Mass Species Transport Equation in Electrodes

For the porous electrode-gas diffusion layer with bulk fluid motion given by Darcy or Brinkman s equation, the governing species transport is given as 

Substituting Equation 6.66 for the net mass flux owing to the mass species transport equation for electrodes is given as 

In Equation 6.72, the first term represents the unsteady accumulation term S is the volumetric source or sink term given by the three-phase electrochemical reaction region in the active layer of the electrodes. The volumetric reaction term is neglected from the mass species transport equation for the electrode if the active layer is assumed as the electrode-membrane interface with surface reaction and this is taken into account in the assigned boundary condition at the interface. 

For steady-state analysis, a simplified model with negligible thermal diffusion and assuming surface reaction, the equation reduces to 

For the anode gas stream mixture consisting of hydrogen and water, the mass species transport equations are written as 

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