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Section 2.10 Concentration overpotential To transform experimental results, obtained with other redox systems, we can use the dimensionless Sherwood number, which relates to the mass transfer coefficient as shown in Eq. (2-65) [62]. Sh k dF MT Deff Wherein: dF Fiber diameter of the graphite felt Deff Effective diffusion coefficient in the electrolyte (2-65) We can calculate the effective diffusion coefficient from the measured diffusion coefficient using the Bruggeman correction, as shown in Eq. (2-66) [18, 64]. Deff DElε32 DEl Measured diffusion coefficient in the electrolyte (2-66) (m2s-1) (-) Wherein: ε Porosity of the graphite felt We can experimentally relate the Sherwood number to the Reynolds number, Re, as shown in the Eqs. (2-67) and (2-68) [61, 62]. In these two references, the mass transfer coefficient towards carbon fiber electrodes is studied using the reduction of [Fe(CN)6]3- to Fe(CN)6]4-. It is widely assumed that the mass transfer coefficient which is obtained using that reaction is also applicable to the particular vanadium reactions [8]. Sh 7.00Re0.40 (2-67) Sh 6.13Re0.36 (2-68) We can express the Reynolds number in quantities, which are commonly used to describe a VRFB, as shown in Eq. (2-69). Re ρElvEldF (2-69) (m) (m2s-1) Wherein ρEl Electrolyte density μEl Electrolyte dynamic viscosity vEl Electrolyte velocity μEl (kgm-3) (Pas) (ms-1) If we combine the Eqs. (2-65), (2-67) and (2-69), we derive an actual relation for the mass transfer coefficient that only contains known quantities. sectional area. μEl Deff ρ dF 0.40 Q 0.40 44 Deff dF ρ dF 0.40 7.00 El v0.40 (2-70) kMT We can further replace the fluid velocity by the flow rate over the electrode cross kMT 7.00ElC dF μEl CSAE (2-71)PDF Image | Model-based Design Vanadium Redox Flow Batteries
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