Mixing continued length, turbulent

Continuous flocculation in stirred tanks shows similar trends with regard to agitation/mixing conditions as for batch systems. The overall performance of continuous flocculation processes tends to be inferior to that which can be obtained in batch systems. This is attributed to a closer approach to equilibrium in the continuous case. In-line flocculation, by injection of polymer into turbulent flow in a pipe, is widely practised in industry and offers certain advantages. Multiple addition at several points along the length of a pipe is preferred to single-point addition. 

In the mixing length theory it is assumed basically that lumps of fluid are carried transversely across the fluid flow by the turbulent eddies and during this motion they preserve their initial momentum and enthalpy. The motion continues over a transverse distance, lm, after which the "lumps interact with other fluid "lumps ... 

This relation has been used successfully for many boundary layer flows. However, it is today generally accepted that the physical equivalence between the turbulent mixing length and the molecular mean free path is completely erroneous. The turbulent eddies are not small compared to the width of the mean flow, and they interact continuously rather than collide instantaneously. This model limitation was already recognized by Taylor [157]. 

For analytical studies assuming single-phase fluid dynamics, mixing length models are employed for turbulence. Since this type of model requires the distribution of turbulent viscosity in advance, a special assumption is used to incorporate effects of excessive change of thermophysical properties. In this case, validity of the special assumption is somewhat contentious even if the calculation results agree with the experimental values. In addition, change of density is not considered in the continuity and momentum equations, which implies that buoyancy force and fluid expansion are not incorporated. Therefore, these studies are applicable only to limited flow conditions. 

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