Final Stage Model

A similar procedure to that for lattice diffusion gives 

This equation indicates that the densification rate is inversely proportional to the cube of grain size. This result is the same as that found for the dependence of neck growth and shrinkage on particle size in the initial stage model. 

So far, Coble s model has been a standard for interpreting and predicting the densification at final stage sintering. In Coble s model, however, a fundamental aspect is not taken into account, namely, the grain boundary as the atom source for densification. In addition, it is hard to accept Coble s flux equation (Eq. (5.7) under ri JCr2) that predicts a constant material flux from grain boundaries to the surface of a pore irrespective of pore size. 

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Coble, R.L. (1961) Sintering crystalline solids 1. Intermediate and final stage models II. Experimental test of diffusion models in powder compacts, J. Appl, Phys, 32, 787. 

The kinetic models are the same until the final stage of the solution of the reactor balance equations, so the description of the mathematics is combined until that point of departure. The models provide for the continuous or intermittent addition of monomer to the reactor as a liquid at the reactor temperature. 

In this paper we present a meaningful analysis of the operation of a batch polymerization reactor in its final stages (i.e. high conversion levels) where MWD broadening is relatively unimportant. The ultimate objective is to minimize the residual monomer concentration as fast as possible, using the time-optimal problem formulation. Isothermal as well as nonisothermal policies are derived based on a mathematical model that also takes depropagation into account. The effect of initiator concentration, initiator half-life and activation energy on optimum temperature and time is studied. 

Silveston et al. (1994) use a one-dimensional plug flow model to represent the packed bed in the final stage. Because the intent of their work was to model the experiments of Briggs et al. discussed earlier, they allowed for heat loss or gain in the bench scale reactor used by Briggs through wall... 

Having selected the major features, the final stage of QSAR model building involves a feature mapping procedure. 

Explicit forms for the stress tensors d1 are deduced from the microscopic expressions for the component stress tensors and from the scheme of the total stress devision between the components [164]. Within this model almost all essential features of the viscoelastic phase separation observable experimentally can be reproduced [165] (see Fig. 20) existence of a frozen period after the quench nucleation of the less viscous phase in a droplet pattern the volume shrinking of the more viscous phase transient formation of the bicontinuous network structure phase inversion in the final stage. 

Lasofoxifene is a SERM that also protects from bone loss, reduces cholesterol levels, and exerts a positive effect on bone strength in rats, specifically in male models (Ma et al. 2002). This compound is in the final stages of clinical development. Two other SERMs also in advanced phase III trials are bazedoxifene and arzoxifene, both with protective effects against ovariectomy-induced bone loss. Arzoxifene has shown both bone remodeling reduction with positive effects on bone quality as well as a reduction in cholesterol levels in oophorectomized rats (Biskobing2003). 

The mechanism shown in Scheme 5 postulates the formation of a Fe(II)-semi-quinone intermediate. The attack of 02 on the substrate generates a peroxy radical which is reduced by the Fe(II) center to produce the Fe(III) peroxide complex. The semi-quinone character of the [FeL(DTBC)] complexes is clearly determined by the covalency of the iron(III)-catechol bond which is enhanced by increasing the Lewis acidity of the metal center. Thus, ultimately the non-participating ligand controls the extent of the Fe(II) - semi-quinone formation and the rate of the reaction provided that the rate-determining step is the reaction of 02 with the semiquinone intermediate. In the final stage, the substrate is oxygenated simultaneously with the release of the FemL complex. An alternative model, in which 02 attacks the Fe(II) center instead of the semi-quinone, cannot be excluded either. 

Mehendale HM. 1991. Role of hepatocellular regeneration and hepatolobular healing in the final outcome of liver injury A two-stage model of toxicity. Biochem Pharmacol 42(6) 1155-1162. 

The hybrid approach tries to combine the model-based optimization approach with the heuristic approach, thereby, avoiding the problems of unavailability of models. In the initial stages, a property-based approach (where properties are obtained through model or experimental measurements) is applied and in the final stages (where models are usually easy to develop), a model-based optimization approach is applied (see for example, Gani (2004)). More work is needed to establish this technique for food-process applications. 

Laubriet et al. [Ill] modelled the final stage of poly condensation by using the set of reactions and kinetic parameters published by Ravindranath and Mashelkar [112], They used a mass-transfer term in the material balances for EG, water and DEG adapted from film theory J = 0MMg — c ), with c being the interfacial equilibrium concentration of the volatile species i. 

Laubriet, C., LeCorre, B. and Choi, K. Y., Two-phase model for continuous final stage melt polycondensation of poly(ethylene terephthalate). 1. Steady-state analysis, Ind. Eng. Chem. Res., 30, 2-12 (1991). 

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