Homogeneous turbulence, definition

The velocity field is statistically homogeneous if all statistics are invariants under a shift in position. If the field is also statistically invariant under rotations and reflections of the coordinate system, then it is statistically isotropic. In chemical reaction engineering these mathematical definitions are usually somewhat relaxed, since turbulence is said to be isotropic if the individual velocity fluctuations are equal in all the three space dimensions. Otherwise it is said to be an-isotropic. Similarly, a flow field where turbulence levels do not change from one point to another is called homogeneous. 

In a homogeneous system we were able to define the RTD for the system and to determine it experimentally by the use of perfect tracers. Each species in a homogeneous system has the same RTD equal to the RTD of the system. The above argument is based on the fact that RTDs in homogeneous systems of interest, such as reactors, are flow dominated. Convection and turbulence determine the RTD and do not allow differences in residence times to develop due to differences in species diffusivities. In heterogeneous systems various components in the feed phase (e.g, gas) may have different adsorption affinities for the solid or different solubilities in the liquid. Therefore, they will have different residence times in the reactor. Measuring all these RTDs would definitely be impractical. 

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