Gibbs-Duhem equations matrices

If we add the three equations in equation (8.70), we see that the Gibbs-Duhem equation holds ZQVpi = 0. Let us fix species 3, which might represent the membrane, with velocity = 0. The third equation in (8.70) is superfluous, as Kyy = K. The remaining 2x2 matrix equation can be inverted to determine the velocities and thus the fluxes of species 1 and 2. 

By using Gibbs-Duhem s equation, it follows that the sum of the terms on the left hand side of the second line of eq 14.17 times c is zero. As the second line of eq 14.17 holds for an arbitrary measurable heat and molar fluxes it follows that the resistivities in the matrix are dependent, and satisfy... 

---