The animated demo for the Continuity Equation with a Sink Term effectively demonstrates the conservation law's dependence on two distinct effects: convective transport and internal generation/destruction. The simulation shows the concentration ( $n$ ) of particles decreasing much faster than in a flow-only scenario because the positive divergence ( $\nabla \cdot J$, the spreading due to outward flow) works in tandem with the uniform, internal sink term ( $-R$, or evaporation). This principle highlights that when modeling real-world transport phenomena, any change in local concentration must be mathematically accounted for by balancing the movement of the material across boundaries ( $\nabla \cdot J$ ) with the rate at which the material is created or destroyed inside the volume ( $S$ ).
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%% Proof and Derivation
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