Bernardi-Verbrugge model

One of the first and most often cited PEM fuel cell models is the Bernardi-Verbrugge model [5]. This is a one-dimensional model that treats the cathode gas diffusion electrode bonded to a polymer electrolyte and transport of neutral and charged species within. The model results in a set of differential equations, which once solved allow determination of species concentration profiles, spatial dependence of the pressure and potential drop, and identification of various contributions to the total potential drop. The model is based on simplifying assumptions such as ... 

Not surprisingly, the Bernardi and Verbrugge model forms the basis for many other models that came after it. most notably the computational-fluid-dynamics (CFD) models, as discussed in the next section. In terms of direct descendants of this model, the model of Chan et al. " takes the Bernard and Verbrugge model and incorporates carbon monoxide effects at the anode as per the Springer et al. ° description. The models of Li and co-workers - " " ... 

With the increased computational power of today s computers, more detailed simulations are possible. Thus, complex equations such as the Navier—Stokes equation can be solved in multiple dimensions, yielding accurate descriptions of such phenomena as heat and mass transfer and fluid and two-phase flow throughout the fuel cell. The type of models that do this analysis are based on a finite-element framework and are termed CFD models. CFD models are widely available through commercial packages, some of which include an electrochemistry module. As mentioned above, almost all of the CFD models are based on the Bernardi and Verbrugge model. That is to say that the incorporated electrochemical effects stem from their equations, such as their kinetic source terms in the catalyst layers and the use of Schlogl s equation for water transport in the membrane. 

One-Dimensional through-the-Membrane Model (Bernardi-Verbrugge [5])... 

FIGURE 7-5. Modeling domain of 1-D through the membrane model (Bernardi-Verbrugge). 

The first model to describe the membrane in the above fashion was that of Bernardi and Verbrugge, "° which was based on earlier work by Verbrugge and Hill. " 214 model utilized a dilute solution approach that used the Nernst— Planck equation (eq 29) to describe the movement of protons, except that now v is not equal to zero. The reason is that, because there are two phases, the protons are in the water and the velocity of the water is give by Schlogl s equation ... 

The first numerical models of PEFC were developed about 15 years ago. Springer et al. published a one-dimensional (ID) steady-state model of PEFC [7]. At the same time Bernardi and Verbrugge developed a model of the PEFC cathode [5] (and later extended it to the whole cell [6]), which in many respects is close to the model of Springer et al. 

D. M. Bernardi and M. W. Verbrugge, A Mathematical Model of the Solid-Polymer Electrolyte Fuel Cell, J. Electrochem. Soc., 139, TAll (1992). 

One of the earliest hydraulic models is that of Bernardi and Verbrugge [42,43] and is based on the Nernst-Planck equation for the transport of species within the fluid phase, and on the Schloegl equation to describe fluid transport,... 

In the formulation of Bernardi and Verbrugge, the membrane is assumed fully hydrated, and the gases are taken to be dissolved in the pore fluid [42]. A more general variant of this hydraulic model was proposed by Eikerling et al. [44] and allows water content variation, and dependence of conductivity, permeability, and electro-osmotic drag coefficient on the local water content. 

Bernardi, D.M. and Verbrugge, M.W. (1992) A mathematical model of the solid-polymer-electrolyte fuel cell. 

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