First deceleration stage

Separating the variables involved and integrating the equations between Mpo and 0, the distance the particle traveled in the first decelerating stage, i.e., the maximum depth of penetration into the opposed stream, xmax, can be obtained as... 

As mentioned above, in impinging streams, it is possible for the particle to penetrate to and fro many times between the two opposing streams. In other words, it would experience multiple decelerations-accelerations of motion. The time for each deceleration or acceleration motion, ruj or /aci (i = 1, 2, ) can be analyzed and calculated with the same principles and procedures as described above. Of course, the distance the particle travels in each of the deceleration stages,. v,u, can also be calculated however, those distances lack of significance, except for that in the first deceleration stage,. vdj =. vmav... 

The fonnation of these substances contradicts common ideas on nucleophilic substitution. The presence of radical traps (oxygen or tetrabromobenzoquinone) decelerates the formation of both unexpected compounds and product of thioarylation. Consequently, the first stage of the reaction depicted in Scheme 4.5 produces phenylthiyl radical and anion-radical of the substrate. Both electron-transfer products undergo further conversions The phenylthiyl radical gives diphenyldi-sulfide, and the anion-radical of the substrate produces 9-fluorenyl radical. The latter reacts in two directions—dimerizing, it forms bifluorenyl reacting with the nucleophile, it gives the anion-radical of the substitution product. The chain continues because the electron from the anion-radical is transferred to the unreacted molecule of the substrate. The latter loses bromine and then reacts with the nucleophile, and so on (Scheme 4.6). 

---