The Generalized Ficks Law

For the binary systems already discussed, we may regard Eq. 3.1.1 as a linear relationship between the independent flux /j and driving force Vxp For a ternary mixture there are two independent fluxes (7i, J2) and two independent driving forces (Vxj, VX2). Thus, assuming a linear relationship between the fluxes and composition gradients, we may write 

Here we see that 7i and J2 depend on both of the independent mole fraction gradients Vxj and Vx2. The in Eqs. 3.2.1 and 3.2.2 are the multicomponent diffusion coefficients note that four of them are needed to characterize a ternary system. These coefficients are not to be confused with the binary diffusion coefficient in Eq. 3.1.1 they may take positive or negative signs and they are not, in general, symmetric ( 12 21)- Also, the multicompo- 

For n-component systems there are n — 1 independent diffusion fluxes and composition gradients and we simply continue to add terms and equations. Thus, 

No additional equation is needed for 7 , which is given in terms of the other diffusion fluxes 

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