Application to Mixing in Microchannels

If this aggregate is now placed in a shear flow with a velocity gradient du 

It can be seen that, provided that the segregation scale is large (this notion will be clarified further), stretching is the controlling process for mixing and mechanical dissipation is an interesting tool to decrease the mixing time. 

This section considers the case of flow in a channel of diameter d at low Re. After the flow has been in the pipe for a distance much longer than the entry length, the fluid velocity only varies with radial position. In the case of a cylindrical channel with flow along the axis, the velocity distribution is a simple quadratic, known as Hagen-Poiseuille or simply Poiseuille flow. The pressure drop is given by the following relation  

The energy dissipation rate 8 per unit mass of fluid (W kg ) is proportional to the 

The mean shear rate in the tube can be easily calculated by 

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