Newton's aerodynamic problem in media of chaotically moving particles

Plakhov, A.Y.; Torres, D., (2005) 'Newton's aerodynamic problem in media of chaotically moving particles', Sbornik: Mathematics 196(6) pp.885-933 RAE2008

Preparation and characterisation of ceria particles

Cerium dioxide (ceria) nanoparticles have been the subject of intense academic and industrial interest. Ceria has a host of applications but academic interest largely stems from their use in the modern automotive catalyst but it is also of interest because of many other application areas notably as the abrasive in chemical-mechanical planarisation of silicon substrates. Recently, ceria has been the focus of research investigating health effects of nanoparticles. Importantly, the role of non-stoichiometry in ceria nanoparticles is implicated in their biochemistry. Ceria has well understood non-stoichiometry based around the ease of formation of anion vacancies and these can form ordered superstructures based around the fluorite lattice structure exhibited by ceria. The anion vacancies are associated with localised or small polaron states formed by the electrons that remain after oxygen desorption. In simple terms these electrons combine with Ce4+ states to form Ce3+ states whose larger ionic radii is associated with a lattice expansion compared to stoichiometric CeO2. This is a very simplistic explanation and greater defect chemistry complexity is suggested by more recent work. Various authors have shown that vacancies are mobile and may result in vacancy clustering. Ceria nanoparticles are of particular interest because of the high activity and surface area of small particulates. The sensitivity of the cerium electronic band structure to environment would suggest that changes in the properties of ceria particles at nanoscale dimensions might be expected. Notably many authors report a lattice expansion with reducing particle size (largely confined to sub-10 nm particles). Most authors assign increased lattice dimensions to the presence of a surface stable Ce2O3 type layer at low nanoparticle dimensions. However, our understanding of oxide nanoparticles is limited and their full and quantitative characterisation offers serious challenges. In a series of chemical preparations by ourselves we see little evidence of a consistent model emerging to explain lattice parameter changes with nanoparticle size. Based on these results and a review of the literature it is worthwhile asking if a model of surface enhanced defect concentration is consistent with known cerium/cerium oxide chemistries, whether this is applicable to a range of different synthesis methods and if a more consistent description is possible. In Chapter one the science of cerium oxide is outlined including the crystal structure, defect chemistry and different oxidation states available. The uses and applications of cerium oxide are also discussed as well as modelling of the lattice parameter and the doping of the ceria lattice. Chapter two describes both the synthesis techniques and the analytical methods employed to execute this research. Chapter three focuses on high surface area ceria nano-particles and how these have been prepared using a citrate sol-gel precipitation method. Changes to the particle size have been made by calcining the ceria powders at different temperatures. X-ray diffraction methods were used to determine their lattice parameters. The particles sizes were also assessed using transmission electron microscopy (TEM), scanning electron microscopy (SEM), and BET, and, the lattice parameter was found to decrease with decreasing particle size. The results are discussed in light of the role played by surface tension effects. Chapter four describes the morphological and structural characterization of crystalline CeO2 nanoparticles prepared by forward and reverse precipitation techniques and compares these by powder x-ray diffraction (PXRD), nitrogen adsorption (BET) and high resolution transmission electron microscopy (HRTEM) analysis. The two routes give quite different materials although in both cases the products are essentially highly crystalline, dense particulates. It was found that the reverse precipitation technique gave the smallest crystallites with the narrowest size dispersion. This route also gave as-synthesised materials with higher surface areas. HRTEM confirmed the observations made from PXRD data and showed that the two methods resulted in quite different morphologies and surface chemistries. The forward route gives products with significantly greater densities of Ce3+ species compared to the reverse route. Data are explained using known precipitation chemistry and kinetic effects. Chapter five centres on the addition of terbia to ceria and has been investigated using XRD, XRF, XPS and TEM. Good solid solutions were formed across the entire composition range and there was no evidence for the formation of mixed phases or surface segregation over either the composition or temperature range investigated. Both Tb3+ and Tb4+ ions exist within the solution and the ratios of these cations are consistent with the addition of Tb8O15 to the fluorite ceria structure across a wide range of compositions. Local regions of anion vacancy ordering may be visible for small crystallites. There is no evidence of significant Ce3+ ion concentrations formed at the surface or in the bulk by the addition of terbia. The lattice parameter of these materials was seen to decrease with decreasing crystallite size. This is consistent with increased surface tension effects at small dimension. Chapter six reviews size related lattice parameter changes and surface defects in ceria nanocrystals. Ceria (CeO2) has many important applications, notably in catalysis. Many of its uses rely on generating nanodimensioned particles. Ceria has important redox chemistry where Ce4+ cations can be reversibly reduced to Ce3+ cations and associated anion vacancies. The significantly larger size of Ce3+ (compared with Ce4+) has been shown to result in lattice expansion. Many authors have observed lattice expansion in nanodimensioned crystals (nanocrystals), and these have been attributed to the presence of stabilized Ce3+ -anion vacancy combinations in these systems. Experimental results presented here show (i) that significant, but complex changes in the lattice parameter with size can occur in 2-500 nm crystallites, (ii) that there is a definitive relationship between defect chemistry and the lattice parameter in ceria nanocrystals, and (iii) that the stabilizing mechanism for the Ce3+ -anion vacancy defects at the surface of ceria nanocrystals is determined by the size, the surface status, and the analysis conditions. In this work, both lattice expansion and a more unusual lattice contraction in ultrafine nanocrystals are observed. The lattice deformations seen can be defined as a function of both the anion vacancy (hydroxyl) concentration in the nanocrystal and the intensity of the additional pressure imposed by the surface tension on the crystal. The expansion of lattice parameters in ceria nanocrystals is attributed to a number of factors, most notably, the presence of any hydroxyl moieties in the materials. Thus, a very careful understanding of the synthesis combined with characterization is required to understand the surface chemistry of ceria nanocrystals.

Real time analysis of atmospheric single particles in urban environments using aerosol time of flight mass spectrometry

In order to determine the size-resolved chemical composition of single particles in real-time an ATOFMS was deployed at urban background sites in Paris and Barcelona during the MEGAPOLI and SAPUSS monitoring campaigns respectively. The particle types detected during MEGAPOLI included several carbonaceous species, metal-containing types and sea-salt. Elemental carbon particle types were highly abundant, with 86% due to fossil fuel combustion and 14% attributed to biomass burning. Furthermore, 79% of the EC was apportioned to local emissions and 21% to continental transport. The carbonaceous particle types were compared with quantitative measurements from other instruments, and while direct correlations using particle counts were poor, scaling of the ATOFMS counts greatly improved the relationship. During SAPUSS carbonaceous species, sea-salt, dust, vegetative debris and various metal-containing particle types were identified. Throughout the campaign the site was influenced by air masses altering the composition of particles detected. During North African air masses the city was heavily influenced by Saharan dust. A regional stagnation was also observed leading to a large increase in carbonaceous particle counts. While the ATOFMS provides a list of particle types present during the measurement campaigns, the data presented is not directly quantitative. The quantitative response of the ATOFMS to metals was examined by comparing the ion signals within particle mass spectra and to hourly mass concentrations of; Na, K, Ca, Ti, V, Cr, Mn, Fe, Zn and Pb. The ATOFMS was found to have varying correlations with these metals depending on sampling issues such as matrix effects. The strongest correlations were observed for Al, Fe, Zn, Mn and Pb. Overall the results of this work highlight the excellent ability of the ATOFMS in providing composition and mixing state information on atmospheric particles at high time resolution. However they also show its limitations in delivering quantitative information directly.

Displacement of particles in microfluidics by laser-generated tandem bubbles.

The dynamic interaction between laser-generated tandem bubble and individual polystyrene particles of 2 and 10 μm in diameter is studied in a microfluidic channel (25 μm height) by high-speed imaging and particle image velocimetry. The asymmetric collapse of the tandem bubble produces a pair of microjets and associated long-lasting vortices that can propel a single particle to a maximum velocity of 1.4 m∕s in 30 μs after the bubble collapse with a resultant directional displacement up to 60 μm in 150 μs. This method may be useful for high-throughput cell sorting in microfluidic devices.

Magnetophoretic circuits for digital control of single particles and cells.

The ability to manipulate small fluid droplets, colloidal particles and single cells with the precision and parallelization of modern-day computer hardware has profound applications for biochemical detection, gene sequencing, chemical synthesis and highly parallel analysis of single cells. Drawing inspiration from general circuit theory and magnetic bubble technology, here we demonstrate a class of integrated circuits for executing sequential and parallel, timed operations on an ensemble of single particles and cells. The integrated circuits are constructed from lithographically defined, overlaid patterns of magnetic film and current lines. The magnetic patterns passively control particles similar to electrical conductors, diodes and capacitors. The current lines actively switch particles between different tracks similar to gated electrical transistors. When combined into arrays and driven by a rotating magnetic field clock, these integrated circuits have general multiplexing properties and enable the precise control of magnetizable objects.

Surface area, porosity and water adsorption properties of fine volcanic ash particles

Our understanding on how ash particles in volcanic plumes react with coexisting gases and aerosols is still rudimentary, despite the importance of these reactions in influencing the chemistry and dynamics of a plume. In this study, six samples of fine ash (<100 μm) from different volcanoes were measured for their specific surface area, as, porosity and water adsorption properties with the aim to provide insights into the capacity of silicate ash particles to react with gases, including water vapour. To do so, we performed high-resolution nitrogen and water vapour adsorption/desorption experiments at 77 K and 303 K, respectively. The nitrogen data indicated as values in the range 1.1-2.1 m2/g, except in one case where as of 10 m2/g was measured. This high value is attributed to incorporation of hydrothermal phases, such as clay minerals, in the ash surface composition. The data also revealed that the ash samples are essentially non-porous, or have a porosity dominated by macropores with widths >500 Å All the specimens had similar pore size distributions, with a small peak centered around 50 Å These findings suggest that fine ash particles have relatively undifferentiated surface textures, irrespective of the chemical composition and eruption type. Adsorption isotherms for water vapour revealed that the capacity of the ash samples for water adsorption is systematically larger than predicted from the nitrogen adsorption as values. Enhanced reactivity of the ash surface towards water may result from (i) hydration of bulk ash constituents; (ii) hydration of surface compounds; and/or (iii) hydroxylation of the surface of the ash. The later mechanism may lead to irreversible retention of water. Based on these experiments, we predict that volcanic ash is covered by a complete monolayer of water under ambient atmospheric conditions. In addition, capillary condensation within ash pores should allow for deposition of condensed water on to ash particles before water reaches saturation in the plume. The total mass of water vapour retained by 1 g of fine ash at 0.95 relative water vapour pressure is calculated to be ∼10-2 g. Some volcanic implications of this study are discussed. © Springer-Verlag 2004.

Molecular dynamics simulation of adsorption of Ag particles on a graphite substrate

We have performed for the first time a molecular dynamics simulation of the adsorption of gas-phase Ag particles on a graphite substrate to provide an insight into the results of a comprehensive STM-based experiment on this system. Both pair-wise and many-body interatomic potentials have been employed, and a Morse-type Ag–C potential was specifically constructed to describe the interactions at the interface. Our simulation has successfully reproduced a significant portion of the experimental findings. We have also observed the intercalation of silver in graphite.

Numerical modelling of adsorption of metallic particles on graphite substrate via molecular dynamics simulation

A computer-based numerical modelling of the adsorption process of gas phase metallic particles on the surface of a graphite substrate has been performed via the application of molecular dynamics simulation method. The simulation relates to an extensive STM-based experiment performed in this field, and reproduces part of the experimental results. Both two-body and many-body inter-atomic potentials have been employed. A Morse-type potential describing the metal-carbon interactions at the interface was specifically formulated for this modelling. Intercalation of silver in graphite has been observed as well as the correct alignments of monomers, dimers and two-dimensional islands on the surface. PACS numbers: 02.60.Cb, 07.05.Tp, 68.55.-a, 81.05.Tp

Computational modelling of bubbles, droplets and particles in metals reduction and refining

The CFD modelling of metals reduction processes particularly always seems to involve the interaction of liquid metals, a gas (often air) top space, liquid droplets in the top space and injection of both solid particles and gaseous bubbles into the bath. These phases all interact and exhange mass, momentum and energy. Often it is the extent to which these multi-phase phemomena can be effectively captured within the CFD model which determines whether or not a tool of genuine use to the target industry sector can constructed. In this paper we discuss these issues in the context of two problems - one involving the injection of sparging gases into a steel continuous caster and the other based on the development of a novel process for aluminium electrolysis.

Computational modelling of bubbles, droplets and particles in metals reduction and refining

A multi-phase framework is typically required for the CFD modelling of metals reduction processes. Such processes typically involve the interaction of liquid metals, a gas (often air) top space, liquid droplets in the top space and injection of both solid particles and gaseous bubbles into the bath. The exchange of mass, momentum and energy between the phases is fundamental to these processes. Multi-phase algorithms are complex and can be unreliable in terms of either or both convergence behaviour or in the extent to which the physics is captured. In this contribution, we discuss these multi-phase flow issues and describe an example of each of the main “single phase” approaches to modelling this class of problems (i.e., Eulerian–Lagrangian and Eulerian–Eulerian). Their utility is illustrated in the context of two problems – one involving the injection of sparging gases into a steel continuous slab caster and the other based on the development of a novel process for aluminium electrolysis. In the steel caster, the coupling of the Lagrangian tracking of the gas phase with the continuum enables the simulation of the transient motion of the metal–flux interface. The model of the electrolysis process employs a novel method for the calculation of slip velocities of oxygen bubbles, resulting from the dissolution of alumina, which allows the efficiency of the process to be predicted.

Manufacturing of uniformly-sized silicon particles for solar cell from molten metal jet by electromagnetic pinch force

Spherical silicon solar cells are expected to serve as a technology to reduce silicon usage of photovoltaic (PV) power systems[1, 2, 3]. In order to establish the spherical silicon solar cell, a manufacturing method of uniformly sized silicon particles of 1mm in diameter is required. However, it is difficult to mass-produce the mono-sized silicon particles at low cost by existent processes now. We proposed a new method to generate liquid metal droplets uniformly by applying electromagnetic pinch force to a liquid metal jet[4]. The electromagnetic force was intermittently applied to the liquid metal jet issued from a nozzle in order to fluctuate the surface of the jet. As the fluctuation grew, the liquid jet was broken up into small droplets according to a frequency of the intermittent electromagnetic force. Firstly, a preliminary experiment was carried out. A single pulse current was applied instantaneously to a single turn coil around a molten gallium jet. It was confirmed that the jet could be split up by pinch force generated by the current. And then, electromagnetic pinch force was applied intermittently to the jet. It was found that the jet was broken up into mono-sized droplets in the case of a force frequency was equal to a critical frequency[5], which corresponds to a natural disturbance wave length of the jet. Numerical simulations of the droplet generation from the liquid jet were then carried out, which consisted of an electromagnetic analysis and a fluid flow calculation with a free surface of the jet. The simulation results were compared with the experiments and the agreement between the two was quite good.

Synthesis and properties of polyelectrolyte microgel particles

A series of cationic poly(N-isopropylacrylamide/4-vinylpyridine) [poly(NIPAM/4-VP)] polyelectrolyte co-polymer microgels have been prepared by surfactant free emulsion polymerization (SFEP) with varying compositions of 4-VP and NIPAM. The compositions of 4-VP were 15, 25, 35, 45, 55 wt.% relative to NIPAM. The temperature and pH responsive swelling–deswelling properties of these microgels have been investigated using dynamic light scattering (DLS) and electrophoretic mobility measurements. DLS results have shown that the particle diameter of the poly(NIPAM/4-VP) microgels decreases with increasing concentration (wt.%) of 4-VP over the 20–60 °C temperature range due to the increased amount of hydrophobic group. The particle size of all poly(NIPAM/4-VP) microgel series increases with decreasing pH, as the 4-VP units become more protonated at low pH below the pKa (5.39) of the monomer 4-VP. Electrophoretic mobility results have shown that electrophoretic mobility increases as the temperature/pH increases at a constant background ionic strength (1 × 10− 4 mol dm− 3 NaCl). These results are in good agreement with DLS results. The temperature/pH sensitivity of these microgels depends on the ratio of NIPAM/4-VP concentration in the co-polymer microgel systems. The combined temperature/pH responsiveness of these polyelectrolyte microgels can be used in applications where changes in particle size with small change in pH or temperature is of great consequence.

Electrostatic modelling and measurement of airborne particles concentration

Granular air-borne particles generally carry very small amounts of electric charge as a consequence of charging by the triboelectric effect. The presence of such particles induces charge of opposite polarity on a stationary conducting electrode. The amount of charge carried by the particles and the trajectories of the particles have significant random components and the signals produced are of very low level. The signal processing is further complicated by the random variation in the concentration of particles, i.e. the solid/gas ratio. This paper compares the results obtained from the electrostatic modelling of such sensors with those obtained from experiments.

Preparation of o/w emulsions stabilized by solid particles and their characterization by oscillatory rheology

The purpose of this investigation was to examine the preparation and characterisation of hexane-in-water emulsions stabilised by clay particles. These emulsions, called Pickering emulsions, are characterised by the adsorption of solid particles at the oil/water (o/w) interface. The development of an elastic film at the o/w interface following the adsorption of colloidal particles helps to promote emulsion stability. Three different solid materials were used: silica sand, kaolin, and bentonite. Particles were added to the liquid mixtures in the range of 0.5–10 g dm−3. Emulsions were prepared using o/w ratios of 0.1, 0.2, 0.3, and 0.4. The effect of sodium chloride, on the stability of the prepared emulsions, was assessed in the range of 0–0.5 mol dm−3. In addition the use of a cationic surfactant hexadecyl-trimethylammonium bromide (CTAB) as an aid to improving emulsion stability was assessed in the concentration range of 0–0.05% (w/v). Characterisation of emulsion stability was realised through measurements of rheological properties including non-Newtonian viscosity, the elastic modulus, G', the loss modulus, G", and complex modulus, G*. The stability of the emulsions was evaluated immediately after preparation and 4 weeks later. Using the stability criteria, that for highly stable emulsions: G' > G" and both G' and G" are independent of frequency (varpi) it was concluded that highly stable emulsions could be prepared using a bentonite concentration of 2% (or more); an o/w ratio greater than 0.2; a CTAB concentration of 0.01%; and a salt concentration of 0.05 M or less—though salt was required.