Balancing Material Movement and Internal Change

The fundamental distinction between pure convective transport and transport coupled with internal generation or destruction, both described by the continuity equation. The first source provides the specific form of the continuity equation for a convective flow without sources, such as the idealized dispersal of sand grains where no new material is produced ($\frac{\partial n}{\partial t}+\nabla \cdot(n \vec{v})=0$). In contrast, the second source highlights that real-world transport phenomena often require accounting for an additional factor: internal generation/destruction (a "sync term"), which means that any change in local concentration must balance both the convective transport (movement across boundaries) and the rate at which the material is created or destroyed within the volume. This internal sink term causes the concentration of particles to decrease much faster than if the change were due solely to external flow.

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