Page 134 - Introduction to Transfer Phenomena in PEM Fuel Cells

×
×
λ
−
7
if λ ≤
) 1 exp
3


D
m
[3.87]
= 
HO
2
    3.1 10 ⋅ ⋅   exp (0.28 λ −  ⋅      − 2346  − T 2346  Mass Transfer Phenomena 123
−
×
8
λ
⋅
if λ >
−
1 161 exp λ  ⋅
4.17 10 ⋅ ⋅ +
( ) exp
3
      T  
Finally, again for Nafion membranes, Neubrand et al. [NEU 99] have
adopted the following empirical formula:
2
D m = 1 0 − 10.77 5 + 0.3436 ⋅λ − 0.189 ⋅λ + 0.0004 ⋅λ 3 ⋅
HO
2
  1 1   [3.88]
( 0.6 × λ
e xp  ( 2 64 0 ⋅− ) + 15 17 ) ⋅  −  
  35 3 T  
A few years ago, a study presented a relationship derived from experience
for estimating the coefficient ( D m ) in a Gore-Select membrane [YE 07]:
H 2 O

1
×
D m 2 = 0.5 10 − 10 ⋅ exp 2416⋅      303 − T  1      . [3.89]
HO
( 2.563 0.33⋅λ + 0.0264⋅λ − 0.000671⋅λ 3 )
2
−
3.6.5.4. The electro-osmotic coefficient
The coefficient (ξ), involved in equation [3.54], has been experimentally
measured by Springer et al. [SPR 91] for a Nafion membrane:
2.5
ξ = ⋅ λ [3.90]
22
For the same Nafion membrane, Zawodzinski et al. [ZAW 95] took a
constant value of 1 for (ξ) for the water content range [GUP 08, BLU 07]. For
(λ < 5), a proportionality relationship is adopted, with the authors
considering that the electro-osmotic coefficient is (λ = 0). For (λ > 14), (ξ)
increases linearly [ZAW 93]:
 0.2⋅λ for λ > 5
ξ=  1  for 5≤ λ ≤ 14 [3.91]

 0.1875⋅λ − 1.625 for λ > 14