Kolmogorov theory

Middleman, S., 1965. Mass transfer from particles in agitated systems Application of the Kolmogorov theory. American Institute of Chemical Engineers Journal, 11, 750-752. 

The hydrogen absorption/desorption kinetics are usually analyzed by applying the JMAK (Johnson-Mehl-Avrami-Kolmogorov) theory of phase transformations, which is based on nucleation and growth events [166-168] where a is the fraction transformed at time t or alternatively for hydrides the fraction absorbed... 

When the turbulence is not too large, the main force on the droplets is caused by the shear imposed by the surrounding eddies. With the help of the Kolmogorov theory for turbulent flow, the external, disrupting force is can estimated as Text = V(e /c)- We then end up with a definition of the critical Weber number ... 

The energy dissipation number is derived from the Kolmogorov theory [289, 290]. This theory is based on the concept, that in the turbulent flow range the kinetic energy is transferred by inertial forces from large to ever smaller eddies, until it is finally dissipated through viscosity forces. The eddies produced by the stirrer have the size of the stirrer head and are responsible for the macroscopic turbulence, the smallest eddies on the other hand are directionless. On the microscale so-called isotropic turbulence exists, see Section 1.4.2. 

With increasing the droplets of the dispersed phase damp the turbulence. On the other hand droplet coalescence increases in the turbulence-deficient flow regions in the stirred tank. The result is an increase in the average droplet size. Doulah s [103] deliberations based on the Kolmogorov theory led to the following relationship for... 

If Redr < 1, the flow near a drop is laminar, and it would be broken up in the regime TV. Now the local flow velocity is needed at the scale of a droplet d [i.e., u (d)], and this scale is (much) smaller than /e. According to the Kolmogorov theory the velocity is given by... 

The dependence of the Reynolds number on the local velocity can be established in terms of the Kolmogorov theory of turbulence. 

Some results are given in Table 2.3. It should be remembered that eqn. (2.16), like all equations in Kolmogorov theory, has scaling relations. Often, eqn. (2.16) is also applied for the average droplet size resulting from emulsification, say d - In that case, the proportionality constant would be smaller than for [Pg.67]

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