Turbulent mixing of one-phase mediums

One should know turbulence characteristics to estimate the characteristic time of reagents mixing. They proposed a lot of various methods for estimation of mixing time in turbulent flows particularly the review on this theme and mixing models classification are presented in [130]. Since in [125] liquid movement is described by average over Reynolds Navie-Stocks equations with the use of K-e closing, so the characteristic time of turbulence mixing can be estimated as [1,32,125]  

If one supposes that turbulence diffusion coefficient Dt is equal to kinematic coefficient of turbulence viscosity Vt which in its turn can be expressed by specific kinetic turbulence energy K (mVsec ) and rate of dissipation of last one is e (mVsec ) then (1.16) will be as following  

In a number of cases homogenization of medium is limited by exchange processes between large turbulent flows and presenting in them smaller flows, i.e. mesomixing [132,134]  

The fact that in highly turbulent flows liquid viscosity doesn t influence on main volume medium movement is interesting and important enough [3, 135]. In this case they say that flow is self-simila in relation to viscosity and the influence of the last one is displayed in a narrow enough wall layer. The value of Reynolds criterion above which the self-simila field is observed in many respects is determined by flow geometry. For example, in [3] they showed that under sphere flow the 

The fundamental approaches to definition of turbulent flows macro-kinetics and macro-mixing processes are considered in [136-139]. Special attention was focused on micro-mixing models in the context of method based on equation for density of random variables probabilities distribution. Advantage of this method is that we can calculate average rate of chemical reaction if know the corresponding density of concentration and temperature possibility distribution. 

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