Models of Flooded Porous Electrodes

The special case where the conductivity of the electrolyte inside the pore is constant, possibly due to a large excess of inert electrolyte, was treated by Austin [17]. Let us introduce q as  

Austin demonstrated that the solution of the problem described reduces to Eq. 22 for control by the discharge step and electrolytic conductance at q 5, while diffusion (Eq. 36) is predominant at q 0.5. Both the potential and concentration vary with x for intermediate values of q. 

Gurevich and Bagotzky [16] considered the case where the flux of neutral species participating in the electrode reaction is much smaller than the flux of charged species for a pore operating from both sides. Approximate solutions were given in a closed form for a linear current-potential dependence and for a Tafel type dependence. The reader is referred to the original paper for the discussion of the influence of various parameters on performance. 

The porous structure filled with electrolyte is considered as the superposition of two continua, the electrode matrix and the solution in the unoccupied spaces within the matrix. The two phases, which complement one another, are supposed to be homogeneous and isotropic. Effective parameters rather than actual parameters are used for the description of the properties like pore size, conductivity, diffusion coefficient etc. The problem is treated as a one-dimensional one. This is equivalent to the assumption that the penetration depth of the current is larger than the size of the structural units (grains, holes) of the porous electrode. Continuum models were analyzed under different assumptions in references 1,4,9,12 to 14,16 to 20. Comprehensive treatments with strict derivations were published by Tobias and coworkers [21, 22] and by Micka [23]. 

Let us discuss the two cases corresponding to the potential distribution without influence of mass transport processes and to the concentration distribution in the single pore under the influence of diffusion. If cp designates the average electric potential inside the continuum and I the average current, it is  

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