*Briefly, rigorous treatment of solute dispersion in an open, straight circular tube considers the relation between **axial** and **radial** dispersion on the shape of a sample plug as it moves downstream at a constant flow rate at a laminar flow conditions.*

*Under laminar flow conditions all fluid elements follow streamlines parallel to the direction of flow and the **velocity profile** has a parabolic shape (**A**). At this, Poisseile flow, the velocity u at the tube walls is zero and it reaches is maximum value at the centre of the tube where **r=0**. The flow velocity **u **at any coordinate is:*

*where r is the radial distance and a is the radius of*

*the channel, while is mean flow velocity.*

*Therefore a bolus, of initially square profile, injected at t=0, will disperse along the velocity profile, forming a hollow, bullet shaped, three dimensional concentration gradient (**B**). While traveling through a detector***** the gradient will yield a a sharp, asymmetric RTD curve with a long tailing section. caused by the slow movement of streamlines adjacent to the walls. *

* Fast responding, with minimum volume and monitoring perpendicularly through the passing gradient