Statistical Size Distribution Research Articles

Effect of the wall presence on the bubble interfacial forces in a shear flow field

Understanding the interactions between the bubbles and solid walls is important for predicting how the bubbly flow characteristics, such as void fraction and statistical distribution of bubble sizes, are affected by the presence of solid boundaries. In the present research, the numerical simulations with interface tracking method are performed to evaluate the interfacial forces’ closures in shear flow field under well-controlled conditions. The proportional-integral-derivative bubble controller is adopted to keep a single bubble at fixed position near the wall by balancing the forces in all three directions. This allows the extraction of the interfacial forces and the calculation of the corresponding coefficients. Validation tests have previously been conducted by the authors to compare the interfacial closures’ results against the experimental data. In this work, the influence of wall distance, relative velocity and bubble deformation on the interfacial forces are investigated. The results show that as the bubble approaches the wall, it experiences a transition from attractive force to repulsive force normal to the wall. The bubble Reynolds number also has significant impact on the interfacial forces: the net lateral force changes direction at Reb=35. The coupled phenomenon of bubble deformation and wall effect is investigated as well. The net lift sign change is observed at Eo=2.3 when the dimensionless wall distance (the ratio between the distance from the bubble center to the wall and the bubble diameter) is equal to 1. The presented studies complement the state-of-the-art knowledge and those are aimed to help improve the closure laws for interfacial forces and contribute to the multiphase computational fluid dynamics (M-CFD) closure model development.

Condensation heat transfer in a sessile droplet at varying Biot number and contact angle

Dropwise condensation has been identified as a promising heat transfer mechanism because it can yield heat fluxes up to an order of magnitude higher than typically found in filmwise condensation. Models for dropwise condensation generally assume a statistical distribution of droplet sizes and integrate heat transfer over the droplet size spectrum, considering droplet curvature effects on saturation temperature, conduction thermal resistance, and interfacial resistance. Most earlier studies have assumed a constant heat transfer factor (f=O(1)) to account for the conduction contribution to total thermal resistance. However, f varies with droplet Biot number (Bi) and contact angle (θ). Formulations for f with broad ranges of applicability are not currently available. In this study, finite element simulations are performed to determine f and corresponding numerical uncertainties for 0.0001⩽Bi⩽1000 and 10°⩽θ⩽170°. This spans the active droplet size range considered in most droplet condensation studies (e.g., for water condensing at Patm on a surface 10K below the ambient temperature, active droplets have 0.0005<Bi<300). An explicit correlation is proposed for f and is validated with published results. The proposed correlation can facilitate modeling and analysis of dropwise condensation.

Fractal-based models for the unsaturated soil hydraulic functions

Reliable estimates of the unsaturated soil hydraulic properties are needed in many research and engineering projects. Fractal based approaches have become popular for describing the hydraulic functions. New models based on fractal geometry are presented to describe the wetting phase relative permeability (unsaturated hydraulic conductivity) of porous media. Analytical expressions were derived using the fractal capillary pressure (water retention) model proposed by Alfaro Soto and Vilar (2006) and the statistical pore size distribution models of Mualem (1976a) and Burdine (1953) for the unsaturated hydraulic conductivity. The newly derived models provide predictions of the relative permeability to water, as well as of the fractal dimension for modeling the pore structure of a soil. Results are compared with previous formulations by Brooks and Corey (1964), van Genuchten (1980) and Kosugi (1996), as well as with experimental water retention and hydraulic conductivity data of four soils having widely different soil textures. The proposed models agreed closely with observed data. The analytical models may be attractive alternative for estimating the unsaturated hydraulic conductivity when no laboratory or field measurements are available.

Insights on Tuning the Nanostructure of rGO Laminate Membranes for Low Pressure Osmosis Process.

In this research, rGO laminates were prepared by a controlled partial reduction step, aimed to avoid aggregation and tune the interlayer spacing (d) between the rGO layers. The mild reducing agent vitamin C (l-AA) and cross-linker poly(carboxylic acid)s were used to improve the stability of the assembled rGO laminate membranes. AFM was used for the first time to further investigate the statistical size distribution of spacing between rGO layers. Topographical images of the edges of the rGO layers were obtained with an AFM instrument; interlayer spacing profiles were extracted, and then the data was plotted and fitted with Gaussian curves. We confirmed that the differently sized spacing coexisted, and their size distribution was affected by the reduction degree of rGO. At greater levels of reduction, more interlayer spacing was formed in the smaller size range, while few large gaps were still present. The obtained rGO laminate composite membranes were evaluated in a low pressure osmosis process such as forward osmosis (FO). The water permeation was higher in the rGO membrane prepared with a medium reduction degree (1.2-R) than the sample prepared by higher reduction degree (2.0-R) due to well-balanced nanochannels in hydrophilic regions and hydrophobic walls for fast transport of water molecules. The solute flux of the FO membrane was inversely correlated to the reduction degree. These findings helped in developing future strategies for designing high water flux and low reverse solute flux rGO membranes that are ideal for an FO process.

Excitation-dependent photoluminescence from WS2 nanostructures synthesized via top-down approach

Crystalline and hetero-dimensional nanostructures of WS2 quantum dots and a few layered sheets have been successfully synthesized in a single-step process using liquid exfoliation in deionized water. The X-rays diffraction analysis confirmed the presence of hexagonal as well as tetragonal phase of WS2 in quantum dots. The nanostructures so obtained exhibit strong photoluminescence, which is otherwise difficult to detect (due to low quantum yield) when WS2 is in bulk form. The UV–Vis spectra from these nanostructures display strong excitonic absorptions together with band edge absorption at ≈5.1 eV, sufficiently larger than the indirect band gap (≈1.3 eV) of bulk WS2. The average statistical size distribution of quantum dots was found to be 3–4.5 nm and corresponds to a band gap of 6 and 3.4 eV, respectively, under effective mass approximation. Further, the photoluminescence spectra shifts with the excitation wavelength, a signature of size-dependent photoluminescence emission from these nanostructures. These results suggest that quantum confinement effects together with band gap transformation from indirect to direct, not only shift the band edge in the ultraviolet region but also give rise to enhancement in the photoluminescence emission.

Virtual modeling of polycrystalline structures of materials using particle packing algorithms and Laguerre cells

The influence of the microstructural heterogeneities is an important topic in the study of materials. In the context of computational mechanics, it is therefore necessary to generate virtual materials that are statistically equivalent to the microstructure under study, and to connect that geometrical description to the different numerical methods. Herein, the authors present a procedure to model continuous solid polycrystalline materials, such as rocks and metals, preserving their representative statistical grain size distribution. The first phase of the procedure consists of segmenting an image of the material into adjacent polyhedral grains representing the individual crystals. This segmentation allows estimating the grain size distribution, which is used as the input for an advancing front sphere packing algorithm. Finally, Laguerre diagrams are calculated from the obtained sphere packings. The centers of the spheres give the centers of the Laguerre cells, and their radii determine the cells’ weights. The cell sizes in the obtained Laguerre diagrams have a distribution similar to that of the grains obtained from the image segmentation. That is why those diagrams are a convenient model of the original crystalline structure. The above-outlined procedure has been used to model real polycrystalline metallic materials. The main difference with previously existing methods lies in the use of a better particle packing algorithm.

Monodisperse mesoporous silica nanoparticles of distinct topology

Monodisperse and uniform high-quality MCM(Mobil Composition of Matter)-48-type CMSNs (Cubic Mesoporous Silica Nanoparticles) are readily prepared by simply optimizing the molar ratio of ethanol and surfactant in the system TEOS-CTAB-NaOH-H2O-EtOH (TEOS=tetraethyl orthosilicate, CTAB=cetyltrimethylammonium bromide, EtOH=ethanol). In the absence of ethanol only hexagonal mesoporous silica with ellipsoidal and spherical morphology are obtained. The presence of ethanol drives a mesophase transformation from hexagonal to mixed hexagonal/cubic, further to purely cubic, and finally to a mixed cubic/lamellar. This is accompanied by a morphology evolution involving a mixture of ellipses/spheres, regular rods, uniform spheres, and finally a mixture of spheres/flakes. Preserving the three-dimensional (3D) cubic MCM-48 structure, use of a small amount of ethanol is beneficial to the improvement of the monodispersity of the CMSNs. Moreover, the quality of the CMSNs can also be controlled by changing the surfactant concentration or adjusting the stirring rate. All MSNs were characterized using powder X-ray diffraction, transmission electron microscopy, scanning electron microscopy, and N2 physisorption, indicating highly long-range ordered pore arrays, high specific surface areas (max. 1173 m2g−1) as well as high pore volumes (max. 1.14 cm3g−1). The monodispersity of the CMSNs was verified by statistical particle size distribution from SEM (scanning electron microscopy)/TEM (transmission electron microscopy) images and DLS (dynamic light scattering). The mesophase transformation can be rationalized on the basis of an ethanol-driven change of the surfactant packing structure and charge matching at the surfactant/silicate interface. The corresponding morphology evolution can be elucidated by an ethanol-controlled hydrolysis rate of TEOS and degree of condensation of oligomeric silicate species via a nucleation and growth process.

Effect of defect size on P-S-N curves in Very-High-Cycle Fatigue

It is well-known that internal defects play a key role in the Very-High-Cycle Fatigue (VHCF) response of metallic materials. VHCF failures generally nucleate from internal defects, whose size strongly affects the material strength and life. Therefore, S-N curves in the VHCF regime are defect size dependent and the scatter of fatigue data is significantly influenced by the statistical distribution of the defect size within the material.The present paper proposes an innovative approach for the statistical modeling of Probabilistic-S-N (P-S-N) curves in the VHCF regime. The proposed model considers conditional P-S-N curves that depend on a specific value of the initial defect size. From the statistical distribution of the initial defect size, marginal P-S-N curves are estimated and the effect of the risk-volume on the VHCF response is also modeled. Finally, the paper reports a numerical example that quantitatively illustrates the concepts of conditional and marginal P-S-N curves and that shows the effect of the risk-volume on the VHCF response.

Investigating equality: The poverty and riches indices

As noise is omnipresent, real-world quantities measured by scientists and engineers are commonly obtained in the form of statistical distributions. In turn, perhaps the most compact representation of a given statistical distribution is via the mean-variance approach: the mean manifesting the distribution’s ‘typical’ value, and the variance manifesting the magnitude of the distribution’s fluctuations about its mean. The mean-variance approach is based on an underlying Euclidean-geometry perspective. So very often real-world quantities of interest are non-negative sizes, and their measurements yield statistical size distributions. In this paper, and in the context of size distributions, we present an alternative to the Euclidean-based mean-variance approach: a mean-equality approach that is based on an underlying socioeconomic perspective. We establish two equality indices that score, on a unit-interval scale, the intrinsic ‘egalitarianism’ of size distributions: (i) the poverty equality index which is particularly sensitive to the existence of very small “poor” sizes; (ii) the riches equality index which is particularly sensitive to the existence of very large “rich” sizes. These equality indices, their properties, their computation, their application, and their connections to the mean-variance approach – are explored and described comprehensively.

Effect of polyoxymethylene dimethyl ethers addition on spray and atomization characteristics using a common rail diesel injection system

PODE is named for the mixture of polyoxymethylene dimethyl ethers. Recently, it is used as diesel oxygen additive to reduce diesel engine smoke. In this study, the effect of PODE addition on the spray and atomization of diesel spray was investigated by using a high pressure common rail system. The spray tip penetration (STP), the spray cone angle and the spray projected area were extracted at the injection pressure of 60, 90 and 120MPa and the ambient pressure of 4MPa through a high speed photographic device. The results show that as PODE is added into diesel, the STP is slightly decreased and the average spray cone angle and projected area are slightly increased. In addition, the microscopic spray characteristics such as statistical droplets size distribution and characteristic diameters and relative size range were obtained by a particle/droplet image analysis (PDIA) technique. The results shows that as PODE is added into diesel, the droplets number tends to be uniformly distributed around 12–20μm range and smaller characteristic diameters are observed and the relative size range keeps constant. All of such characteristics of the spray indicate that PODE addition can better the atomization of diesel spray.

Experimental investigation on spray and atomization characteristics of diesel/gasoline/ethanol blends in high pressure common rail injection system

The effects of gasoline and ethanol addition on the spray and atomization characteristics of diesel spray from a common rail injection system, was investigated in a constant volume chamber at different ambient and injection pressures. The fuel spray evolution process was recorded with high spatial and time resolution and the corresponding spray tip penetration (STP), the cone angle were extracted. The results show that increased gasoline proportion in the test blends causes decreased STP and increased spray cone angle. Additionally, the microscopic spray characteristics such as the local average droplet diameter and statistical size distributions were measured by particle/droplet image analysis (PDIA) technique. As gasoline blending ratio increases, significantly smaller droplet size was observed which indicates that the spray breakup and atomization processes were promoted. Further adding ethanol slightly increased the droplet size, but it is still much smaller than the droplet size of neat diesel spray. Moreover, the local droplet size increases along the radial direction but the local droplet volume fraction and normalized droplet number density decreases, indicating a reduced fuel concentration along the radial direction. Along the axial direction, the droplet size, the local droplet volume fraction and the normalized droplet number density were almost constant.

Modelado fractal de la distribución del tamaño de dolinas en el macizo kárstico de la Sierra de las Nieves (Málaga, España)

El estudio de la distribución espacial de dolinas en terrenos kársticos puede proporcionar una información muy valiosa acerca de la geomorfología e hidrogeología del macizo kárstico, además de posibles controles tectónicos. En este trabajo se ha analizado la distribución espacial de dolinas en el macizo kárstico de la Sierra de las Nieves en la provincia de Málaga (España). Es este un karst mediterráneo de relieve alto, caracterizado por una elevada precipitación y que forma un importante acuífero kárstico donde las dolinas actúan de colectores de recarga concentrada y muestran un marcado control estructural, habiéndose desarrollado a lo largo de las direcciones preferentes de fracturación. Las dolinas aparecen en grupos, pudiéndose distinguir tres grupos principales relacionados con el funcionamiento hidrogeológico del macizo; aunque, atendiendo al control tectónico, se pueden diferenciar dos familias de dolinas en función de su localización geográfica. La distribución estadística de los tamaños de todo el conjunto de dolinas sigue una ley potencial que indica un comportamiento fractal y se ha especulado con los motivos para tal comportamiento. Asimismo se propone el vuelo de Lévy como modelo estocástico para la distribución espacial y tamaño de las depresiones. Esta información puede ser de gran utilidad para mejorar el conocimiento geomorfológico y de evolución del macizo kárstico.

Quartz grain assessment for reconstructing the coastal palaeoenvironment

This study proposes a combination of sedimentological techniques as a tool to understand depositional palaeoenvironments. Grain size, mineralogy, compositional data, stratigraphic framework, degree of rounding, optical appearance and microtextures of quartz grains were analyzed; sub-surface sediments were collected from 4 boreholes spaced across coastal settings, from the beach towards the continent, from locations on the south-central coast of the state of Espírito Santo, southeast Brazil. Five palaeoenvironments were identified: fluvial (characterized by gravelly sand facies, composed predominantly of sub-angular and sub-rounded dirty quartz grains with microtexures caused by sudden impact and grain surfaces modified by chemical action, as well as other non-quartz terrigenous minerals); continental deposit with marine influence, such as an estuary (characterized by muddy sand facies, composed of immature grains with natural glow and non-abraded grains with a “fresh” clean surface, little to no chemical change, a few bioclastic fragments, carbonate nodules and grains embedded with carbonate); modern estuary (characterized by sandy mud facies, composed of mixed mature and immature quartz grains, chemically frosted, bioclastic fragments, carbonate nodules, and high organic matter content); bay (characterized by sandy mud and mud facies, composed predominantly of mature grains, highly chemically frosted, with microtextures clearly associated with post-depositional alteration, many bioclastic fragments, and organic matter); and beach (characterized by gravelly sand facies, composed predominantly of sub-rounded dirty grains, followed by shiny grains, with smooth edges, signs of former impact, little chemical dissolution on the quartz grain, and bioclastic fragments). The association between the degree of rounding, optical aspect and microtextures of quartz grains was essential to estimate the extent and strength of seawater intrusion in filling of the sedimentation basin. The palaeoenergy of each deposition was not always clearly recognized using only statistical particle size distribution parameters and compositional data.

Experimental study on bubble dynamics and wall heat transfer arising from a single nucleation site at subcooled flow boiling conditions – Part 1: Experimental methods and data quality verification

A novel experimental method and data acquisition/analysis strategy that ensures reliable measurements of various subcooled flow boiling parameters is discussed. In this study, all experiments were performed by keeping a single active nucleation site within the entire heated area in a square upward flow channel. This approach greatly facilitated the observation of bubble and wall heat transfer features in subcooled boiling flow.Vapor bubbles originating from the nucleation site were observed with both micro- and macroscopic views from high-speed cameras while corresponding wall temperature was measured by an infrared camera. This allowed simultaneously capturing various bubbles characteristics with multiple scales (both space and time) as well as their impact on wall heat transfer. In addition, efforts were made to characterize the observed boiling behavior with high statistical accuracy by analyzing numerous images taken at each test condition.This study proves that by taking the current strategy excellent repeatability and thus reliability can be achieved for a wide range of flow boiling parameters such as bubble size, bubble velocity, statistical distribution of bubble size and time-averaged wall heat transfer coefficients. Also, the major sources of uncertainty for each measurement are thoroughly investigated, from which the final uncertainties are determined. Overall, the present study suggests what we must concern to achieve truly reliable and useful data from any boiling experiments.

An efficient algorithm to generate random sphere packs in arbitrary domains

Particle-based methods based on material models using spheres can provide good approximations for many physical phenomena at both the micro and macroscales. The point of departure for the simulations, in general, is a dense arrangement of spherical particles (sphere pack) inside a given container. For generic domains, the generation of a sphere pack may be complex and time-consuming, especially if the pack must comply with a prescribed sphere size distribution and the stability requirements of the simulation. The primary goal of this paper is to present an efficient algorithm that is capable of producing packs with millions of spheres following a statistical sphere size distribution inside complex arbitrary domains. This algorithm uses a new strategy to ensure that the sphere size distribution is preserved even when large particles are rejected in the growing process. The paper also presents numerical results that enable an evaluation of the proposed algorithm.

Исследование способа повышения точности горячекатаных труб при раздаче

At present, the main characteristics of steel pipes are their mechanical properties, surface finish and dimensional accuracy. Accuracy is one of characteristics that defines the service life in such industries as machine building, oil and petrochemical industry, nuclear power engineering, etc. In domestic and foreign standards for hot-rolled pipes there are no dimensionless accuracy factors taking into account the statistical distribution of sizes. This aspect complicates the analysis of dimensional accuracy of products, as well as the assessment of its increase feasibility. For this reason, the accuracy factor that takes into account the statistical distribution of pipe sizes before and after deformation is offered by authors. Thus, the influence of different technological factors may be assessed and calculation of the accuracy factor for pump and compression pipes can be carried out. The effective way to increase the accuracy of the internal diameter and surface finish of hot-rolled pipes is the calibration operation by means of pipe expansion on the mandrel. With the aim to assess calibration efficiency, computer simulation in the finite element modelling package Deform-3D was carried out. Pump and compressor pipes with different internal channel diameters within the state GOST standard were chosen as a simulation object. Computer simulation showed features of forming pipes under expansion on the mandrel. As a result of the experiment the graph of accuracy changes before and after expansion was obtained and recom­mendations were formulated on their basis. Finite element simulation showed that under optimum conditions of the accuracy of the pipe internal channel can be increased more than three times.

Effect of micro-cracks in nonhomogeneous stress field on fracture instability in structural components

The paper analyses the effects of statistical distribution in sizes of micro-cracks on scatter of fracture toughness of steels under brittle conditions. The results are utilized for reliability assessment of selected functional parts. The reliability considered as a complementary probability of brittle fracture initiation is discussed in dependence on the character of statistical distribution of micro-crack sizes, mechanical properties of steel, mechanisms of energy dissipation during cracks propagation, variation of loading, stress state of functional part and its service life. This probability approach is compared with deterministic reliability access originating from computation of safety factor. Its rational evaluation as a function of acceptable probability of fracture instability provides high economical effects saving materials and energy.

An investigation of exciton behavior in type-II self-assembled GaSb/GaAs quantum dots

We report the investigation of exciton dynamics in type-II self-assembled GaSb/GaAs quantum dots. The GaSb/GaAs quantum dots (QDs) were grown using a modified liquid phase epitaxy technique. Statistical size distributions of the uncapped QDs were investigated experimentally by field-emission scanning electron microscopy (SEM) and atomic force microscopy (AFM), and theoretically by an eight-band k · p calculation, which demonstrated a dissolution effect. Furthermore, the low-temperature luminescence spectra of type-II GaSb/GaAs QDs with a thick capping layer exhibit well-resolved emission bands and LO-phonon-assisted transitions in the GaSb wetting layer. However, the luminescence lines quench at temperatures above 250 K, which is attributed to the weak quantum confinement of electrons participating in indirect exciton recombination. It was demonstrated that the room temperature stability of the excitons in type-II GaSb/GaAs QDs could be achieved by growing thin a capping layer, which provides strong quantum confinement in the conduction band and enhances the electron–hole Coulomb interaction, stabilizing the excitons.

The Bubble Box: Towards an Automated Visual Sensor for 3D Analysis and Characterization of Marine Gas Release Sites.

Several acoustic and optical techniques have been used for characterizing natural and anthropogenic gas leaks (carbon dioxide, methane) from the ocean floor. Here, single-camera based methods for bubble stream observation have become an important tool, as they help estimating flux and bubble sizes under certain assumptions. However, they record only a projection of a bubble into the camera and therefore cannot capture the full 3D shape, which is particularly important for larger, non-spherical bubbles. The unknown distance of the bubble to the camera (making it appear larger or smaller than expected) as well as refraction at the camera interface introduce extra uncertainties. In this article, we introduce our wide baseline stereo-camera deep-sea sensor bubble box that overcomes these limitations, as it observes bubbles from two orthogonal directions using calibrated cameras. Besides the setup and the hardware of the system, we discuss appropriate calibration and the different automated processing steps deblurring, detection, tracking, and 3D fitting that are crucial to arrive at a 3D ellipsoidal shape and rise speed of each bubble. The obtained values for single bubbles can be aggregated into statistical bubble size distributions or fluxes for extrapolation based on diffusion and dissolution models and large scale acoustic surveys. We demonstrate and evaluate the wide baseline stereo measurement model using a controlled test setup with ground truth information.

Variability in group size and the evolution of collective action

Models of the evolution of collective action typically assume that interactions occur in groups of identical size. In contrast, social interactions between animals occur in groups of widely dispersed size. This paper models collective action problems as two-strategy multiplayer games and studies the effect of variability in group size on the evolution of cooperative behavior under the replicator dynamics. The analysis identifies elementary conditions on the payoff structure of the game implying that the evolution of cooperative behavior is promoted or inhibited when the group size experienced by a focal player is more or less variable. Similar but more stringent conditions are applicable when the confounding effect of size-biased sampling, which causes the group-size distribution experienced by a focal player to differ from the statistical distribution of group sizes, is taken into account.