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reactants and products, the same equation can be used with the migration term set to zero, resulting in the equation of convective diffusion310. Dilute-solution theory considers only the interactions between each dissolved species and the solvent, and thus one can consider the conductivity of the solution to be given by (9.64) The motion of each charged species is described by its transport properties, namely, the mobility and the diffusion coefficient. These transport properties con be related to one another at infinite dilution vie Nernst-Einstein equation309,311,312 (9.65) For more complicated systems than binary electrolytes or where the interactions between species are important and/or non-ideal, concentrated-solution theory can be used as discussed by Newman and Thomas-Alyea308. In this approach, the transport coefficients of merit include the conductivity of the solution, and the transference numbers and diffusivities of the ions. It should be noted that many RFBs operate at higher concentrations such that concentrated-solution theory may be required; however, the use of supporting electrolytes does mitigate this to a certain extent in that detailed speciation is not required to predict cell performance fairly well. The total current in the electrolyte can be expressed as (9.66) and the ionic conductivity of the electrolyte can be related to the above transport properties308. For most RFB applications, the system is one phase (liquid) and so complicated expressions for multiphase flow are unnecessary, in stark contrast to low- temperature fuel cells. Thus, for the convective flow one can use the Navier-Stokes equations309 (9.67) where p is the pressure, and μ and ρ are the viscosity and density of the liquid, respectively. Since most RFB electrodes are porous, the above equation can be extended using various methodologies such as Brinkman303,309,313, or even replaced by Darcy’s law303. 236PDF Image | Redox Flow Batteries Vanadium to Earth Quinones
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