Kinetic modeling complex viscosity

Although the simple rate expressions, Eqs. (2-6) and (2-9), may serve as first approximations they are inadequate for the complete description of the kinetics of many epoxy resin curing reactions. Complex parallel or sequential reactions requiring more than one rate constant may be involved. For example these reactions are often auto-catalytic in nature and the rate may become diffusion-controlled as the viscosity of the system increases. If processes of differing heat of reaction are involved, then the deconvolution of the DSC data is difficult and may require information from other analytical techniques. Some approaches to the interpretation of data using more complex kinetic models are discussed in Chapter 4. 

While the model apparently leads to improved predictions, its complexity has discouraged many researchers. Therefore, in a later study Deardorff [31] reverted to an isotropic eddy-viscosity model in order to decrease the computational costs. In the latter model version an additional equation was used to determine the residual kinetic energy, as the eddy viscosity vsgs was expressed by ... 

Campanelli et al (2004) discuss a model of rubber mixing in an internal mixer based on kinetic, thermodynamic and rheological equations that is used to determine the extent of dispersion, batch temperature and relative batch viscosity over time. The chemoviscosity model is complex in that a model must be developed for the compaction zone, the incorporation zone and the size-reduction zone, as defined by the mixing-time zones in Figure 6.21. 

Many mathematical expressions of varying complexity and form have been proposed in the literature to model shear-thinning characteristics some of these are straightforward attempts at cmve fitting, giving empirical relationships for the shear stress (or apparent viscosity)-shear rate curves for example, while others have some theoretical basis in statistical mechanics - as an extension of the application of the kinetic theory to the liquid state or the theory of rate processes, etc. Only a selection of the more widely used viscosity models is given here more complete descriptions of such models are available in many books [Bird et al., 1987 Carreau et al., 1997] and in a review paper [Bird, 1976],... 

With their combination of complex kinetics and thermal, convective, and viscosity effects, polymerizing systems would seem to be fertile ground for generating oscillatory behavior. Teymour and Ray reported both laboratory-scale Continuous Stirred-Tank Reactor (CSTR) experiments and modeling studies on vinyl acetate polymerization [63-66]. The period of oscillation was long, about 200min, which is typical for polymerization in a CSTR (Figure 2.8). Papavasiliou and Teymour [67] reviewed nonlinear dynamics in CSTR polymerizations. 

Figure 11.6 shows logarithmic plots of rf vs. c for the system CPyCl + NaSal [21]. It has been shown that this system can he described by the Maxwell model with one (f and one T value above the first viscosity maximum. In this range the complex behaviour is due to the concentration dependence of t, while steadily increases with concentration. Furthermore, it was found that t is controlled by the kinetics of breaking and reforming of the micelles [28]. These processes are faster than the reptation of the rods under the given experimental conditions. 

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