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Mass is conserved always. That's the known fact. To show this holds true in convection-diffusion equation, I need to introduce material derivative to you. The material derivative of a scalar quantity as $C(\mathbf{r},t)$ is defined as: $$\frac{D C(\mathbf{r},t)}{D t} = \frac{\partial C}{\partial t} + \mathbf{v} \cdot \nabla C$$ Where $\mathbf{v}$ is the ...