Inertial Mechanism of Coagulation

Consider a drop with radius R2. The number of times that this drop encounters a drop with radius i i in unit time due to the inertial mechanism in turbulent flow may be estimated by means of the following expression [2]  

Let us estimate the growth rate of drops, assuming them to be identical. The coagulation frequency, Eq. (15.6), must then be averaged over drop sizes  

The value of the average size certainly depends on the form of drop distribution over their sizes Although there is not a fixed form of distribution, it is possible to obtain an estimate using  

Now it is easy to write an equation of balance for drop number n  

The factor of 1/2 appears on the right-hand side of Eq. (15.10) since in calculating the number of collisions the interactions of identical drops are taken into account twice. 

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Note that Eq. (15.48) applies for drops of greatly differing sizes. For the inertial mechanism of coagulation, this case is of greatest interest, because for drops of commensurable size the basic mechanism of coagulation is turbulent diffusion. 

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