Expansion ratio, critical, saturation

Further experiments show a second crilical expansion ratio corresponding to a satu ration ratio of about eight. At higher saturation ratios, dense clouds of fine drops form, the number increasing with the supersaturation. The number of drops produced between the two critical values of the saturation ratio i.s small compared with the number produced above the second limit. 

Of critical importance, analysis of poly(methyl methacrylate) (PMMA) showed that at a saturation temperature, T, of 40°C, a saturation pressure, P%, of 1,500 psig (at these conditions, carbon dioxide is considered a supercritical fluid), and a saturation time, ts, of 24 h, a 1 mm thick disk absorbed 16.4 wt% carbon dioxide. Additionally, at a foaming temperature, Tf, of 120°C and a foaming time, tf, of 1 min, PMMA had a stable volumetric expansion ratio of 20. Other polymers also absorbed significant quantities of carbon dioxide, such as polystyrene (PS) and poly(vinylidene chloride-co-acrylonitrile) (P(VDC-AN)), which absorbed 8.9 and 2 wt% carbon dioxide, respectively, yet the stable foams that were formed had expansion ratios of less than 2 at the same conditions used to form the PMMA samples. Another polymer poly(vinyl methyl ketone) (PVMK) achieved an expansion ratio of 20. However, the foams were unstable, readily collapsed, and exhibited large voids ( 5 mm diameter), which are inconsistent with microcellular foams. The fact that PVMK readily collapsed after the foaming process made it difficult to determine the concentration of carbon dioxide in the sample. These results led to the eventual incorporation of the MMA monomer into the polymer formulation from the standpoint of carbon dioxide-induced microcellular foamability. 

With the clean system, no aerosol forms unless the expansion exceeds a limit cone-sponding to a saturation ratio of about four. At this critical value, a shower of drops forms and fails. The number of drops in the shower remains about the same no matter how often the expansion process is repeated, indicating that these condensation nuclei arc regenerated. 

Ice particle measurements in the expansion experiment with 40% OC soot aerosol markedly differ from the 16% OC sample. Note that the optical particle spectrometer hardly detects any ice particles. Additionally, extinction signatures of ice are barely visible in the infrared spectra and diere is only a weak intensity increase of the back-scattered laser light in course of the expansion. The number concentration of ice crystals is less than 10 cm, thus < 1% of the seed aerosol particles act as deposition ice nuclei. In contrast to the 16% OC experiment, no precise critical ice saturation ratio can be specified for the 40% OC soot sample. RHi continues to increase to 190% because very little water vapour is lost on the small surface area of the scarce ice crystals. In summary, die comparison of the two expansion experiments provides first evidence that a higher fraction of organic carbon notably suppresses the ice nucleation potential of flame soot particles. 

The self-similar solution of an unsteady rarefaction wave in a gas-vapour mixture with condensation is investigated. If the onset of condensation occurs at the saturation point, the rarefaction wave is divided into two zones, separated by a uniform region. If condensation is delayed until a fixed critical saturation ratio Xc > 1 is reached, a condensation discontinuity of the expansion type is part of the solution. Numerical simulation, using a simple relaxation model, indicates that time has to proceed over more then two decades of characteristic times of condensation before the self-similar solution can be recognized. Experimental results on heterogeneous nucleation and condensation caused by an unsteady rarefaction wave in a mixture of water vapour, nitrogen gas and chromium-K)xide nuclei are presented. The results are fairly well described by the numerical rdaxation model. No plateau formation could be observed. 

A typical experiment is shown in Fig. 4. Pressure, temperature, vapour mass fraction and saturation ratio are compared with numerical calculation. The characteristic time r, required for numerical evaluation, is obtained by a fit of the experimental vapour mass fraction signal, resulting in r = 5 ms. The chosen values of critical saturation ratio and piston velocity are rather arbitrary. The experimental saturation ratio is calculated from pressure, temperature and vapour mass fraction. When no liquid mass can be detected, the vapour mass fraction is set to the initial value. Experiment and numerical simulation agree fairly well. The first part of the expansion of the gas-vapour mixture is isentropic and accounts for an increase of the saturation ratio. Condensation on the heterogeneous nuclei starts at a value of the measured saturation ratio of about three. After the onset of condensation a rise in temperature is observed due to the release of latent heat. The saturation ratio tends to unity as time increases. The plateau formed in the numerical solution is not observed in the experimental signal. Obviously, the experimental condition is far from self-similarity, and the expansion process is still in its early stage, where relaxation is dominant. The simple numerical model does not describe accurately the... 

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