Page 133 - Introduction to Transfer Phenomena in PEM Fuel Cells

122 Introduction to Transfer Phenomena in PEM Fuel Cells

2
+
<
0.043 17.81a −


(1 a≤
<
+
λ = 
 14 1.4 (a − ) 1 39.85a + 36a 3 (0 a≤ ) 1 ) 3 [3.82]
  16.8 (a > ) 3
with:
⋅
P HO P x HO
a = 2 = 2 [3.83]
P sat P sat
3.6.5.2. The ionic conductivity of the membrane
Work by Siegel [SIE 03] and Ge [GE 03] propose, for the ionic
+
conductivity (of protons H ) as a function of the water content, and in the
case where (λ > 1), the following empirical determination:
  1 1  
σ + = ( 5139.0 ⋅ λ − .0 326 )⋅ exp  1268  ⋅ −   [3.84]
H T
  303  
On the contrary, in an article by Neubrand et al. [NEU 99], we find the
following formula, valid irrespective of the value of (λ):
⋅
σ + = (0.2658 λ⋅ + 0.0298 λ + 0.0014 λ 3 ) ⋅
⋅
2
H
  1 1   [3.85]
( 0.6 λ +
⋅
exp  (2640 exp − × ) 1183 ⋅ −  
) 
  303 T  
3.6.5.3. The diffusion coefficient of water in the membrane
The water diffusion coefficient in the membrane depends on the type of
membrane. For a Nafion membrane, A.C. West and T.F. Fuller [WES 96]
gave, in their study, the following formula:

×
D m = 3.5 10 − 7 ⋅ exp − 2436   ⋅ λ [3.86]

HO  T 
2
Motupally [MOT 00] presented another formula for determining this
water transport coefficient as a function of (λ):