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3638 Paths tSouSsutastianianbalbeleEEnneergrgyy 3.1.1 Electron exchange rate Obviously, the concentration changes are proportional to the reaction rate; and from (1) we also know that an electron is involved each time a redox reaction occurs. Therefore, the concentration changes are also proportional to the electrical current. Thus, the pace of the concentration variation is set by the electrical current flowing through the cell: Qc = ne− e = where Qc is the charge, i the current, t the time, ne− the number of electrons and e the i(t)dt [C] (11) elementary charge. Therefore, the number of electrons ne− involved for a given current2 is: 1 electrons N ̇ e− : eNA Physically, an electron is released by the oxidation of a vanadium ion, travels through the electrodes and is captured by the reduction of another vanadium ion in the opposite half-cell. In the case of a stack composed of Ncell cells, the electrons travel through the bipolar electrode to the adjacent cell (Fig. 4). Thus, for one electron flowing through the external electrical circuit, Ncell redox reactions have occurred. Therefore, the total molar flowrate of electrons N ̇ e− tot for a stack is obtained by multiplying (13) by the number of cells: tot eNA F ne− = eN N ̇e−(t)= 1 i(t) [mol/s] (13) i(t)dt [mol] (12) where NA is the Avogadro number. Then (12) leads to the definition of a molar flowrate of N ̇ e− (t) = Ncell i(t) = Ncell i(t) [mol/s] (14) A (a) (b) Fig. 4. (a) Illustration of the redox reactions required to produce a one electron flow in a 3 elements stack during the discharge. When the battery is charged, the flow and the reactions are inverted. (b) Illustration of the hydraulic circuit (half cell) where the concentrations are shown. 2By convention, the current is positive during the VRB discharge in order to have a positive power delivered by the battery.PDF Image | Understanding the Vanadium Redox Flow Batteries
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