Taylor Dispersion in Microchannels

The convection-diffusion equation for the tracer, that is, species-1, can be written as 

Expanding the above equation in Cartesian coordinate, we have 

As L /i, in the large-time limit t the transverse diffusion term can be neglected 

This equation can be integrated as c does not depend on y. We do not perform the integration here, which is rather long. The final solution of the problem is 

Vq is the mean velocity of the Poiseuille flow and o is the molecules per area at time 

---