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The rheological properties of polymer melts and polymer/blowing agent (BA) solutions are determined experimentally and the influences of material rheological properties and crystallization on low-density foaming behaviour of polylactic acid (PLA) are investigated. Understanding the rheological properties of foaming polymers allows the optimization of polymer chemical structure and the development of technologies that produce desired cell morphologies. Although the technology for producing CO2-blown polystyrene (PS) foams is well established, the rheological properties of a PS/CO2 solution, especially its extensional property, are not well understood. In this study, these properties are determined with an in-house developed, online technique, and the measured data are compared with those from commercial rheometers. The online measurement system consists of a tandem foam extrusion system and a die for measuring pressure drops. Shear viscosity is determined from the pressure drop over a straight rectangular channel, while planar extensional viscosity from the pressure drop over a thin hyperbolic channel, taking into account the pressure drop due to shearing. Measured viscosities of the polystyrene without CO2 compare well with those from commercial rheometers. With the presence of dissolved CO2, both the shear and extensional viscosities of the polystyrene are significantly reduced. The influence of CO2 on the two viscosities is found to be similar to an increase of temperature. Polylactic acid is the first mass-produced biodegradable polymer, and has potential to replace petroleum-based polymers in foaming applications. In this study, the influences of material rheological properties and crystallization on the low-density, microcellular extrusion foaming behaviour of polylactic acids (PLAs) are investigated. Comparisons are made between linear and branched PLAs and between amorphous and crystalline PLAs. The branched PLAs are found to produce foams with higher expansion ratios and reduced open-cell content compared to the linear PLA. The foaming behaviour of the linear PLA, then, is significantly improved by adding a small amount of long-chain-branched PLA. The improved cell structure with branched PLAs is attributed to their relatively high melt strength and strain to break. For the first time, it is shown that crystallization, induced by cooling and macroscopic flow during processing, increases melt strength, which aids the production of low-density foams.

Superconductors present great potential for weight reduction and increased power delivery when compared to traditional copper power delivery systems, but current systems require cryogenic cooling systems. Traditional superconductor cooling systems consist of helium cooled by helical heat exchangers made of Oxygen Free High thermal Conductivity (OFHC) copper tube. The helium is cooled by bulky heat exchangers consisting of OFHC copper coils wrapped around a cryogenic cooler heat sink for heat transfer into the working fluid. Metal foams have recently been studied in a variety of heat transfer applications, and could greatly reduce the weight of heat exchanger modules in superconductor cooling systems while simultaneously providing increased heat transfer effectiveness. Aluminum and Copper foams have been available for several years, but more recently, graphite foams, such as PocoFoam™, have been developed which have particularly good heat transfer characteristics. Using Computational Fluid Dynamics (CFD) to model a cryogenic heat exchanger application, this study examines the effectiveness and pressure drop of several metal foam heat exchangers, and compares their performance with the traditional helical coil design for superconductor cooling applications. The CFD simulation results show that a heat exchanger with the same heat sink contact area as existing helical heat exchangers weighs up to 95 percent less and can be up to 25 percent more effective, depending on system conditions such as pressure, cryogenic cooler temperature and helium inlet temperature. Aluminum and copper foam heat exchangers had comparable weight to the PocoFoam heat exchanger, but were significantly less effective than the helical or PocoFoam heat exchanger models.

In this study, crystal formation of polypropylene (PP) and poly lactic acid (PLA) in the presence of CO2 in foam extrusion process was investigated using a visualization chamber and a CCD camera. The role of pre-existing crystals on the foaming behavior of PP and PLA were studied by characterizing the foam morphology. Visualization results showed that crystals formed within the die before foaming and these crystals affect the cell nucleation behavior and expansion ratio of PP and PLA significantly. Due to the fast crystallization kinetics of PP, crystallinity should be optimum to achieve uniform cell structure with high cell density and high expansion ratio. In PLA, enhancement of crystallinity is crucial for getting foam with a high expansion ratio. It was also visualized that CO2 significantly suppresses the crystallization temperature in PP through the plasticization effect as well as its influence on flow induced crystallinity.

In this study, crystal formation of polypropylene (PP) and poly lactic acid (PLA) in the presence of CO2 in foam extrusion process was investigated using a visualization chamber and a CCD camera. The role of pre-existing crystals on the foaming behavior of PP and PLA were studied by characterizing the foam morphology. Visualization results showed that crystals formed within the die before foaming and these crystals affect the cell nucleation behavior and expansion ratio of PP and PLA significantly. Due to the fast crystallization kinetics of PP, crystallinity should be optimum to achieve uniform cell structure with high cell density and high expansion ratio. In PLA, enhancement of crystallinity is crucial for getting foam with a high expansion ratio. It was also visualized that CO2 significantly suppresses the crystallization temperature in PP through the plasticization effect as well as its influence on flow induced crystallinity.

We construct a 4d Lorentzian spin foam model capable of describing both spacelike and timelike surfaces. To do so we use a coherent state approach inspired by the Riemannian FK model. Using the coherent state method we reproduce the results of the EPRL model for Euclidean tetrahedra and extend the model to include Lorentzian tetrahedra. The coherent states of spacelike/timelike triangles are found to correspond to elements of the discrete/continuous series of SU(1,1). It is found that the area spectrum of both spacelike and timelike surfaces is quantized. A path integral for the quantum theory is defined as a product of vertex amplitudes. The states corresponding to timelike triangles are constructed in a basis diagonalised with respect to a noncompact generator. A derivation of the matrix elements of the generators of SL(2,C) in this basis is provided.