Alteration Constraints

Theory:

general constraints on flow and alteration rates obtainable from simple flow model and analytic solution results [Norton(1988)].

taking the governing equation describing transport of the general intensive property $\mathcal{G}$ as

$$\underbrace{{\color{red} \frac{\partial (\phi \mathcal{G})_f}... ...dot\mbox{$\nabla{\rm\mathcal{G}_f}$ }}}_{\rm Advection}\ =\ 0$$ (1)

a general constraint on time (or length or advective) scales of a system producing observed alteration can be written as

$$\Delta t\ =\ -\frac{\Delta l}{v} \left\{ \frac{{\color{blue}... ...or{magenta} (\mathcal{G}^{x_1}-\mathcal{G}^{x_o})_f}} \right\}$$ (2)