Flux boundary conditions on Y

Mass fractions Y of all species, except the background “inert” specie, are found by solving a partial differential equation. Mass is transferred through the electrode boundaries, so these boundary fields are cast to a fixedGradient type, to which a (generally non-uniform) gradient value is assigned. The mass fraction gradient of a specie i will be due to both mass flux of i and to the mass fluxes of the other species. Letting Y_i be the mass fraction boundary field of specie i on the electrode boundary, we have

$$\frac{\partial {{Y}_{i}}}{\partial n}={1\over{\rho D}}\left(\dot{m}_{i}^{''}\left( 1-{{Y}_{i~}} \right)-{{Y}_{i}}\underset{j\ne i}{\mathop \sum }\,\dot{m}_{j}^{''}\right)$$