Flow and diffusion modelling

While an understanding of the molecular processes at the fuel cell electrodes requires a quantum mechanical description, the flows through the inlet channels, the gas diffusion layer and across the electrolyte can be described by classical physical theories such as fluid mechanics and diffusion theory. The equivalent of Newton s equations for continuous media is an Eulerian transport equation of the form 

When A - V, the molecular transfer of velocity is related to the stress tensor Tij by (see, e.g., Sorensen, 2004a) 

Examples of employing the fluid dynamics or finite element method will be shown in the following sections. The methods can obviously be used also for variables other than the velocity, by a suitable selection of A in (3.50), such as, e.g., temperature, once the basic velocity field has been determined (as it enters in the equations for all other quantities). In the case of temperature T, the source term Ej in (3.50) includes external sources of heat and condensation, and the ideal gas law may be used to connect temperature and pressure. 

Neither the finite element method nor a discretised integration will catch eddy or other motion below a certain scale determined by the choice of mesh. Small-scale motion in many cases may be better described as random, in which case the transport of the quantity A is called diffusion. Diffusion can be described by Pick s law, assuming that the flux density /, i.e., the number of particles (here a small parcel of a gas), passing a unit square in a given direction, is proportional to the negative gradient of particle concentration n (Bockris and Despic, 2004), 

The proportionality factor D characterising the medium is called the diffusion constant. It is assumed that each particle, i.e. each parcel of the fluid, is moving imder the influence of the average field from the rest of the fluid. Pick s law is then combined with the continuity equation similar to (3.51) 

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