Concentration fluctuations turbulence theory

The smallest size for turbulent eddies is given by the Kolmogorov microscale A. Energy loss below this size only occurs via viscous dissipation. Here also, several scales have been introduced in the framework of turbulence theory, depending whether velocity or concentration fluctuations are considered, namely Ak> Ag, and Ac (see Table I). In liquids, Ak is typically between 10 and 100 ym. The Kolmogorov microscale Ak is frequently used in the in-... 

Thus, in a perfectly macromixed batch system, the mean concentration is constant (obviously), and the variance of the fluctuations decreases exponentially with time—the latter is obverved in turbulent systems, and is also predicted from isotropic, homogeneous turbulence theory (see Fig. 2). 

These scale-up parameters are similar to what would be found from simpler dimensional arguments, of course, but the theory also indicates how this information can be used to predict concentration fluctuations (micromixing). In addition, more rigorous turbulence theories, or experiments, could be used to provide more exact values of P for a specific situation. 

The theory of mixing of a passive scalar concentration field subject to advection and diffusion in a high Reynolds number turbulent flow is based on the works of Obukhov (1949) and Corrsin (1951). Consider a statistically stationary state with a large-scale source of scalar fluctuations in the case when both Pe and Re are large. The... 

Concentrations in the turbulent regime typically fluctuate around a mean value shown in Figure 1.8a and Figure 1.8b. These fluctuations cannot be easily quantified, and they do not lend themselves readily for the formulation of a rate law. This can be overcome by postulating the existence of an equivalent linear concentration profile that extends from the boundary into the bulk fluid. This postulate is enshrined in the concept known as film theory,... 

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