Plastics modelling diffusion from plastic

It is well known that enhanced deposition in the first few airways occurs due to the turbulence produced. Turbulent diffusion is accounted for by using factors (ratio of observed deposition to calculated diffusion deposition) to correct the diffusion deposition. These had formerly been measured by Martin and Jacobi (1972) in a dichotomous plastic model of the upper airways. The data used here are from measurements performed by Cohen (1986) using hollow casts of the upper bronchial tree which included a larynx. This cast was tested using cyclic flow with deposition measured for 0.03, 0.15 and 0.20 urn diameter particles. Her turbulent diffusion factors are used in the calculation here (14 for generation 0, and 2 for generations 1 to 6). 

Figge, K. 1980, Migration of Components from Plastics-Packaging Materials Into Packed Goods - Test methods and Diffusion Models. Progress Polymer Science, 6, 187-252. 

Figge, K., 1980, Migration of components from plastics-packaging materials into packed goods - test methods and diffusion models. Prog. Polym. Sci., 6,187-252. 

An effect not considered in the above models is the added resistance, caused by fouling, to solute back-diffusion from the boundary layer. Fouling thus increases concentration polarization effects and raises the osmotic pressure of the feed adjacent to the membrane surface, so reducing the driving force for permeation. This factor was explored experimentally by Sheppard and Thomas (31) by covering reverse osmosis membranes with uniform, permeable plastic films. These authors also developed a predictive model to correlate their results. Carter et al. (32) have studied the concentration polarization caused by the build-up of rust fouling layers on reverse osmosis membranes but assumed (and confirmed by experiment) that the rust layer had negligible hydraulic resistance. 

Tick s second law of diffusion was used to model removal of plasticizer from packaging films using different solvents to simulate the extracting action of food products. Good agreement between the model and the experiment was obtained. The rate of di-(2-ethylhexyl) phthalate extraction depends on its content in PVC (for 50% plasticizer, the extraction rate was 30 g m h" and for 35% plasticizer in formulation, the extraction rate was 2.3 g m h" This is an example of mutual (cooperative) diffiisioa The plasticizer is replaced by solvent. In another study of cooperative diffusion of DOP in dilute solution of polystyrene, a temperature decrease to the neighborhood of the glass transition temperature had profound effect on solvent mobility and thus on the diffusion proeess. Further theoretical discussion of mutual diffusion can be found elsewhere. ... 

We have known for years that the behaviour of volatile materials migrating from and through plastics can be described by Pick s Law of Diffusion. Theory and practical experience with these materials indicate that they can be monitored to ensure their safe and satisfactory use with foods. But the migration of non-volatiles from plastics is by no means so well understood and has been the subject of research, not only at PIRA, but at several other Packaging Research Laboratories over the last five years. Simple model migration systems have been used at PIRA for example, systems based on a single polymer containing one non-volatile additive, exposed to pure liquids either separately or in mixtures. The major results of this work are as follows ... 

Sewell and co workers [145-148] have performed molecular dynamics simulations using the HMX model developed by Smith and Bharadwaj [142] to predict thermophysical and mechanical properties of HMX for use in mesoscale simulations of HMX-containing plastic-bonded explosives. Since much of the information needed for the mesoscale models cannot readily be obtained through experimental measurement, Menikoff and Sewell [145] demonstrate how information on HMX generated through molecular dynamics simulation supplement the available experimental information to provide the necessary data for the mesoscale models. The information generated from molecular dynamics simulations of HMX using the Smith and Bharadwaj model [142] includes shear viscosity, self-diffusion [146] and thermal conductivity [147] of liquid HMX. Sewell et al. have also assessed the validity of the HMX flexible model proposed by Smith and Bharadwaj in molecular dynamics studies of HMX crystalline polymorphs. 

Another approach to obtain migration data particularly for some plastic materials is the use of modelling. Today this approach is only suitable for certain materials but is accepted by the EU Commission. Diffusion within, and migration from, food contact materials are predictable processes that can be described by mathematical equations. Mass transfer from a plastic material, for instance, into food simulants obeys Tick s laws of diffusion in most cases. Physico-mathematical diffusion models have been established, verified and validated for migration from many plastics into food simulants and are accepted in the USA and in the EU. 

In the previous subsection, we used the example of diffusion to illustrate the proliferation of temporal scales in one of the central problems in the study of materials. The present discussion has a similar aim in that we will briefly review fhe features of plasticity that place modeling demands at many different spatial scales. Though plasticity is also an area of immense importance, the conceptual foundations for its analysis both at the macroscopic level as well as from a reductionist perspective are not nearly as mature as is the study of diffusion. Recall that at the macroscopic scale in the context of diffusion we have the time-honored diffusion equation while at the microseopic scale we have the machinery of transition state theory as the basis of a well-defined scheme for informafion passage. By way of contrast, the macroscopic equations of plasticity are not nearly as robust as the diffusion equafion and there is no clear path for... 

The kinetic aspect common to all the topics discussed in this chapter is the pyrolysis reactions. The same kinetic approach and similar lumping techniques are conveniently applied moving from the simpler system of ethane dehydrogenation to produce ethylene, up to the coke formation in delayed coking processes or to soot formation in combustion environments. The principles of reliable kinetic models are then presented to simulate pyrolysis of hydrocarbon mixtures in gas and condensed phase. The thermal degradation of plastics is a further example of these kinetic schemes. Furthermore, mechanistic models are also available for the formation and progressive evolution of both carbon deposits in pyrolysis units and soot particles in diffusion flames. 

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