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Sphericity, as one of the most important shape parameter for non-spherical objects, is extensively applied in evaluating the porosity or packing density of particles. In this paper, the sphericities of common non-spherical objects are deduced and investigated. Maximum sphericities and optimum shapes of these objects are presented as well. A decreas...
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In a multi-component homogeneous system, the relationship between partial molar and molar quantity (RPMQ) is proved to be an equivalent relation of the Gibbs-Duhem equation. The universal characteristics of a thermodynamic model to conform to the Gibbs-Duhem equation are inferred from the RPMQ. Based on the inference, an asymmetric regular solution...
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... Even the one which is available is limited to a single particle. [56][57][58][59][60][61] The concentration effects of non-spherical particles have not been studied extensively, both experimentally and numerically. The even available one is limited to rod-like particles 37,55,62 and oblate spheroids. ...
This study investigates the dynamics of disk-shaped particles using direct numerical simulations with the smoothed profile method for rigid particles. These disk-shaped particles are formed by joining the spherical beads and are allowed to settle/sediment in a Newtonian fluid. The concentration effects of the mono-dispersed particles are studied in the Stokes regime, varying the volume fraction (ϕ) from 0.0003 to 0.1. Strong inhomogeneities in the system were noticed, producing multiple peaks in the radial distribution function caused by the orientation preference of particles, while settling. A histogram analysis of the particles' orientation angle suggests that particles prefer horizontal orientation at very low volume fractions and then start orienting vertically with subsequent increase in the volume fraction. Average settling velocity increases initially till volume fraction 0.001, creating a local maxima, and then decreases monotonically following the Richardson–Zaki law. It was also found that velocity fluctuations increased with increasing volume fraction, following the ϕ1/3 trend. These fluctuations are smaller than those of rod-like particles and larger than spherical particles, though the qualitative trend is quite similar.
... The sphericity (ψ) of a non-spherical particle is defined as the ratio of the surface area of a sphere having the same volume as the particle to the actual area of the particle i.e. ψ = A s /A p . The sphericity and other geometric parameters for some common non-spherical isometric shapes can be found in ref. [22]. Haider and Levenspiel [18] used a fourparameter empirical drag law to show that a drag law for spherical particles could be applied to non-spherical particles if the fitting parameters are adjusted properly. ...
Closed-form analytical solutions have been derived for the gravitational fall of a non-spherical particle in a quiescent fluid. The Boussinesq-Basset-Oseen equation accounting for history force and particle slip effects was applied to derive the particle motion equation, using a sphericity-dependent drag law for transitional flow in the range 0.001<=Re<=100000 and valid for sphericities >0.50. The derived closed-form solutions were validated with published experimental data and the accuracy was verified using published approximate analytical solutions and numerical results. The closed-form solutions were found to agree with experiments and produced more accurate results than other published approximate analytical solutions. Also, the effects of sphericity, Basset force and particle slip on the particle motion were investigated and discussed. The present analytical solutions are applicable to zero and non-zero initial velocity, steady and unsteady motion, and the corresponding displacements and accelerations. Additionally, new settling velocity formula valid for non-spherical particles was derived.
... 2. Although more than 90 % of whole mineral processing operations use balls as grinding media, other media shapes comprised of bars, cylpebs, ellipsoids, etc., are used in mineral processing plants (Aldrich, 2013;Shahbazi et al., 2020). According to the literature, particles' shape significantly affects the particle beds' voidage (Li et al., 2012). Accordingly, it could be interesting to consider the effect of grinding media shape in modeling the dynamic and static voidage. ...
... Values lower than this (in the 1 − 0 range) indicate deviations from a perfect sphere. For a reference, the ϕ value for a hemisphere is 0.83 [29]. when the number of images in the tilt series is small. ...
Electron Tomography (ET) reconstructions can be analysed, via segmentation techniques, to obtain quantitative, 3D-information about individual nanoparticles in supported catalysts. This includes values of parameters out of reach for any other technique, like their volume and surface, which are required to determine the dispersion of the supported particle system or the specific surface area of the support; two figures that play a major role in the performance of this type of catalysts.
However, both the experimental conditions during the acquisition of the tilt series and the limited fidelity of the reconstruction and segmentation algorithms, restrict the quality of the ET results and introduce an undefined amount of error both in the qualitative features of the reconstructions and in all the quantitative parameters measured from them.
Here, a method based on the use of well-defined 3D geometrical models (phantoms), with morphological features closely resembling those observed in experimental images of an Au/CeO 2 catalyst, has been devised to provide a precise estimation of the accuracy of the reconstructions. Using this approach, the influence of noise and the number of projections on the errors of reconstructions obtained using a Total Variation Minimization in 3D (TVM-3D) algorithm have been determined. Likewise, the benefits of using smart denoising techniques based on Undecimated Wavelet Transforms (UWT) have been also evaluated.
The results clearly reveal a large impact of usual noise levels on both the quality of the reconstructions and nanometrological measurement errors. Quantitative clues about the key role of UWT to largely compensate them are also provided.
... For example, sphericity has been proposed to evaluate the geometric consistency between different objects. It was defined as the ratio of the surface area of a sphere, which has the same volume as the given particle to the surface area of that particle (Li et al., 2012). The surface-areavolume ratio has been applied in investigating the taxonomic groups of insects (Kühsel et al., 2017), as well as the relationship between human brain size and cortex folding (Toro et al., 2008). ...
Background: The three-dimensional (3D) geometry of coronary atherosclerotic plaques is associated with plaque growth and the occurrence of coronary artery disease. However, there is a lack of studies on the 3D geometric properties of coronary plaques. We aim to investigate if coronary plaques of different sizes are consistent in geometric properties.
Methods: Nineteen cases with symptomatic stenosis caused by atherosclerotic plaques in the left coronary artery were included. Based on attenuation values on computed tomography angiography images, coronary atherosclerotic plaques and calcifications were identified, 3D reconstructed, and manually revised. Multidimensional geometric parameters were measured on the 3D models of plaques and calcifications. Linear and non-linear (i.e., power function) fittings were used to investigate the relationship between multidimensional geometric parameters (length, surface area, volume, etc.). Pearson correlation coefficient (r), R-squared, and p-values were used to evaluate the significance of the relationship. The analysis was performed based on cases and plaques, respectively. Significant linear relationship was defined as R-squared > 0.25 and p < 0.05.
Results: In total, 49 atherosclerotic plaques and 56 calcifications were extracted. In the case-based analysis, significant linear relationships were found between number of plaques and number of calcifications (r = 0.650, p = 0.003) as well as total volume of plaques (r = 0.538, p = 0.018), between number of calcifications and total volume of plaques (r = 0.703, p = 0.001) as well as total volume of calcification (r = 0.646, p = 0.003), and between the total volumes of plaques and calcifications (r = 0.872, p < 0.001). In plaque-based analysis, the power function showed higher R-squared values than the linear function in fitting the relationships of multidimensional geometric parameters. Two presumptions of plaque geometry in different growth stages were proposed with simplified geometric models developed. In the proposed models, the exponents in the power functions of geometric parameters were in accordance with the fitted values.
Conclusion: In patients with coronary artery disease, coronary plaques and calcifications are positively related in number and volume. Different coronary plaques are consistent in the relationship between geometry parameters in different dimensions.
... Sphericity (Ψ) and SMI were used to infer the geometry of inclusions in conjunction with Eqs. (1)-(2) (Li et al., 2012). ...
... (1) (herein); Fig. 1, Li et al., 2012). By definition, a cylinder with h / d < (1 = ideal) is considered a disk. ...
... 5A, 6, and S3-S4, and in other literature such as (Galley et al., 2015), results in w = h / d = 0.3 using Ψ = 0.75 (Eq. (2) (herein); Fig. 19, Li et al., 2012). ...
As climate change brings reduced sea ice cover and longer ice-free summers to the Arctic, northern Canada is experiencing an increase in shipping and industrial activity in this sensitive region. Disappearing sea ice, therefore, makes the Arctic region susceptible to accidental releases of different types of oil and fuel pollution resulting in a pressing need for the development of appropriate scientific knowledge necessary to inform regulatory policy formulation.
In this study, we examine the microstructure of the surficial layers of sea ice exposed to oil using X-ray microtomography. Through analysis, 3D imaging of the spatial distribution of the ice's components (brine, air, and oil) were made. Additional quantitative information regarding the size, proximity, orientation, and geometry of oil inclusions were computed to ascertain discernable relationships between oil and the other components of the ice. Our results indicate implications for airborne remote sensing and bioremediation of the upper sea ice layers.
... Experimentation may give detailed information of such systems; however, the development of experimental setup and associated diagnostic and analytical techniques is an expensive task (Batchelor, 1970;Bretherton, 1962;Park et al., 2010;Pignatel et al., 2011). In recent years, advanced computational and numerical techniques have been developed to solve such complex problems precisely and accurately (Butler and Shaqfeh, 2002;Khan et al., 2021;Li et al., 2012;Marchioli et al., 2010;Rong, 2007;Salmela et al., 2007;Shin et al., 2009). However, these mathematical techniques require thorough the validation of the model used for simulation purposes. ...
Prediction of correct drag and lift forces acting on immersed bodies is vital for optimized efficiency and industrial economics. Particulate suspensions involving non-spherical particles are extensively used in chemical and medical industry. In recent years, the hydrodynamics of non-spherical particles has attracted much attention. The hydrodynamic forces acting on these particles are function of particle size, shape, orientation and physical properties of fluid. In current research the drag and lift coefficient of non-spherical particles of disc and prolate shapes at different inclination angles and Reynolds number (Re) are calculated using simplified Eulerian approach of computational fluid dynamics (CFD). The method adopted for simulation is first validated for a simple case of sphere. The effect of orientation and Re on drag and lift coefficient (CD and CL respectively) is studied and compared with available data. It is found that CD and CL increase as the angle of inclination increases, but decrease with Re. CD and CL are smaller for prolate at given Re and orientation than for the case of disc. The effects of finite size geometry cause some deviation in results from the literature. The results obtained with this simple and less computationally intensive method agree well with highly resolved numerical simulations with minor deviations.
... The term, Δk r in Equation (1) can be written as: (2) where h is capping layer thickness and h =1 nm [23], Tref is a reference temperature and Tref = 293 K, cp bf and cp ref are specific heat of base fluid and reference specific heat and cp ref is equal to 4182.2 J/kg (specific heat of water at 293 K) [40]. The particle sphericity, ψ in Equation (2) is equal to the sphere surface area including equivalent volume as the actual particle [41]. ψ = 0.5 and ψ = 1 for cylindrical and spherical nanoparticles, respectively. ...
A trial-error procedure is applied for the derivation of correlations to estimate the relative thermal conductivity (kr) and dynamic viscosity (µr) of nanofluids using MATLAB. Thermophysical properties of particles and base fluids, particle diameter (dp), sphericity, capping layer thickness, Brownian motion of a particle, temperature, and volume fraction (φ) are considered. The accuracy of predicting kr and µr of nanofluids is developed using dimensionless parameters involving base fluid and particle characteristics. The results reveal that the estimated values are in a good agreement with the experimental data with a standard deviation of 2.16% and 8.16% for kr and µr of nanofluids, respectively. Besides that, 97.5% of the predicted kr values suit experimental data of kr with a mean deviation of ±5%, whereas 90.4% of the estimated µr values match the data of µr with a mean deviation of ±10%. Therefore, the proposed new equations will be useful for numerical simulation studies and the engineering design of heat transfer devices such as refrigeration systems, solar collectors, and heat exchangers. © 2021, Advanced Researches and Engineering Journal (IAREJ) and the Author(s).
... It was concluded that the considered models to determine a particle's shape can induce an error of 30% when calculating the settling velocity; additionally, particles with high irregularities may result in high errors (Bagheri et al. 2015). Li et al. (2012) carried out research to determine the sphericity of non-spherical objects. Firstly, they considered spheres with a sphericity of 1.0. ...
Settling velocity or depositional velocity is considered a key parameter to account for in the drilling technology of oil and gas wells as well as hydrocarbon processing since an accurate estimation of this parameter allows the transport of cuttings efficiently, avoids non-productive time, and helps avoid costly problems. Understanding the settling velocity in fluid with high salinity will help for the better separation of oil and natural gas streams in processing facilities. Although a great amount of effort was given to rheology and settling velocity measurements for power-law fluid and Bingham fluids, there are limited studies available in the literature for Herschel–Bulkley (H–B) fluid with salinity. The present study analyzes the fluid rheology of non-Newtonian fluids with, and without, salinity. Moreover, experiments have been conducted to measure the settling velocity of different diameters of solid particles through Herschel–Bulkley fluids with various salinity conditions. For the rheology analysis, it is found that higher weight percentages of NaCl lead to low values of shear stresses. As well, higher weight percentages of CaCl2 concentration result in a slight increase in shear stresses per a given shear rate. On the other hand, higher percentages of salt concentration cause an increase in the terminal velocity.
... We validated our numerical model against a well-known benchmark problem which uses cylindrical-shape grains and uses Kozeny-Carman equation to calculate permeability as a function of domains porosity ( Hommel et al. 2018 ;Voronov et al, 2010 ;( Lee and Yang, 1997 )): where s is the sphericity, a dimensionless particle geometry parameter computed from Li et al. (2012), D p is the characteristic particle diameter, and is the porosity. ...
Clogging of porous media is controlled by attachment of particles and their subsequent detachment. In this study, we explore particle transport at the pore scale by considering attachment and detachment processes. We use pore structures of three samples which have similar topological properties but different initial porosities. The main focus is on particle detachment, after they are attached to the solid grain boundaries, and to explore how particle detachment affects hydraulic properties and clogging of porous media. A new approach was proposed by combining the lattice Boltzmann method with a Lagrangian method to simulate fluid flow and particle transport, respectively. Comparisons between several simulations, with and without detachment, were used to evaluate the impact of particle detachment on fluid flow velocity distributions. The coefficients of Carman-Kozeny relation were used to relate porosity changes of each sample to its permeability alterations. Additionally, the influence of the initial porosity of the sample and flow velocity on the detachment process was analysed. The results show that compared to the impact of flow velocity, the initial porosity of the media has a greater influence on controlling the rate of detachment and change of pore structures.
