1.3 Current and Mass Conservation

Species volumetric source terms (kg/m $^3$-s) in the triple-phase boundaries due to electrochemical reactions for the PEMFC, SOFC, and Electrolysis, respectively, are:

For PEMFC:

$$S_{{\rm H}_2} = -\frac{M_{w,{\rm H}_2}}{2F} R_{\rm an} < 0$$ (1.3-1)

$$S_{{\rm O}_2} = -\frac{M_{w,{\rm O}_2}}{4F} R_{\rm cat} < 0$$ (1.3-2)

$$S_{{\rm H}_2{\rm0}} = \frac{M_{w,{\rm H}_2{\rm0}}}{2F} R_{\rm cat} > 0$$ (1.3-3)

For SOFC:

$$S_{{\rm H}_2} = -\frac{M_{w,{\rm H}_2}}{2F} R_{\rm an} < 0$$ (1.3-4)

$$S_{{\rm O}_2} = -\frac{M_{w,{\rm O}_2}}{4F} R_{\rm cat} < 0$$ (1.3-5)

$$S_{{\rm H}_2{\rm0}} = \frac{M_{w,{\rm H}_2{\rm0}}}{2F} R_{\rm an} > 0$$ (1.3-6)

For Electrolysis:

$$S_{{\rm H}_2} = \frac{M_{w,{\rm H}_2}}{2F} R_{\rm an} > 0$$ (1.3-7)

$$S_{{\rm O}_2} = \frac{M_{w,{\rm O}_2}}{4F} R_{\rm cat} > 0$$ (1.3-8)

$$S_{{\rm H}_2{\rm0}} = -\frac{M_{w,{\rm H}_2{\rm0}}}{2F} R_{\rm an} < 0$$ (1.3-9)

Since the total electrical current produced in the cathode and the anode TPBs, respectively, is the same, we have the following equation for current conservation: