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Monodisperse micron-sized silica particle monolayers deposited onto plasma-grown SiOx-ultra-thin films have been used as reference systems to investigate wetting, water adsorption and capillary bridge formation as a function of silica surface functionalization. 1H,1H, 2H,2H perfluorooctyltriethoxysil (FOTS) monolayers, have been deposited on the respective surfaces by means of chemical vapor deposition resulting in macroscopically low energy surfaces. X-ray photoelectron spectroscopy (XPS) and Fourier transform infrared (FTIR) reflection absorption spectroscopy confirmed the monolayer formation. Water adsorption isotherms were studied by a combination of in-situ FTIR reflection spectroscopy and quartz crystal microbalance (QCM) while macroscopic wetting was analysed by contact angle measurements. The comparative data evaluation indicates that the macroscopic wetting behaviour was changed as expected, however, that water nanodroplets formed both at intrinsic defects of the FOTS monolayer and at the FOTS/SiOx interface. Capillary bridges of liquid water are dominantly formed in the confined particle contact areas and between surface asperities on the particles. The comparison of wetting, adsorption and capillary bridge formation shows that the hydrophobization of porous materials by organosilane monolayers leads to the formation of morphology dependent nanoscopic defects that act as sites for preferential capillary bridge formation.

Capillary forces are very important considering the handling of powders as they, in general, exceed other adhesion forces. These capillary forces are dependent on several different parameters. Especially the distance between the particles is an important parameter. For example, in moving bulk solids a large variety of distances between particles will occur. Therefore, the distance-dependence of capillary bridges was investigated with a numerical simulation method, assuming thermodynamic equilibrium which is attained very fast for small particles. This method uses the Kelvin equation and the Young-Laplace equation to calculate numerically the shape of the capillary bridge without any assumption regarding the shape. The force is eventually derived from the meniscus shape. The distance becomes extremely important when the capillary liquid bridge between two surfaces is only determined by capillary condensation depending on relative humidity. Only a slight increase of the distance within the fraction of a nanometer changes the behaviour of the capillary force significantly. Furthermore, the influence of the force on the separation of particles will be presented. The force decreases almost linearly with increasing distance for a wide range of distances and consequently, a contact stiffness for capillary bridges could be derived. These results may e.g. be used in DEM models. Also, the maximum separation distance of capillary bridges in thermodynamic equilibrium and the correlation with the according bridge volume was investigated. As two limiting cases for capillary bridges at varying distances one can assume either a constant curvature, i.e. infinitely fast attainment of equilibrium, or a constant volume, i.e. infinitely slow attainment of equilibrium. Therefore, a comparison of these two possibilities will be presented and discussed as well.

In this report, a flame spray pyrolysis setup has been examined with various in situ extraction methods of particle samples along the flame axis. First, two precursor formulations leading to the formation of iron oxide nanoparticles were used in a standardized SpraySyn burner system, and the final particle outcome was characterized by a broad range of established powder characterization techniques (TEM/HRTEM, SAXS, XRD, BET). The characterization of the powder products evidenced that mostly homogeneous gas-to-particle conversion takes place when applying an acidic precursor solution, whereas the absence of the acid leads to a dominant droplet-to-particle pathway. Our study indicates that a droplet-to-particle-pathway could be present even when processing the acidic formulation. However, even if a secondary pathway might take place in this case as well, it is not dominant and nearly negligible. Subsequently, the in situ particle structure evolution was investigated for the dominant gas-to-particle pathway, and particles were extracted along the flame axis for online SMPS and offline TEM/HRTEM analysis. Due to the highly reactive conditions within the flame (high temperatures, turbulent flow field, high particle number concentrations), the extraction of representative samples from spray flames is challenging. In order to handle the reactive conditions, two extraction techniques were tailored in this report. To extract an aerosol sample within the flame for SMPS measurement, a Hole in a Tube probe was adjusted. Thus, the mobility particle diameter as well as the corresponding distribution widths were obtained at different heights above the burner along the flame axis. For TEM/HRTEM image analysis, particle samples were collected thermophoretically by means of a tailored shutter system. Since all sampling grids were protected until reaching the flame axis and due to the low sampling time, momentary captures of local particle structures could be extracted precisely. The particle morphologies have clearly shown an evolution from spherical and paired particles in the flame center to fractal and compact agglomerates at later synthesis stages.

Temperature effects in the polymer laser sintering process are an important aspect regarding the process reproducibility and part quality. Depending on the job layout and position within the part cake, individual temperature histories occur during the process. Temperature history dependent effects are for example part warpage, the crystallization rate and powder ageing effects. This work focuses on temperatures and heat flow within laser sintered part cakes. Therefore, a thermal Finite Element (FE) model of a part cake is developed based on experimental in-process temperature measurements. Thermal boundary conditions and properties of the used bulk polymer powder are analyzed and relevant parameters are identified. The model is validated and optimized considering different job heights and ambient conditions during the cooling phase. It is finally possible to predict position-dependent temperature histories as a function of significant job parameters. The model allows a transfer of the results for varied boundary conditions during cooling. In combination with an implementation of built parts, this model will be an important tool for the development of optimized process controls and cooling strategies.

The layered structure of Additive Manufacturing processes results in a stair- stepping effect of the surface topographies. In general, the impact of this effect strongly depends on the build angle of a surface, whereas the overall surface roughness is additionally caused by the resolution of the specific AM process. The aim of this work is the prediction of the surface quality in dependence of the building orientation of a part. These results can finally be used to optimize the orientation to get a desired surface quality. As not all parts of the component surface are equally important, a preselection of areas can be used to improve the overall surface quality of relevant areas. The model uses the digital AMF format of a part. Each triangle is assigned with a roughness value and by testing different orientations the best one can be found. This approach needs a database for the surface qualities. This must be done separately for each Additive Manufacturing process and is shown exemplarily with a surface topography simulation for the laser sintering process. A validation of the model is done with a monitor bracket of EOS GmbH. Measurements of five different orientations of the part, optimized according selected surface areas, show a good accordance between the real surface roughness and the predicted roughness of the simulation.

Suspensions are subject to confinement induced structuring, i.e. layering, at the confining surfaces. While most of the previous work focused on layering in Couette cells, the present study aimed to characterize the resulting layers at the plates of a parallel plate rheometer with regard to their relative particle concentration. The particle concentration profile over the radial distance was characterized for various mean concentrations and gap heights. To this end, we mapped the distribution of fluorescently dyed tracer particles in density and refractive index matched suspensions. The results indicate that layering at the surfaces stabilizes as the ratio between gap height and particle diameter increases. For lower gap heights, i.e. as the suspension approaches a two dimensional state, the layer concentration was non-uniform over the plates. In general, results were quantitatively different for the upper and lower plate and the concentration profiles were noticeably asymmetric. We conclude that this is probably the result of the rheometer loading or the start-up process. The stable layers as well as the inhomogeneous particle distribution in general offer an explanation for the lack of transferability of viscosimetric results between different setups.

The conditioning of the aerosol particle population into a bipolar charge equilibrium is an essential prerequisite to calculate the particle number size distribution using mobility particle size spectrometers. This is commonly realized by diffusion charging of bipolar air ions generated by e.g. a 85Kr source. Because of strict legal regulations on radioactive sources in several countries, soft-X-ray (SXR) appears as a suitable alternative. However, multiple measurements showed a systematical and significant difference between the particle charge distribution delivered by a radioactive source and an SXR charger, respectively. In this investigation, a calibrated particle charge distribution, suitable for the SXR chargers, was calculated based on the Fuchs model. An approximation analogous to the commonly used Wiedensohler approximation formula ( Wiedensohler, 1988 ) was computed. The use of the new SXR approximation of the bipolar charge equilibrium for the inversion of an electrical mobility distribution to a particle number size distribution improves the comparability of these results, compared to measurements involving a 85Kr charger or to bipolar chargers using radioactive material in general. A systematic error in case of using the SXR charger could be eliminated and hence the root mean square deviation could be reduced from 13% using the common parameters for both charger types to 7% using the new SXR approximation for the SXR bipolar charger.

An essential part of mobility particle size spectroscopy is the prediction of the aerosol charge distribution in a highly concentrated bipolar ion environment. This charge distribution can be readily calculated, but is depending on several environmental conditions. These influences are investigated theoretically. The first part of this work deals with a sensitivity analysis using the Fuchs model ( Fuchs, 1963 ) to determine the variation of the resulting charge distributions depending on the input parameters. It is demonstrated, that the main influencing variable is the difference between the positive and negative ion mobility. A sensitivity analysis reveals that a reasonable variation of the ion mobilities may lead to variations of the particle density distribution up to±20%. The second part investigates the evolution of the charge distribution along the tubing downstream of the bipolar charger exit starting with equal ion concentrations for positive and negative ions. Due to wall losses depending on ion mobility a non-equilibrium charge distribution is developing along the plumbing. The evolution of the particle charge distribution is determined using a coupled population balance model. Even though the non-equilibrium character is clearly shown, it turns out that this effect is negligible at conditions typical for particle size measurements.

The precipitation of sticky and ultrafine particles has become increasingly important. Biomass burners are one important example for ultrafine dust emission sources with ever growing importance. Therefore, a baghouse filter has been developed, which combines excellent separation efficiency (> 99%, clean air dust loading of Therefore, extended tests on recycling of used precoat material have been performed. Particularly, the influence of precoat injection parameters and various mixing strategies of used and virgin powder for refreshing the precoat material have been investigated. Different mixtures have been characterised by their ability to disintegrate, flowability and filtration behaviour. It is clearly demonstrated that upon redispersing the used precoat fine dust mainly adheres to the coarse precoat with only a limited number of dust agglomerates being produced in addition. For each kind of precoat a minimum amount is determined in order to ensure a long-term stable process. This way a saving potential of between 40–67% has been found. An economic and ecologic process has been developed to precipitate ultrafine dust in a baghouse filter system using precoat materials.

Capillary forces between particles often dominate other adhesion forces. However, the calculation of the shape of capillary bridges and the resulting force is complex, so often assumptions and approximations are used. These assumptions are not useful for nanoscale particles. Therefore, a simulation method was established to calculate numerically the shape of the meniscus and derive the corresponding capillary bridge force. The main focus are nanoscaled particles with liquid bridges formed by condensing air humidity. The dependence of the capillary force on various parameters such as particle sizes, contact angle and humidity was investigated and it is demonstrated that often-used assumptions cannot be used for nanoscaled particles without remarkable mistake.

Because of the large surface area of colloids interface effects are dominant in contrast to volume effects. The study presents experimental results of the direct transfer of magnetite nanoparticles from an aqueous to a non-miscible organic phase. The starting point is a water-based colloid that is synthesized through a precipitation reaction. The transfer is based on the adsorption of surfactants onto the particle surface at the liquid–liquid interface. While penetrating the liquid–liquid interface, the particles are covered with surfactants and a partial de-agglomeration is initiated. The intention is to produce a stable organic colloid, which has important applications in industry. The optimized process parameters for the successful phase transfer process, the adsorption reactions at the liquid–liquid interface and the stabilization of primary particles in the organic phase are demonstrated.

The sintering of vitreous nanoparticle doublets is investigated numerically by a volume of fluid method coupled to Hamaker summation and experimentally by a high-temperature sintering flow reactor as well as by doublet shape analysis in the transmission electron microscope. In particular, the characteristic differences between nanoparticulate and bulk sintering are studied. The sintering mechanism of vitreous nanoparticles is determined to be viscous flow with interparticle van der Waals interactions acting as additional driving force. The early stages of the nanoparticle sintering kinetics are inversely proportional to the square of the particle size, instead of an indirect proportionality to the first order of the particle size for the entire bulk process. The transition between nanoparticulate and bulk sintering is localised to primary particle diameters of approx. 200–300 nm.

This work investigates the mechanisms which lead to the formation of silicon nanoparticles with narrow size distributions by means of population balance modeling. The model accounts for the full aerosol process, including chemical reaction, nucleation from supersaturated vapor, growth and agglomeration. The results are in good agreement with experimental data. The effects of the process parameters temperature, silane concentration and reactor total pressure are systematically investigated. The simulation allows an in-depth insight into the particle formation mechanism and reveals the key requirements which are necessary for the generation of narrow particle size distributions. In this mechanism, only a short nucleation burst occurs, while surface growth plays the dominant role in silane precursor consumption. A key role is attributed to condensation, because the numerical calculations can only reflect the experimental observations, if the condensation mechanism is included in the model.

A study on the feasibility of aerosol processing of nearly monodisperse silicon nanoparticles via pyrolysis of monosilane in a hot wall reactor is presented. For optimal conditions silicon nanoparticles with a geometric standard deviation of 1.06 were synthesized at a production rate of 0.7 g/h. The size of the particles could be precisely controlled in the range of 20–40 nm, whilst maintaining a geometric standard deviation in the range of 1.06–1.08, by proper choice of the governing parameters temperature, residence time and precursor concentration. The results show that narrow particle size distributions can only be obtained in the temperature range between 900 and 1100 °C, as long as both the initial silane concentration (1 mbar silane partial pressure) and the reactor total pressure are low (25 mbar). This regime for the production of narrow particle size distributions has not been identified in prior work on the thermal decomposition of silane. Narrowly distributed particles can be obtained under conditions where nucleation and particle growth are separated and the agglomeration rates are negligible.

In this paper, we consider a model for precipitation experiments based on the population balance equation. The study revealed a high sensitivity of the system with respect to the modeling of intrinsic parameters, motivating a comprehensive validation of the estimates. In the forward simulation the impact of the influencing parameters including surface energy, nucleus size and distribution is investigated. Subsequently we construct a simplified model of the precipitation process in such a way that it is orbitally flat in terms of control theory, which enables the inverse calculation of the parameters. The numerical results of the inverse simulation for the interfacial energy have been compared to a physical model. The possibility of solving the inverse problem provides a promising way of estimating hardly measurable quantities for more complex molecules.

In this work, a new model for the simulation of nanostructured aggregates by simultaneous coagulation, sintering and surface growth is presented. Coagulation is treated as cluster–cluster agglomeration along the line connecting the center of mass of both agglomerates and is implemented using a Monte Carlo algorithm. Sintering is modeled as successive overlapping of spheres which cause reduction in the surface area based on a rate law for surface reduction. Surface growth is modeled as an increase in primary particle diameter, e.g. as a result of surface reactions. The evolved aggregates are analyzed by calculating their fractal dimension, radius of gyration, mobility diameter and mobility shape factor. It is found that the aggregates structure tends to be more compact when introducing the surface growth in shorter time comparing to the coagulation-sintering step only. Fractal dimension and the mobility shape factor of the resulting aggregates are correlated to an effective dimensionless time that combines the characteristic times of these three fundamental mechanisms. It is shown that the mobility diameter in the free molecular regime is not proportional to the radius of gyration. A power law relation that correlates the aggregates projected area and the equivalent number of primary particles is found to be in a very good agreement with estimates published in literature.

The study presents first experimental results of the transfer of magnetite nanoparticles from an aqueous to a second non-miscible non-aqueous liquid phase. The transfer is based on the adsorption of macromolecular surfactants onto the particle surface at the liquid–liquid interface. For a successful direct phase transfer, it is essential to have cations, like ammonium ions, present in the aqueous phase as well as a threshold concentration of surfactant in the organic liquid phase. While penetrating the liquid–liquid interface, the particles are covered with the surfactant and therefore a partial de-agglomeration is initiated. Based on literature and experimental data a mechanism of surfactant adsorption is proposed. The competing adsorption of the surfactant molecules at the liquid–liquid interface leads to the formation of emulsions and therefore to a hindrance for particles passing the interface. Nevertheless a high efficiency of 100% yield can be reached using optimized process parameters for the phase transfer process.

Modeling of particle deposition on adjacent walls is a key issue in various applications like separation or transport processes. The present paper focuses on the modeling of turbophoretic deposition of particles in the micron size range. The first step is to evaluate the important range where turbophoresis plays an important role in comparison to other mechanisms e.g. gravity or electrostatic separation. The disadvantages of commonly used models will be analyzed and overcome by implementing a more sophisticated approach considering damping of turbulent fluctuations in the wall-boundary layer. In contrast to previous work, commonly used turbulence models are applied to solve the mean flow field of the examples under consideration. The results will show a good prediction of particle deposition in comparison to experimental values [B.Y.H. Liu, J.K. Agarwal, Experimental observation of aerosol deposition in turbulent flow, Aerosol. Sci. 5 (1974) 145–155.] by using the advanced model.

The drag force on aggregates and partially sintered agglomerates is assessed using the lattice Boltzmann method (LBM) and accelerated Stokesian dynamics (ASD). Both methods have been compared in terms of accuracy and computational effort. It is shown that they give comparable results if all numerical parameters are controlled carefully. LBM requires a much higher computational effort, however, in contrast to ASD it is able to simulate partially sintered agglomerates as well. The results show that even a very small amount of sintering leads to a significant reduction in the drag force. The analysis of the drag force on agglomerates as well as on aggregates shows that there is no simple geometric quantity which is uniquely related to the drag force. Moreover, there is a significant variation in drag force for single aggregates at different orientations or for the orientation averaged drag force of different aggregates of the same size. This is explained by the structural effects which may lead to a variation in the drag force up to +/-20%.

Nanoparticle precipitation is an interesting process to generate particles with tailored properties. In this study we investigate the impact of various process steps such as solid formation, mixing and agglomeration on the resulting particle size distribution (PSD) as representative property using barium sulfate as exemplary material. Besides the experimental investigation, process simulations were carried out by solving the full 1D population balance equation coupled to a model describing the micromixing kinetics based on a finite-element Galerkin h-p-method. This combination of population balance and micromixing model was applied successfully to predict the influence of mixing on mean sizes (good quantitative agreement between experimental data and simulation results are obtained) and gain insights into nanoparticle precipitation: The interfacial energy was identified to be a critical parameter in predicting the particle size, poor mixing results in larger particles and the impact of agglomeration was found to increase with supersaturation due to larger particle numbers. Shear-induced agglomeration was found to be controllable through the residence time in turbulent regions and the intensity of turbulence, necessary for intense mixing but undesired due to agglomeration. By this approach, however, the distribution width is underestimated which is attributed to the large spectrum of mixing histories of fluid elements on their way through the mixer. Therefore, an improved computational fluid dynamics-based approach using direct numerical simulationwith a Lagrangian particle trackingstrategy is applied in combination with the coupled population balance–micromixing approach. We found that the full DNS-approach, coupled to the population balance and micromixing model is capable of predicting not only the mean sizes but the full PSD in nanoparticle precipitation. 2005 Elsevier Ltd. All rights reserved.

Simulation results on the evolution of aggregate structure in aerosol processes with coagulation and sintering as the dominant mechanisms are presented. A model for simulation of the three-dimensional morphology of nano-structured aggregates formed by concurrent coagulation and sintering is applied. The model is based on a stochastic diffusion controlled cluster–cluster aggregation algorithm and sintering is modeled as a successive overlapping of spherical primary particles, which are allowed to grow in order to maintain mass conservation. This leads to computer simulated structured aggregates which are then subject to evaluation. Two different methods to determine the fractal dimension are presented which give comparable results. It is shown that even very small particles show the same fractal behavior. Furthermore, equilibrium structures assuming a constant ratio of the characteristic collision time to the characteristic fusion time are considered as well as the kinetics of structural changes due to a change in the ambient conditions.

This work investigates the effects of reduced accessible surface area of aggregate particles and of surface energy on relevant particle formation and growth mechanisms during titania formation from the vapour phase at industrial process conditions. Growth due to surface reaction and due to condensation is related to the fraction of the surface area that is exposed to the collision with single molecules. Surface shielding is found to hamper surface reaction and condensation once fractal aggregates start to form. It leads to significantly retarded precursor consumption and produces aggregate particles, which consist of more, but smaller primary particles. Surface energy data are varied within a range as proposed by available literature data. Moderate and high surface energy values result in a thermodynamic barrier to the formation of new particles and are shown to reduce the formation of seed particles by several orders of magnitude. This leads to the formation of aggregate particles which consist of a rather small number of primary particles and mainly grow by surface reaction. The primary contribution of condensation to growth of individual primary particles is shown to be very little. However, condensation should not be neglected as it has a strong impact on particle formation rates and hence on product characteristics such as the number of primary particles and primary particle size.

This work investigates effects of reduced accessible surface area of aggregate particles and surface energy on titania particle formation and growth. It is taken into consideration that surface-related growth mechanisms, i.e. surface reaction and condensation, are limited to the fraction of the surface area of primary particles which is exposed to the collision with single molecules. Surface energy data determine the critical particle size with respect to evaporation and values are varied within the published range. This implies to develop a model which considers “surface shielding” and accounts for the formation of stable clusters from a supersaturated vapour due to nucleation and condensation besides considering the generation of monomers due to chemical reaction, growth due to surface reaction, agglomeration and sintering. Taking the accessible surface area into account is found out to be especially important if agglomerates contain a large number of primary particles or if agglomerate structure is rather compact. In this case, precursor consumption and primary particle growth turn out to be significantly retarded. Surface energy data are shown to be decisive with respect to the thermodynamic barrier to the formation of particles, thus to active particle formation and growth mechanisms, besides affecting sintering kinetics. Elevated surface energy data typically retard precursor consumption and favour primary particle growth.

A simulation method is applied to calculate particle dynamics in electrostatic precipitators as characterised by particle flux density and concentration profiles in arbitrary channel cross-sections and flux density profiles of dust precipitated at the collecting electrodes (CEs). A simple statistical model allows the determination of confidence intervals for flux profiles. First, a ‘standard case’ considering full coupling of all physical phenomena occurring in this problem, i.e., electric field, flow field and particle dynamics is simulated. Subsequently, this standard case is compared to simulations with one quantity (e.g., electric field strength, turbulence intensity) substituted by a mean value which is homogeneously distributed in the precipitation zone. This reveals the relevance of the various physical phenomena: It turned out that the secondary flows had only a minor influence on the overall particle precipitation although they cause some ‘patterning’ of local precipitation. Turbulence inhomogeneity shows a stronger effect on particle dynamics. However, the electric field appears to be by far the most important quantity in simulating particle dynamics. Consequently, in order to achieve most reasonable simulation results for a given numerical effort most attention has to be devoted to field calculations, including correct boundary conditions.

A population balance model is presented, which tracks particle growth in the gas phase and accounts for simultaneous agglomeration and sintering: Simulations reveal the evolution of the full distribution of a volume equivalent diameter and, amongst others, the evolution of the agglomerate collision diameter, a mean primary particle size and the number of primary particles per agglomerate. Furthermore, assuming fractal behaviour of the growing agglomerate particles—for the 7rst time—a model for the evolution of a mean value of the fractal dimension based on physical and process parameters is proposed and incorporated into the simulation model. PARSIVAL, a commercial solver for integro-di;erential equations is employed to solve the equations involved. It is based on a generalised 7nite-element scheme with self-adaptive grid- and order construction. Calculations are performed to validate the model against monodisperse and sectional models published in literature for the exemplary case of Si production. The results are in good agreement if the same simplifying assumptions are made. However, results obtained from the new model for both—isothermal and non-isothermal process conditions—clearly show that it is important to consider the changing fractal dimension in many cases. ? 2003 Elsevier Science Ltd. All rights reserved.

The connection between orthogonal polynomials and cubature formulae for the approximation of multivariate integrals has been studied for about 100 yr. The article J. Radon published about 50 yr ago (J. Radon, Zur mechanischen Kubatur, Monatsh. Math. 52 (1948) 286–300) has been very influential. In this text we describe some of the results that were obtained during the search for answers to questions raised by his article.

An overview of the lower bounds for the number of points for integrals over the square and triangle is presented. This is compared with the number of points in known cubature formulae.

In this paper a geometrical interpretation of the Hungarian method will be given. This special algorithm to solve the dual transportation problem is not restricted to the edges of the convex polyhedron of feasible solutions. Each covering-step can be considered as a determination of a direction of steepest descent, each reduction-step as movement along that direction to a boundary point of the polyhedron. The dimension of the face that will be crossed depends on the covering that is chosen.