Click here to see the input file for this example: kks_example_ternary.i

When additional chemical components are added to the KKS model, a Cahn-Hilliard equation must be added for each additional component. (For $$$n$$$ components, $$$n-1$$$ Cahn-Hilliard equations are required). Each additional Cahn-Hilliard equation requires the kernels:

`KKSSplitCHCRes`

`CoupledTimeDerivative`

`SplitCHWRes`

To enforce the composition and chemical potential constraints, each additional component also requires the kernels

`KKSPhaseConcentration`

`KKSPhaseChemicalPotential`

The Allen-Cahn equation is also modified when additional components are added. The residual becomes

$$$$R=-\frac{dh}{d\eta} \left(F_a-F_b- \sum_{i=1}^{n-1} \frac{dF_a}{dc_{ia}}(c_{ia}-c_{ib})\right) + w\frac{dg}{d\eta}.$$$$

where $$$n$$$ is the number of components. A single `KKSACBulkF`

kernel is needed as in the 2-component case, and an additional `KKSACBulkC`

kernel must added for each additional component.