4.2.2.1 Boundary Flux Equation System

Under the assumption of $N_1$ and $N_2$ quantities on the segments 1 and 2, respectively, (4.7) and (4.8) represent a linear equation system for the partial current densities of all involved quantities crossing the interface in normal direction. In these equations

Figure 4.1: PROMIS-NT interface model scheme

$$\sum_{j=1}^{N_1} ( \beta^{11}_{i,j} {\cdot} J^{1}_{j} ) + \... ...} J^{2}_{j} ) + \phi^1_{i} = 0, {\quad} i = 1 {\dots} N_1 \\$$ (4.7)

$$\sum_{j=1}^{N_1} ( \beta^{21}_{i,j} {\cdot} J^{1}_{j} ) + \... ...\cdot} J^{2}_{j} ) + \phi^2_{i} = 0, {\quad} i = 1 {\dots} N_2$$ (4.8)

All coefficients $\beta^{11}$, $\beta^{12}$, $\beta^{21}$, and $\beta^{22}$ are functions of the simulation time $t$, the process temperature $T$, and the spatial coordinates $x$ and $y$. The coefficients $\phi^1$ and $\phi^2$ may depend on the concentrations of the quantities on both sides of the interface. The model developer has to provide MDL classes which determine the actual values of the coefficients and their derivatives to the quantity concentrations which are the dependent variables in the PROMIS-NT internal equation system.