Changes In Surface Density Research Articles

Effects of surface wettability and density change during solidification of paraffin phase change materials

Phase change materials (PCMs) are widely used for thermal energy storage and other applications. During the solidification of a PCM, a volume change occurs due to thermal expansion and structural change of the molecules. A concave shape may be created during the solidification shrinkage. This paper investigates the shrinkage profile formed during the solidification of paraffin wax and its relationship with the surface wettability (contact angle), considering the effect of density changes. The contact angle of a paraffin droplet on a surface indicates the extent of adhesion between the solid surface and paraffin. The experimental study examines a mixture of wax with nanoparticles, wax with surfactants, different coatings on the container surface, and different solidification temperatures. Enhanced adhesion and increased shrinkage height are observed due to the non-polar interaction between coated surfaces and paraffin, facilitated by induced dipole-induced dipole forces. The addition of 3% octadecylamine enhances adhesion between paraffin and the container, as driven by dipole–dipole forces between the hydroxyl group on epoxy resin-container surfaces and the hydrophilic amine group of octadecylamine. The shrinkage height increases with a decrease in the contact angle of paraffin on the surface. The shrinkage profile also changes with the solidification temperature. The highest shrinkage profile is achieved for the highest solidification temperature.

Prediction of surface urban heat island in Ho Chi Minh City, Viet Nam using remote sensing and logistic regression model

Urban heat island is a concerning environmental issue in major cities, particularly in Ho Chi Minh City. With a high rate of urbanization, the city’s extensive impervious surface area contributes to land surface temperature increase, leading to the expansion of the urban heat island phenomenon. This study was conducted in the Ho Chi Minh city region from 2009 to 2020, images from Landsat 5 (TM) and Landsat 8 (OLI/TIRS) satellites were employed to estimate land surface temperature (LST), examine the spatial distribution of the urban heat island (SUHI), and analyze changes in impervious surface area (ISA). A logistic regression model was established to predict the relationship between SUHI and ISA, with the percentage of ISA calculated by the Kernel Density Estimation method (KDE). The results revealed that the impervious surface area in the city doubled from 2009 to 2020, accounting for 29.54% of the city’s area, which correlated with a significant expansion of SUHI from 37,000 ha to 53,000 ha. The SUHI predicting model exhibited good discrimination ability (AUC = 0.98) and total accuracy of 96% through Hosmer & Lemeshow Test in R. The probability of the predicted SUHI showed a high correlation (R2 = 0.885) with the actual SUHI. In areas where ISA increased from 60% to 80%, the probability of SUHI occurrence also increased from 52.85% to 98%. This study presented a novel approach, utilizing statistical modeling to accurately quantify SUHI based on changes in impervious surface density. This method can contribute to an effective evaluation of heat-related health risks, provide the government and urban planners with a precise orientation in management toward sustainable development.

Impact of Surface Ligand Identity and Density on the Thermodynamics of H Atom Uptake at Polyoxovanadate-Alkoxide Surfaces.

An understanding of how molecular structure influences the thermodynamics of H atom transfer is critical to designing efficient catalysts for reductive chemistries. Herein, we report experimental and theoretical investigations summarizing structure-function relationships of polyoxovanadate-alkoxides that influence bond dissociation free energies of hydroxide ligands located at the surface of the cluster. We evaluate the thermochemical descriptors of O-H bond strength for a series of clusters, namely [V6O13-x(OH)x(TRIOLR)2]-2 (x = 2, 4, 6; R = NO2, Me) and [V6O11-x(OMe)2(OH)x(TRIOLNO2)2]-2, via computational analysis and open circuit potential measurements. Our findings reveal that modifications to the TRIOL ligand (e.g., changing from the previously reported electron withdrawing nitro-backed ligand to the electron-donating methyl variant) have limited influence on the strength of surface O-H bonds as a result of near complete thermodynamic compensation in these systems (i.e., correlated changes in redox potential and cluster basicity). In contrast, changes in surface density of alkoxide ligands via direct alkoxylation of the polyoxovanadate-alkoxide surface result in measurable increases in bond dissociation free energies of surface O-H bonds for the mixed-valent derivatives. Our findings indicate that the extent of (de)localization of electron density across the cluster core has an impact on the bond dissociation free energies of surface O-H bonds across all oxidation states of the assembly.

Numerical Experiments for Surfactant Infiltration in the Vadose Zone to Demonstrate Concentration-Dependent Capillarity, Viscosity, and Sorption Characteristics

Surfactants (i.e., solutes that reduce the surface tension of water) exist in the subsurface either naturally or are introduced to the subsurface due to anthropogenic activities (e.g., agricultural purposes, environmental remediation strategies). Surfactant-induced changes in surface tension, contact angle, density, and viscosity alter the water retention and conduction properties of the vadose zone. This research numerically investigates the effects of surfactants in the vadose zone by comparing the flow and transport of three different surfactant solutions, namely butanol, ethanol, and Triton X-100. For each surfactant case, surfactant-specific concentration-dependent surface tension, contact angle, density, and viscosity relationships were incorporated by modifying a finite element unsaturated flow and transport code. The modified code was used to simulate surfactant infiltration in the vadose zone at residual state under intermittent boundary conditions. The modelling results show that all three surfactant solutions led to unique and noteworthy differences in comparison to the infiltration of pure water containing a conservative tracer. Results indicate that surfactant infiltrations led to complex patterns with reduced vertical movement and enhanced horizontal spreading, which are a function of concentration-dependent surface tension, density, contact angle, viscosity and sorption characteristics. The findings of this research will help understanding the effects of surfactant presence in the subsurface on unsaturated flow and its possible links to future environmental problems.

Surface stress decomposition in large amplitude oscillatory interfacial dilatation of complex interfaces

HypothesisMultiphase materials are often subjected to large deformations during processing, but the rheological responses of complex interfaces (e.g. stabilized by proteins) in this nonlinear deformation regime are still poorly understood. We expect nonlinearities in the response to be introduce by changes of the interfacial network and surface density of the emulsifier. ExperimentsLarge amplitude oscillatory dilatation (LAOD) experiments were performed on WPI-, pea albumin-, pea globulin- and rapeseed lecithin-stabilized interfaces and analyzed with a general stress decomposition (GSD). With GSD, the stress response was decomposed into the four stress terms (τ1-τ4). Here, τ1 and τ2 represent, the elastic and viscous contribution of the odd Fourier harmonics, and τ3 and τ4 represent the dissipative and recoverable contribution of the even harmonics. FindingsAnalysis of WPI-, pea albumin-, pea globulin- and rapeseed lecithin-stabilized interfaces revealed that higher odd harmonics (k≥3) describe in-plane network responses and that even harmonics describe surface density changes. Analysis of these complex interfaces showed that GSD is a valuable tool for (quantitative) description of interfacial responses in LAOD, providing new insights into the origin of asymmetric nonlinear stress responses.

Investigating the effects of carbon-based nanofluids on the interfacial evaporation of salt water under infrared light

Among the numerous alternatives to solving global water scarcity, carbon-based nanoparticles seem to be the likely preference for obtaining fresh water, due to their thermal conductivity, affordability, and effectiveness. In this study, carbon-based nanofluids were prepared using carbon black and graphene inclusions to determine the impact of nanoparticles on salt water evaporation rates and to evaluate the photothermal, heat transfer, and water evaporation kinetics. Different percentages (0.05. 0.5, and 0.1 wt%) of carbon black and graphene were added into a 3.5 wt% sodium chloride (NaCl) solution (simulated sea water), tap water, and deionized (DI) water. Test results revealed that 0.1 wt% of carbon-based nanoparticles homogenized with a base fluid provided higher water evaporation rates than either the 0.5% or 0.05% carbon-based nanoparticles under a simulated infrared light with a power of 125 W and intensity of 440 W/m2 for 2 h. For instance, using 0.1 wt% carbon black along with a black absorber increased evaporation rates by 18.77% for salt water, 17.98% for tap water, and 16.05% for DI water under the same conditions. Adding a black absorber at the base of the fluid further increased the evaporation rate and water temperatures by a considerable amount. Due to the existence of carbon-based nanoparticles, the base fluid’s temperature was increased, and the surface tension was decreased, which in turn increased the water evaporation rates significantly. In all the tests, the addition of carbon black nanoparticles showed slightly better evaporation results than the rest of the nanoparticles, which may be because of the changes in surface oxidation, agglomeration, density and surface area. This study may provide a new direction for fabricating more advanced systems using carbon-based nanoparticles for industrial applications such as solar desalination, wastewater treatment, solvent evaporation, environmental cleaning, and salt and mineral production.

Acoustic Insulation Mechanism of Membrane-Type Acoustic Metamaterials Loaded with Arbitrarily Shaped Mass Blocks of Variable Surface Density.

Membrane-type acoustic metamaterials (MAMs) have recently received widespread attention due to their good low-frequency sound-transmission-loss (STL) performance. A fast prediction method for the STL of rectangular membranes loaded with masses of arbitrary shapes and surface density values is proposed as a semi-analytical model for calculating the STL of membrane-type acoustic metamaterials. Through conformal mapping theory, the mass blocks of arbitrary shapes were transformed into regular shapes, which simplified the calculation model of acoustic propagation loss prediction, and the prediction results were verified by finite element simulations. The results show that the change in mass surface density was closely related to the size and frequency distribution of STL. The influence of the mass center on the STL and characteristic frequency of the film metamaterial is discussed.

On the performance of equiangular mascon solution in GRACE-like missions

Mass concentration (mascon) solutions for GRACE (Gravity Recovery and Climate Experiment) data are widely used in various regional-to-global mass change studies. The current advances in the mascon solution have mainly concentrated on improving the spatial resolution of the solution, enhancing the applied least-squares regularization, and the characterization of the solution errors. Most of the mascon solutions are obtained on the equal-area grid, inducing complexities in creating the grid and its presentation. In this regard, estimation of the mascon solutions on equiangular grids can be appealing. Furthermore, in the equal-area methods, there is no global criterion to determine the size of the mascon areas. The mascon size is usually chosen in a subjective manner which hampers the objective application of different mascon solutions. In view of these challenges, two main questions are addressed in this study: i) what kind of modifications should be made in computation scheme of the mascon solution if equiangular grids are used to account for different areas of the grid patches, and ii) in case of non-equiangular solutions, how to define an objective criterion for the patch sizes based on the resolution of both the observation and the signal of interest. We investigate the performance of the high-resolution mascon-based approach, proposed by Abedini et al. [2021], which uses GRACE-like observations similar to level-1 data for a period of one month over the Greenland region. Two main practical issues are studied on the estimation of the surface density changes as follows. First, we show that for equiangular grids, the area of the patches should be accounted for in the regularization by introducing area-affected weights for the unknown parameters. We investigate the effect of three different area-affected weighting strategies on the derived solution. Secondly in order to obtain proper size for the patches, a novel approach is presented to investigate the performance of the mascon solution using the analysis of the resolution matrix entries. The proposed resolution analysis is used to obtain the optimal patch size for the discretization of the area of interest. Based on the results, it is demonstrated that the minimum legible patch size in the Greenland area for the current settings of the GRACE observations is 0.5 degree in the NS direction and a latitude-adaptive grid-size rather than equiangular grids at high latitude regions in the EW direction.

Effect of Fluorescent Labels on DNA Affinity for Gold Nanoparticles.

Fluorophore (FD) labeling is widely used for detection and quantification of various compounds bound to nanocarriers. The systems, composed of gold nanoparticles (GNPs) and oligonucleotides (ONs) labeled with FDs, have wide applications. Our work was aimed at a systemic study of how FD structure (in composition of ON-FDs) influenced the efficiency of their non-covalent associates’ formation with GNPs (ON-FD/GNPs). We examined ONs of different length and nucleotide composition, and corresponding ON-FDs (FDs from a series of xanthene, polymethine dyes; dyes based on polycyclic aromatic hydrocarbons). Methods: fluorometry, dynamic light scattering, high performance liquid chromatography, gel electrophoresis, molecular modeling and methods of thermodynamic and statistical analysis. We observed significant, differing several times, changes in surface density and Langmuir constant values of ON-FDs vs. ONs, evidence for the critical significance of FD nature for binding of ON-FDs with GNPs. Surface density of ON-FD/GNPs; hydrophobicity and total charge of ON or ON-FD; and charge and surface area of FDs were revealed as key factors determining affinity (Langmuir constant) of ON or ON-FDs for GNPs. These factors compose a specific set, which makes possible the highly reliable prediction of efficiency of ONs and ON-FDs binding with GNPs. The principal possibility of creating an algorithm for predictive calculation of efficiency of ONs and GNPs interaction was demonstrated. We proposed a hypothetical model that described the mechanism of contact interaction between negatively charged nano-objects, such as citrate-stabilized GNPs, and ONs or ON-FDs.

Estimation of surface density changes using a mascon method in GRACE-like missions

Gravity Recovery and Climate Experiment (GRACE) data are a valuable source of information for estimating hydrological mass changes. Several approaches have been conducted to investigate surface density changes from satellite-based observations. The traditional approaches are mainly based on the Stokes coefficients, related to a spherical harmonic representation of the gravitational potential. This study aims to develop an alternative method to estimate the temporal variations in water storage. It is based on a specific type of mascon technique that investigates the possibility of obtaining a solution without Stokes coefficients. The method uses a piecewise constant surface density function to estimate surface density changes based on the GRACE satellite-to-satellite tracking (SST) data. The surface density changes are directly obtained from the variations in positions and velocities of the two GRACE satellites. We therefore avoid the series truncation and aim to improve the leakage problem at the price of higher numerical burden. The proposed method is numerically tested on synthetic data similar to level-1 GRACE data for a period of one month. Two regularization methods, the well-known Tikhonov solution and a method that accounts for the areas of different patches, are employed to obtain a stable solution. The accuracy assessment over the Greenland area indicates that the estimated values are reliable and statistically significant, a further confirmation of the efficacy and stability of the method.

Ring Formation by Coagulation of Dust Aggregates in the Early Phase of Disk Evolution around a Protostar

Abstract Ring structures are observed through (sub)millimeter dust continuum emission in various circumstellar disks from the early stages of class 0 and I to the late stage of class II young stellar objects (YSOs). In this paper, we study one of the possible scenarios for such ring formation, which is the coagulation of dust aggregates in the early stage. The dust grains grow in an inside-out manner because the growth timescale is roughly proportional to the orbital period. The boundary of the dust evolution can be regarded as the growth front, where the growth time is comparable to the disk age. Using radiative transfer calculations based on the dust coagulation model, we find that the growth front can be observed as a ring structure because the dust surface density changes sharply at this position. Furthermore, we confirm that the observed ring positions in YSOs with an age of ≲1 Myr are consistent with the growth front. The growth front could be important in creating the ring structure in particular for the early stage of disk evolution, such as class 0 and I sources.

Time-Dependent Anti-Demineralization Effect of Silver Diamine Fluoride.

This study compared the demineralization resistance of teeth treated with silver diamine fluoride (SDF) to that treated with fluoride varnish. A total of 105 healthy bovine incisors were divided into control, fluoride varnish, and SDF groups. The enamel surface density change was then measured by micro-computed tomography (micro-CT) at three depths. The demineralized zone volume was measured on 3D micro-CT images to evaluate the total demineralization rate. The enamel surface morphology was assessed by scanning electron microscope. The enamel density had continuously decreased while demineralization increased in the control and fluoride varnish groups. The enamel density had increased in the SDF group till the 7th day of demineralization treatment and decreased thereafter. However, the decrease in the SDF group was less severe than that in the other groups (p < 0.05). The demineralized enamel volume had increased through treatment and was the highest in the control group, followed by the fluoride varnish and SDF group. The enamel surface morphology was the roughest and most irregular in the control group, followed by the fluoride varnish group and SDF groups.

Consolidation effects on relationships among soil erosion properties and soil physical quality indicators

Consolidation of soil by wetting and drying cycles following tillage rapidly changes the soil physical properties but little is known about how these changes impact soil erosion. The objective of this study was to develop equations to predict soil erodibility (Kd) and critical shear stress (τc) in response to consolidation based upon changes in soil bulk density, saturated hydraulic conductivity, water content, soil penetration strength and surface shear strength following a series of wetting and drying cycles. Air-dried soil from four contrasting soil series was loosely filled into 20 soil cylinders (80 total) to simulate freshly tilled conditions. Soil physical and erosion properties were determined at six time periods (0, 1, 3, 5, 7, 10 days) following daily simulated rainfall of 33 mm h−1 for 1 h and 24 h of drainage/drying. The Jet Test device was used to determine Kd, and τc. The bulk density increased with time due to consolidation following the simulated precipitation events with the largest increase (50–100 % of the total) occurring after the first wetting/drying cycle. The Onstad consolidation model tended to over-predict this initial surface bulk density increase, whereas, an exponential model better represented the surface and depth-averaged bulk density changes for the four soils tested. The shear strength and soil penetration resistance increased dramatically after the first wetting/drying cycle then decreased to a fairly stable value in response to subsequent wetting/drying cycles. The saturated hydraulic conductivity, Ks, decreased so rapidly with accumulated rainfall that an exponential decay model could not match the decrease in Ks as the soil consolidated. The best indicators of erodibility response to consolidation were accumulated rain, surface bulk density, saturated hydraulic conductivity and soil penetration resistance at the 1.3 cm depth. The best indicators of critical shear stress were accumulated rainfall, soil penetration resistance at 1.3 cm and saturated hydraulic conductivity. Because these erosion parameters had intercepts that were dependent upon the soil series, prediction of changes in soil erosion with time following tillage will be soil-specific.

Effect of instantaneous change of surface temperature and density on an unsteady liquid–vapour front in a porous medium

This article presents a comprehensive analysis of time dependent condensation model embedded in a porous medium with variations in liquid–vapour densities. Both similarity and asymptotic solutions for the unsteady liquid–vapour phase change front are obtained with the manifestation of various pertinent parameters. The obtained results are compared which congregate well as depicted clearly in graphs. Results indicate that with different diffusivity and contrast ratios, the similarity front parameter is found to be gradually declining with variation in a density ratio. We have shown for the condensation process, the ratio of sensible to latent heat is independent of time and is equal to the half of the Stefan number of the liquid phase.

Kynurenic acid as the neglected ingredient of commercial baby formulas

The global increase in resorting to artificial nutritional formulas replacing breastfeeding has been identified among the complex causes of the obesity epidemic in infants and children. One of the factors recently recognized to influence metabolism and weight gain is kynurenic acid (KYNA), an agonist of G protein-coupled receptor (GPR35). Therefore the aim of the study was to determine the concentration of KYNA in artificial nutritional formulas in comparison with its level in human breast milk and to evaluate developmental changes in rats exposed to KYNA enriched diet during the time of breastfeeding. KYNA levels were measured in milk samples from 25 heathy breast-feeding women during the first six months after labor and were compared with 21 time-adjusted nutritional formulas. Animal experiments were performed on male Wistar rats. KYNA was administered in drinking water. The content of KYNA in human milk increases more than 13 times during the time of breastfeeding while its level is significantly lower in artificial formulas. KYNA was detected in breast milk of rats and it was found that the supplementation of rat maternal diet with KYNA in drinking water results in its increase in maternal milk. By means of the immunoblotting technique, GPR35 was evidenced in the mucosa of the jejunum of 1-day-old rats and distinct morphological changes in the jejunum of 21-day-old rats fed by mothers exposed to water supplemented with KYNA were found. A significant reduction of body weight gain of rats postnatally exposed to KYNA supplementation without changes in total body surface and bone mineral density was observed. The rat offspring fed with breast milk with artificially enhanced KYNA content demonstrated a lower mass gain during the first 21 days of life, which indicates that KYNA may act as an anti-obesogen. Further studies are, therefore, warranted to investigate the mechanisms regulating KYNA secretion via breast milk, as well as the influence of breast milk KYNA on mass gain. In the context of lifelong obesity observed worldwide in children fed artificially, our results imply that insufficient amount of KYNA in baby formulas could be considered as one of the factors associated with increased mass gain.

A Comparative Study of Force Measurements in Solution Using Micron and Nano Size Probe

Atomic force microscopy (AFM) is a device that is used for not only high-resolution imaging but also used for measuring forces. It is possible to quantify the surface density change for both colloid and nano probe as well as silica surface. By changing the quantity of ions within a potassium chloride solution, it then becomes possible to evaluate the quantity of ions that attach themselves to AFM colloid probe, nano probe and silica samples. In this study, the force was measured between AFM probes and silica surface in different ionic concentrations. Two different types of AFM probe were used: a colloid probe with a radius of 500 nano-meters and a nano probe with a radius of 10 nano-meters. This study is focused on measuring how the force magnitude, especially electrical double layer force, varied between the two types of probes by changing ionic concentrations. For all test trials, the results agreed with the electrical double layer theory. Although the micron probe was almost an exact match for all ranges, the nano probe was closest within its short-range forces. This is attributed to the formula use when analyzing the electrical double layer force. Because the formula was originally calculated for the micron probe, the shape and size of the nano probe created too many variables for an exact match. Along with quantifying the forces, this experiment allowed for an observation of Van der Waals force making it possible to calculate the Hamaker constant. Conclusively, all results show that the obtained surface charge density increases as the ionic concentration increases. In addition, through the comparison of the results obtained from the nano-sized probe and the micron-sized probe, it was concluded that nano size probe mapped higher surface charge density above the silica surface than the micron-sized probe under the same conditions.

The linear theory of tidally excited spiral density waves: application to CV and circumplanetary disks

We revisit linear tidal excitation of spiral density waves in the disks of cataclysmic variables (CVs), focusing on scalings with orbital Mach number in order to bridge the gap between numerical simulations and real systems. If an inner Lindblad resonance (ILR) lies within the disk, ingoing waves are robustly excited, and the angular-momentum flux they carry is independent of Mach number. But in most CVs, the ILR lies outside the disk. The wave flux and its scaling with Mach number are then very sensitive to conditions near the disk edge. If the temperature and sound speed vanish there, excitation tends to be exponentially suppressed. If the Mach number remains finite in the outer parts but the radial and vertical density scale lengths become comparable due to subkeplerian rotation, resonance can occur with acoustic-cutoff and stratification frequencies. These previously neglected resonances excite waves, but the Mach-number scaling remains very steep if the radial scale length decreases gradually. The scaling can be less strong - algebraic rather than exponential - if there are sharp changes in surface density at finite sound speed. Shocks excited by streamline-crossing or by the impact of the stream from the companion are unlikely to be important for the angular-momentum budget, at least in quiescence. Our results may also apply to circumplanetary disks, where Mach numbers are likely lower than in CVs.

Deep winter convection and phytoplankton dynamics in the NW Mediterranean Sea under present climate and future (horizon 2030) scenarios

Deep water convection (DC) in winter is one of the major processes driving open-ocean primary productivity in the Northwestern Mediterranean Sea. DC is highly variable in time, depending on the specific conditions (stratification, circulation and ocean-atmosphere interactions) of each specific winter. This variability also drives the interannual oscillations of open-ocean primary productivity in this important region for many commercially-important fish species. We use a coupled model system to 1) understand to what extent DC impacts phytoplankton seasonality in the present-day and 2) to explore potential changes in future scenarios (~2030). Our model represents quite accurately the present-day characteristics of DC and its importance for open-ocean phytoplankton blooms. However, for the future scenarios the importance of deep nutrients in fertilizing the euphotic layer of the NW Mediterranean decreases. The model simulates changes in surface density and on the levels of kinetic energy that make mesoscale activity associated with horizontal currents to become a more important fertilization mechanism, inducing subsequently phenological changes in seasonal plankton cycles. Because of our focus on the open-sea, an exact quantification of the impact of those changes on the overall biological production of the NW Mediterranean cannot be made at the moment.

Effects of Mixing Ratio of Silicon Carbide Particles on the Etch Characteristics of Reaction-Bonded Silicon Carbide

We prepared a number of reaction-bonded silicon carbides (RBSCs) made from various mixing ratios of raw SiC particles, and investigated their microstructure and etch characteristics by Reactive Ion Etch (RIE). Increasing the amount of 9.5 μm-SiC particles results in a microstructure with relatively coarser Si regions. On the other hand, increasing that of 2.6 μm-SiC particles produces much finer Si regions. The addition of more than 50 wt% of 2.6 μm-SiC particles, however, causes the microstructure to become partially coarse. We also evaluated their etching behaviors in terms of surface roughness (Ra), density and weight changes, and microstructure development by employing Confocal Laser Scanning Microscope (CLSM) and Scanning Electron Microscope (SEM) techniques. During the etching process of the prepared samples, we confirmed that the residual Si region was rapidly removed and formed pits isolating SiC particles as islands. This leads to more intensified ion field on the SiC islands, and causes physical corrosion on them. Increased addition of 2.6 μm-SiC particles produces finer residual Si region, and thus decreases the surface roughness (Ra.) as well as causing weight loss after etching process by following the above etching mechanism.

STEFAN PROBLEMS FOR MELTING NANOSCALED PARTICLES

Under certain conditions, the mathematical models governing the melting of nano-sized particles predict unphysical results, which suggests these models are incomplete. This thesis studies the addition of different physical effects to these models, using analytic and numerical techniques to obtain realistic and meaningful results. In particular, the mathematical of solutions to ill-posed Stefan problems is examined, and the regularisation of this blow-up via kinetic undercooling. Other effects such as surface tension, density change and size-dependent latent heat of fusion are also analysed.