Calculations experimental limiting viscosity number

In experimental studies, where the loss of fluidity is taken as marking the gel point, the conversion at the observed gel point is almost always found to be higher than that (calculated) at the theoretical gel point. This can be explained by the model proposed by Bobalek et al (1964) for the gelation process, as shown in Fig. 5.8. According to this model, at the theoretical gel point, a number of macroscopic three-dimensional networks (gel particles) form and undergo phase separation. The gel particles so formed remain suspended in the medium and increase in number as reaction continues. At the experimentally observed gel point, the concentration of gel particles reaches a critical value and causes phase inversion as well as a steep rise in viscosity. The lower value of pc predicted by the statistical approach is also attributed to the occurrence of some wasteful intramolecular cy-clization reactions not taken into account in the derivation and also in some cases to the limited applicability of the assumption of equal reactivity of all functional groups of the same type, irrespective of molecular size. 

From Fig. 16.8 we see that in ordinary pipe flow for regions away from the wall the eddy viscosity is typically about 100 times the molecular viscosity (i.e., the Reynolds stresses are about 100 times the stresses due to molecular viscosity), that the eddy viscosity is a strong function of position and Reynolds number, and that it is difficult to calculate values of the eddy viscosity near the center of the pipe. From Eq. 16.15 we see that the sum of the eddy and molecular viscosities is equal to Tl dVJdy) at the center of the pipe both quantities are zero. To obtain the correct limit in this ratio as both numerator and denomnator approach zero requires more precise experimental measurements of and y than are currently available. We may infer from Fig. 16.8 that in this type of pipe flow the heat transfer and mixing will be of the order of 100 times the heat transfer and mixing due to molecular thermal conductivity and molecular diffusion. 

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