Page 92 - Introduction to Transfer Phenomena in PEM Fuel Cells

Charge Transfer Phenomena 81
polarization curve but neglects some electrochemical aspects. However, it is
used in modeling the polarization curve for several types of PEMFC cells
[ERI 01, PIS 02]. Other empirical models have been used, such as that of
Amphlett et al. [AMP 95]; when the analytic constants are not known, the
empirical equations for each parameter and for the overall ohmic loss will be
used. Empirical modeling techniques are also used to develop an equivalent
circuit to model the dynamic performance of the PEMFC. This technique
uses experimental procedures such as Current interruption and
Electrochemical Impedance Spectroscopy (EIS).

2.9. Current transport and charge conservation
In general, the current transport is described by the charge conservation
equations [BAR 05, VAN 04] for the electric current:
)
∇⋅ σ eff ⋅∇ϕ = S s ϕ [2.81]
s
( s
For the ionic current:

∇⋅ σ eff ⋅∇ϕ m ) = S s ϕ [2.82]
( m

where:
–1
– σ eff is the electrical conductivity in the solid phase, in [S.cm ];
s
– σ eff is the electrical conductivity in the electrolyte (membrane), in
m
–1
[S.cm ];
– φ is the potential of the solid phase, in [V];
s
– φ is the potential of the membrane, in [V];
m
– S is the source term representing the volumetric transfer current.
φ

At the anode:

 S =− j a

s φ
 [2.83]
  S φ m = j a