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Section 2.10 Concentration overpotential As mentioned before, the diffusion coefficient in the electrolyte is reported to be different for the positive and negative half-cell [55]. Hence, the mass transfer coefficient is also different for the two half-sides. With the two different relations between Sherwood and Reynolds number (Eqs. (2-67) and (2-68)), two possible combinations to describe the mass transfer are yielded. The relevant input parameters can be found in Section B.2 on page 152. Negative half-cell, Sherwood to Reynolds number relation (2-67) Q 0.40 kMT 1.608⋅10-4 C CSAE Positive half-cell, Sherwood to Reynolds number relation (2-67) Q 0.40 kMT 2.613⋅10-4 C CSAE Negative half-cell, Sherwood to Reynolds number relation (2-68) Q 0.36 kMT 1.322⋅10-4 C CSAE Positive half-cell, Sherwood to Reynolds number relation (2-68) Q 0.36 kMT 2.149⋅10-4 C CSAE (2-72) (2-73) (2-74) (2-75) The proportional factor of the mass transfer coefficients according to the Eqs. (2-74) and (2-75) is 12 % smaller than according to the Eqs. (2-72) and (2-73). The exponent is 10 % smaller as well. However, as the fluid velocity in practice is always smaller than 1 ms−1, a smaller exponent corresponds to a larger mass transfer coefficient. This compensates for the smaller proportional factor. In fact, for a realistic fluid velocity in the range of 0.01 ms-1, the respective coefficients for the negative and the positive half- cell hardly deviate for the two different relations between the Reynolds and the Sherwood number. 2.10.3 Critical assessment of the application in a lumped-parameter model Despite the fact that the above presented model of the concentration overpotential is validated in [30] for a lumped-parameter model, the application of the method is not unproblematic. The mass transfer coefficient as shown in Eq. (2-72) is most often used to describe the concentration overpotential in both half-cells [16, 19, 21, 30, 51, 57, 65– 70]. To the authors best knowledge, no model accounts for the different mass transfer coefficients in the two half-cells. Another issue concerns the current density in the diffusion layer, iDL, in particular to which area it relates. In [17] it is stated that the concentration overpotential “is caused by the difference in electroactive species concentration between the bulk solution and 45PDF Image | Model-based Design Vanadium Redox Flow Batteries
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