Extrusion modeling

Besides the main depolymerization reactions, side reactions should also be considered in the kinetic description of a PET recycling process. This is emphasized by the results obtained from a PET extrusion model [85] shown in Figures 2.19-2.23. The complete set of reactions summarized below in Table 2.10 have been used, but shear effects have not been taken into account. Chain degradation, accompanied by a significant reduction of intrinsic viscosity, occurs even within residence times of a few minutes. Carboxyl end groups, vinyl end groups and acetaldehyde are formed in amounts depending on residence time, temperature and initial moisture content of the PET flakes. 

The classic extrusion model gives insight into the screw extrusion mechanism and first-order estimates. For more accurate design equations, it is necessary to eliminate a long series of simplifying assumptions. These, in the order of significance are (a) the shear rate-dependent non-Newtonian viscosity (b) nonisothermal effects from both conduction and viscous dissipation and (c) geometrical factors such as curvature effects. Each of these... 

Generalizing to any two locations, 1 and 2, in the extruder and substituting in the definition of G the mass flow rate of solid followed by rearranging terms gives an extrusion model, which can predict the width of the solid bed at any location along the screw from knowledge of the melting rate, the solid bed barrel contact area, the solid density (function of solid temperature and internal pressure), the down chaimel solid velocity and the physical dimensions of the screw chaimel (Eq. 12.16). 

Figure 12.21 Mass balance around the melting solid plug showing the key variables needed in an extrusion model.

Finite element modelling of flow distribution in an extrusion die... 

Nassehi, V. and Pittman,. 1. F. T., 1989. Finite element modelling of flow distribution in an extrusion die. In Bush, A. W., Lewis, B.A. and Warren, M.D. (eds), Flow Modelling in Industrial Processes, Chapter 8, Ellis Horwood, Chichester. 

Next is to make sample prototype tooling and sample prototype products for the test. Samples made by machining or other simplified model making techniques do not have the same properties as the product made by molding or extrusion or whatever process is to be used (Chapter 3, PROTOTYPES). A product made this way is a sample rather than a testable prototype. Simplified prototypes may reduce trial mold cost and produce adequate test data in some cases. Its main value is appearance and feel to determine whether the aesthetics are correct. Any testing has to be done with considerable reservation and caution. 

Elucidation of degradation kinetics for the reactive extrusion of polypropylene is constrained by the lack of kinetic data at times less than the minimum residence time in the extruder. The objectives of this work were to develop an experimental technique which could provide samples for short reaction times and to further develop a previously published kinetic model. Two experimental methods were examined the classical "ampoule technique" used for polymerization kinetics and a new method based upon reaction in a static mixer attached to a single screw extruder. The "ampoule technique was found to have too many practical limitations. The "static mixer method" also has some difficult aspects but did provide samples at a reaction time of 18.6 s and is potentially capable of supplying samples at lower times with high reproducibility. Kinetic model improvements were implemented to remove an artificial high molecular weight tail which appeared at high initiator concentrations and to reduce step size sensitivity. 

Obtaining Kinetic Samples for Reactive Extrusion. To develop and test kinetic models, homogeneous samples with a well defined temperature-time history are required. Temperature history does not necessarily need to be isothermal. In fact, well defined nonisothermal histories can provide very good test data for models. However, isothermal data is very desirable at the initial stages of model building to simplify both model selection and parameter estimation problems. 

In a chemical model for mitrochondrial oxidative phosphorylation/ it has been proposed that the mitochondrial membrane, to which ATP and inorganic phosphate are attached, is held in an extended inactive form (50) by coulombic repulsion of positive charges. On reduction of the membrane by NADH one positive centre is removed, and folding of the membrane can occur with extrusion of water. This creates a non-aqueous environment around the ADP (51) and a metal ion can now catalyse the formation... 

Liposomes are formed due to the amphiphilic character of lipids which assemble into bilayers by the force of hydrophobic interaction. Similar assemblies of lipids form microspheres when neutral lipids, such as triglycerides, are dispersed with phospholipids. Liposomes are conventionally classified into three groups by their morphology, i.e., multilamellar vesicle (MLV), small unilamellar vesicle (SUV), and large unilamellar vesicle (LUV). This classification of liposomes is useful when liposomes are used as models for biomembranes. However, when liposomes are used as capsules for drugs, size and homogeneity of the liposomes are more important than the number of lamellars in a liposome. Therefore, "sized" liposomes are preferred. These are prepared by extrusion through a polycarbonate... 

The binding of carotenoids within the lipid membranes has two important aspects the incorporation rate into the lipid phase and the carotenoid-lipid miscibility or rather pigment solubility in the lipid matrix. The actual incorporation rates of carotenoids into model lipid membranes depend on several factors, such as, the kind of lipid used to form the membranes, the identity of the carotenoid to be incorporated, initial carotenoid concentration, temperature of the experiment, and to a lesser extent, the technique applied to form model lipid membranes (planar lipid bilayers, liposomes obtained by vortexing, sonication, or extrusion, etc.). For example, the presence of 5 mol% of carotenoid with respect to DPPC, during the formation of multilamellar liposomes, resulted in incorporation of only 72% of the pigment, in the case of zeaxanthin, and 52% in the case of (1-carotene (Socaciu et al., 2000). A decrease in the fluidity of the liposome membranes, by addition of other... 

The flow toward the surface is caused by the pressure under the indenter. It is analogous to the upward flow around a sphere dropped into a liquid. It is also analogous to inverse extrusion. A model of the flow has been proposed by Brown (2007) in terms of rotational slip. This model reproduces some of the observed behavior, but it is a continuum model and does not define the mechanism of rotational slip. 

---