 Mass transport

Mass transport is movement of material through space, whether as whole-fluid motion, relative motion of constituents or migration driven by an external field. Bulk advection carries a constituent with the local velocity field; diffusion moves it relative to that mean motion because of microscopic fluctuations and spatial variations in its thermodynamic driving quantities.

For a dilute passive constituent with concentration $c$ and constant diffusion coefficient $D$, a simple model writes total flux $\mathbf{J}=c\mathbf{v}-D\nabla c$. The first term transports concentration with the flow, while the second smooths concentration differences. Charged constituents can also migrate under an electric field, requiring an additional flux term and appropriate electrochemical constraints. Combining the flux with a local conservation equation predicts how concentration evolves. Measuring only total material crossing a boundary does not by itself distinguish which transport mechanism supplied it.