Advection with and without diffusion in pipe- and rotating- flow

These video demonstrates liquid species transport processes. The species are dragged by an alternating flow.
The two cases corresponds to the pure convective transport and to the convection-diffusion transport. The solutions for pure convection cases are obtained analytically.

Miscible vs Immiscible Fluids in pipe flow 2D

The video demonstrates liquid species transport processes. The species are dragged by an alternating flow with a parabolic profile in both cases. The top case corresponds to the pure convective transport, while the bottom one to the convection-diffusion transport.

Miscible vs Immiscible Fluids in shear flow within a cylinder 2D

The video demonstrates species transport processes. In both examples, the species is dragged by an alternating flow. The flow profile corresponds to a cylinder with a rotating wall. The right picture corresponds to the pure convective transport while the left one to the convection-diffusion case.

Mathematical background

\[ \frac{\partial c}{\partial t} = -\vec v \cdot \vec\nabla c\]

\[ \frac{\partial c}{\partial t} = D\Delta c + \vec v \cdot \vec\nabla c\]