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9.2 Active surface area The previously explained kinetic constants and equations (e.g. (9.22)) are for rates per unit catalyst area. As mentioned, one way to compensate for a slower reaction is to increase the roughness factor or catalyst surface area per unit geometric area. For example, ignoring double-layer charging and assuming electro neutrality, one can write a current balance between ionic and electronic current, (9.49) where is evident that the current generation source term is directly proportional to the specific interfacial area, a1,2, which can be related to the roughness factor discussed above Table 9.1 by accounting for the thickness of the electrode. In the above equation, represents the total anodic rate of electrochemical reactions per unit volume of electrode and ih,1-2 is the transfer current for reaction h between the ionic and electronic materials; for RFBs, the electronic current (i) is the electrons and the ionic current (ii) are the reactive ion species. Thus, the surface area in the porous electrode is critical to RFB performance. An optimum surface area in a porous medium is directly linked to the physical and transport properties of the medium, namely, porosity and permeability, respectively. From an electrochemical standpoint it is desirable to have the need to minimize pressure drop and pumping costs, which favor high permeability. A brief analysis of the interplay between these two key parameters follows. Typical RFB carbon-fiber-paper or carbon-felt electrode materials have a porosity around 0.8, a fiber diameter of approximately 10 μm and a permeability of 2 x 10-8 cm2. A qualitative estimate of the surface area variation with fiber diameter can be obtained using a filament analogue model which simply involves finding the number of cylinders N of a given diameter df that give a specific porosity ε (cm3/cm2), then determining the specific surface area a1,2 (cm2/cm3) of N cylinders. A simple formula for this relationship is given by Carta et al.302 (9.50) The actual surface area in a real fiber bed may be less than this value since fibers contact and overlap each other. Even more if the fibers are not truly cylindrical but rough or ridged. In terms of a roughness factor, using a typical felt properties and a thickness of a few millimeters, a value of around 50 is obtained. Also the absolute permeability change expected as calculated from the Carman-Kozeny equation303, which has been shown to adequately describe the variation of permeability with porosity due to compression in fibrous materials304 and is assumed to apply here. Clearly, the fiber diameter dramatically impacts both aspects and unfortunately in opposing directions. Increasing the fiber diameter from 10 to 100 μm improves the permeability by a factor of 100, but reduces the surface area by a factor of 10. The 229PDF Image | Redox Flow Batteries Vanadium to Earth Quinones
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