Numerical study of two ill-posed one-phase Stefan problems

We treat two related moving boundary problems. The first is the ill-posed Stefan problem for melting a superheated solid in one Cartesian coordinate. Mathematically, this is the same problem as that for freezing a supercooled liquid, with applications to crystal growth. By applying a front-fixing technique with finite differences, we reproduce existing numerical results in the literature, concentrating on solutions that break down in finite time. This sort of finite-time blow-up is characterised by the speed of the moving boundary becoming unbounded in the blow-up limit. The second problem, which is an extension of the first, is proposed to simulate aspects of a particular two-phase Stefan problem with surface tension. We study this novel moving boundary problem numerically, and provide results that support the hypothesis that it exhibits a similar type of finite-time blow-up as the more complicated two-phase problem. The results are unusual in the sense that it appears the addition of surface tension transforms a well-posed problem into an ill-posed one.

Fred’s Flow (Canada) and Murphy Well (Australia) : thick komatiitic lava flows with contrasting compositions, emplacement mechanisms and water contents

Two Archaean komatiitic flows, Fred’s Flow in Canada and the Murphy Well Flow in Australia, have similar thicknesses (120 and 160 m) but very different compositions and internal structures. Their contrasting differentiation profiles are keys to determine the cooling and crystallization mechanisms that operated during the eruption of Archaean ultramafic lavas. Fred’s Flow is the type example of a thick komatiitic basalt flow. It is strongly differentiated and consists of a succession of layers with contrasting textures and compositions. The layering is readily explained by the accumulation of olivine and pyroxene in a lower cumulate layer and by evolution of the liquid composition during downward growth of spinifex-textured rocks within the upper crust. The magmas that erupted to form Fred’s Flow had variable compositions, ranging from 12 to 20 wt% MgO, and phenocryst contents from 0 to 20 vol%. The flow was emplaced by two pulses. A first ~20-m-thick pulse was followed by another more voluminous but less magnesian pulse that inflated the flow to its present 120 m thickness. Following the second pulse, the flow crystallized in a closed system and differentiated into cumulates containing 30–38 wt% MgO and a residual gabbroic layer with only 6 wt% MgO. The Murphy Well Flow, in contrast, has a remarkably uniform composition throughout. It comprises a 20-m-thick upper layer of fine-grained dendritic olivine and 2–5 vol% amygdales, a 110–120 m intermediate layer of olivine porphyry and a 20–30 m basal layer of olivine orthocumulate. Throughout the flow, MgO contents vary little, from only 30 to 33 wt%, except for the slightly more magnesian basal layer (38–40 wt%). The uniform composition of the flow and dendritic olivine habits in the upper 20 m point to rapid cooling of a highly magnesian liquid with a composition like that of the bulk of the flow. Under equilibrium conditions, this liquid should have crystallized olivine with the composition Fo94.9, but the most magnesian composition measured by electron microprobe in samples from the flow is Fo92.9. To explain these features, we propose that the parental liquid contained around 32 wt% MgO and 3 wt% H2O. This liquid degassed during the eruption, creating a supercooled liquid that solidified quickly and crystallized olivine with non-equilibrium textures and compositions.

Fingerprinting of complex mixtures with the use of high performance liquid chromatography, inductively coupled plasma atomic emission spectroscopy and chemometrics

The molecular and metal profile fingerprints were obtained from a complex substance, Atractylis chinensis DC—a traditional Chinese medicine (TCM), with the use of the high performance liquid chromatography (HPLC) and inductively coupled plasma atomic emission spectroscopy (ICP-AES) techniques. This substance was used in this work as an example of a complex biological material, which has found application as a TCM. Such TCM samples are traditionally processed by the Bran, Cut, Fried and Swill methods, and were collected from five provinces in China. The data matrices obtained from the two types of analysis produced two principal component biplots, which showed that the HPLC fingerprint data were discriminated on the basis of the methods for processing the raw TCM, while the metal analysis grouped according to the geographical origin. When the two data matrices were combined into a one two-way matrix, the resulting biplot showed a clear separation on the basis of the HPLC fingerprints. Importantly, within each different grouping the objects separated according to their geographical origin, and they ranked approximately in the same order in each group. This result suggested that by using such an approach, it is possible to derive improved characterisation of the complex TCM materials on the basis of the two kinds of analytical data. In addition, two supervised pattern recognition methods, K-nearest neighbors (KNNs) method, and linear discriminant analysis (LDA), were successfully applied to the individual data matrices—thus, supporting the PCA approach.

Dynamics of transformation and fragmentation of composite liquid nano-particles

Recent research on particle size distributions and particle concentrations near a busy road cannot be explained by the conventional mechanisms for particle evolution of combustion aerosols. Specifically they appear to be inadequate to explain the experimental observations of particle transformation and the evolution of the total number concentration. This resulted in the development of a new mechanism based on their thermal fragmentation, for the evolution of combustion aerosol nano-particles. A complex and comprehensive pattern of evolution of combustion aerosols, involving particle fragmentation, was then proposed and justified. In that model it was suggested that thermal fragmentation occurs in aggregates of primary particles each of which contains a solid graphite/carbon core surrounded by volatile molecules bonded to the core by strong covalent bonds. Due to the presence of strong covalent bonds between the core and the volatile (frill) molecules, such primary composite particles can be regarded as solid, despite the presence of significant (possibly, dominant) volatile component. Fragmentation occurs when weak van der Waals forces between such primary particles are overcome by their thermal (Brownian) motion. In this work, the accepted concept of thermal fragmentation is advanced to determine whether fragmentation is likely in liquid composite nano-particles. It has been demonstrated that at least at some stages of evolution, combustion aerosols contain a large number of composite liquid particles containing presumably several components such as water, oil, volatile compounds, and minerals. It is possible that such composite liquid particles may also experience thermal fragmentation and thus contribute to, for example, the evolution of the total number concentration as a function of distance from the source. Therefore, the aim of this project is to examine theoretically the possibility of thermal fragmentation of composite liquid nano-particles consisting of immiscible liquid v components. The specific focus is on ternary systems which include two immiscible liquid droplets surrounded by another medium (e.g., air). The analysis shows that three different structures are possible, the complete encapsulation of one liquid by the other, partial encapsulation of the two liquids in a composite particle, and the two droplets separated from each other. The probability of thermal fragmentation of two coagulated liquid droplets is discussed and examined for different volumes of the immiscible fluids in a composite liquid particle and their surface and interfacial tensions through the determination of the Gibbs free energy difference between the coagulated and fragmented states, and comparison of this energy difference with the typical thermal energy kT. The analysis reveals that fragmentation was found to be much more likely for a partially encapsulated particle than a completely encapsulated particle. In particular, it was found that thermal fragmentation was much more likely when the volume ratio of the two liquid droplets that constitute the composite particle are very different. Conversely, when the two liquid droplets are of similar volumes, the probability of thermal fragmentation is small. It is also demonstrated that the Gibbs free energy difference between the coagulated and fragmented states is not the only important factor determining the probability of thermal fragmentation of composite liquid particles. The second essential factor is the actual structure of the composite particle. It is shown that the probability of thermal fragmentation is also strongly dependent on the distance that each of the liquid droplets should travel to reach the fragmented state. In particular, if this distance is larger than the mean free path for the considered droplets in the air, the probability of thermal fragmentation should be negligible. In particular, it follows form here that fragmentation of the composite particle in the state with complete encapsulation is highly unlikely because of the larger distance that the two droplets must travel in order to separate. The analysis of composite liquid particles with the interfacial parameters that are expected in combustion aerosols demonstrates that thermal fragmentation of these vi particles may occur, and this mechanism may play a role in the evolution of combustion aerosols. Conditions for thermal fragmentation to play a significant role (for aerosol particles other than those from motor vehicle exhaust) are determined and examined theoretically. Conditions for spontaneous transformation between the states of composite particles with complete and partial encapsulation are also examined, demonstrating the possibility of such transformation in combustion aerosols. Indeed it was shown that for some typical components found in aerosols that transformation could take place on time scales less than 20 s. The analysis showed that factors that influenced surface and interfacial tension played an important role in this transformation process. It is suggested that such transformation may, for example, result in a delayed evaporation of composite particles with significant water component, leading to observable effects in evolution of combustion aerosols (including possible local humidity maximums near a source, such as a busy road). The obtained results will be important for further development and understanding of aerosol physics and technologies, including combustion aerosols and their evolution near a source.

Porous PLGA microspheres effectively loaded with BSA protein by electrospraying combined with phase separation in liquid nitrogen

Polymer microspheres loaded with bioactive particles, biomolecules, proteins, and/or growth factors play important roles in tissue engineering, drug delivery, and cell therapy. The conventional double emulsion method and a new method of electrospraying into liquid nitrogen were used to prepare bovine serum albumin (BAS)-loaded poly(lactic-co-glycolic acid) (PLGA) porous microspheres. The particle size, the surface morphology and the internal porous structure of the microspheres were observed using scanning electron microscopy (SEM). The loading efficiency, the encapsulation efficiency, and the release profile of the BSA-loaded PLGA microspheres were measured and studied. It was shown that the microspheres from double emulsion had smaller particle sizes (3-50 m), a less porous structure, a poor loading efficiency (5.2 %), and a poor encapsulation efficiency (43.5%). However, the microspheres from the electrospraying into liquid nitrogen had larger particle sizes (400-600 m), a highly porous structure, a high loading efficiency (12.2%), and a high encapsulation efficiency (93.8%). Thus the combination of electrospraying with freezing in liquid nitrogen and subsequent freeze drying represented a suitable way to produce polymer microspheres for effective loading and sustained release of proteins.