and the ionic conductivity depends solely on the diffusive term
[BOU 07]:

δ + = D eff + F ⋅ 2 ⋅ C f [3.70]
H H O,H RT
2
Bernardi and Verbrugge only take into account the diffusive term of
conductivity, despite the convective displacement of protons contributing to
the current density. This hypothesis would only be valid in the case where
the velocity of the fluid is zero: u = 0 .

To use the hydraulic model in a global fuel cell model, it is necessary to
know the boundary conditions. Bernardi and Verbrugge use this transport