Homogeneous Sphere Research Articles

Towards realistic characterisation of chemical reactors: An in-depth analysis of catalytic particle beds produced by sieving

Optimization of large-scale fixed particle bed catalytic reactors requires extensive insight into the multi-scale bed structure, even down to the micrometre scale. Theoretical studies of chemical reactors provide a time- and cost-effective means to supporting the optimisation process. However, they rely on simplified assumptions for the particles, e.g. homogeneous perfect spheres. In practise, the preparation of catalytic particles cannot attain this level of uniformity. Typical preparation techniques, such as sieving, are conducted with the aim of obtaining particle size distributions within a pre-defined range, governed by the sizes of the sieves. However, such methods offer limited control in the actual particle sizes and shapes. This paper evaluates the impact of sieving on the resulting particles and overall structural morphology of catalytic beds. The bed structure is quantified using micro-focus computed tomography (µ-CT), enabling the non-destructive examination and analysis of over 150 thousand particles, in terms of particle size, shape, uniformity, and interparticle porosity. Furthermore, the chemical performance of the resulting beds is compared. The detailed characterisation achieved paves the way for the evolution of more rigorous computational models coupling intricate, localised hydrodynamics with realistic chemical processes. Validation of such models at the lab-scale will accelerate the development of more accurate large-scale models.

Efficient single-scattering look-up table for lidar and polarimeter water cloud studies.

Combined lidar and polarimeter retrievals of aerosol, cloud, and ocean microphysical properties involve single-scattering cloud calculations that are time consuming. We create a look-up table to speed up these calculations for water droplets in the atmosphere. In our new Lorenz-Mie look-up table we tabulate the light scattering by an ensemble of homogeneous isotropic spheres at wavelengths starting from 0.35 µm. The look-up table covers liquid water cloud particles with radii in the range of 0.001-500 µm while gaining an increase of up to 104 in computational speed. The covered complex refractive indices range from 1.25 to 1.36 for the real part and from 0 to 0.001 for the imaginary part. We show that we can precisely compute inherent optical properties for the particle size distributions ranging up to 100 µm for the effective radius and up to 0.6 for the effective variance. We test wavelengths from 0.35 to 2.3 µm and find that the elements of the normalized scattering matrix as well as the asymmetry parameter, the absorption, backscatter, extinction, and scattering coefficients are precise to within 1% for 96.7%-100% of cases depending on the inherent optical property. We also provide an example of using the look-up table with in situ measurements to determine agreement with remote sensing. The table together with C++, Fortran, MATLAB, and Python codes to interpolate the complex refractive index and apply different particle size distributions are freely available online.

Test of conductor and semiconductor electrocatalysts in high voltage alkaline electrolyzer as production media for green hydrogen

Despite the restricted success of conductor and semiconductor electrodes in solving hydrogen production problems, they provide a promising alternative to expensive conventional electrodes in water electrolysis investigations. Titanium dioxide (TiO2) and silver (Ag) are widely used as photocatalysts in water splitting systems for hydrogen generation. Though TiO2 is an inactive chemical semiconductor with poor conductivity, it has not been entirely investigated as an electrocatalyst yet. Two criteria were used to achieve this target: supplying high voltage to overcome the TiO2 large band gap and immersing it in an alkaline solution to activate its inert surface. For comparison study, Ag noble metal nanoparticles coating was employed as a competitive electrocatalyst. In this regard, the application of Ag and TiO2 coated on Ti electrodes in a hydrogen production system operated under high voltage was reported. The nanoparticles were synthesized using cost-effective and simple methods based on UV-deposition for Ag nanoparticles and the chemical precipitation method for TiO2 nanoparticles. Then the synthesized nanoparticles were deposited on the Ti electrodes by simple immersion. The synthesized nanoparticles and coated electrodes were tested by XRD, SEM, and EDS to study their morphology, structure, particle size, and surface composition. Based on these results, TiO2 nano-powder and coated electrodes exhibited homogenous spheres with a mixture of rutile and anatase phases, the majority being the anatase phase. The Ag-coated Ti substrate possessed a smaller crystallite size compared to TiO2 coated substrate. To evaluate the performance of Ag/Ti and TiO2/Ti electrodes toward hydrogen production, H2 flow rates were measured in a 3.6 M KOH electrolytic solution at 6 V. Hydrogen flow rates obtained for pure Ti, Ag, and TiO2 electrodes at a steady state were 21, 35, and 37 SCCM (standard cm3/min), respectively. Also, it was found that energy consumption was reduced when the electrodes were coated with nanoparticles. Furthermore, the electrolyzer's performance was assessed by calculating the hydrogen production efficiency and the voltage efficiency. The results showed that using TiO2 electrodes gave the best hydrogen production and voltage efficiencies of 27% and 23%, respectively. This study brings new insights about Ag and TiO2 coated electrodes in alkaline water electrolysis at high voltage regarding nanoparticle performance, hydrogen production, system performance, and energy consumption. In addition, minimizing the fabrication and operation costs of hydrogen production is the major enabler for the broad commercialization of water electrolysis devices.

Machine Learning Captures Synthetic Intuitions for Hollow Nanostructures

Machine learning (ML) has been transforming materials science, making great strides in property prediction and materials discovery; however, how ML can bring benefits to nanostructure synthesis, given that the synthesis routines of nanostructures are usually complex with strongly correlated, highly dimensional parameters with narrow experimental window, is rarely explored. Here, we choose hollow nanospheres and emulsion interfacial polymerization as the prototype of material and synthesis routine and propose an ML method to capture synthetic intuitions for guiding the preparation. The quantitative relationship between the reactants, synthesis parameters, and the product morphologies is captured, and the contributions of each feature are analyzed to optimize the reactant amounts and synthesis parameters for hollow and homogeneous spheres. The experimental results are generally consistent with the ML predictions, with the f1-scores of 0.750 and 0.607 for hollow/solid and homogeneity classification, respectively. The obtained hollow carbon spheres show a superior oxygen reduction electrocatalytic performance than solid spheres owing to their improved active site numbers. With the increasing structural complexity of nanomaterials, ML-driven synthetic design will endow great potential and promising prospects.

Absorption of ultraviolet radiation in bacterial spores in clusters in air and on surfaces: Model calculations using the multi-sphere T-Matrix method

Ultraviolet (UV) germicidal irradiation (UVGI) is used to inactivate viruses and kill other microbes to decrease transmission of disease. Microbes such as bacterial spores can occur within clusters of spores or other particles. Such particles, in air or in water, can in some cases partially shield spores within them from UVGI, whether on a surface or suspended. There is a need to better understand how such shielding varies with particle size, composition, and illumination angle. Here the Multi-Sphere T-Matrix (MSTM) method is used to model the absorption of UVGI by bacterial spores in clusters, where each spore is approximated as a homogeneous sphere. The clusters of spores may be surrounded only by air or may be within an encompassing “host” sphere in air. Calculated results of the UV absorption efficiencies for each spore are illustrated for clusters of 54 spores within host spheres of different optical properties, on surfaces with different compositions (polycarbonate, iron and aluminum), and for illumination with UV light from different directions with respect to the cluster and the surface. For the solar UV wavelengths 302 and 325 nm and the deep purple 450 nm, and the unpigmented bacteria modeled here, the penetration depths in both the spores and host sphere are so much larger than the cluster and host sphere size (5.08 µm) that the general effect on the absorption by spores is relatively insensitive to wavelength. Results at 266 nm suggest that in using and validating UVGI for inactivation, the sizes and compositions of the particles are important.

Longitudinal and transverse photophoretic force on a homogeneous sphere exerted by a Bessel beam with selective polarizations.

Predicting the photophoretic force exerted on an optical absorptive particle in a gaseous medium is a challenging problem because the problems of electromagnetic scattering, heat transfer, and gaseous molecule dynamics are involved and coupled with each other. Based on the calculation of the source function distribution inside a homogeneous sphere excited by a Bessel beam using the generalized Lorenz-Mie theory, analytical expressions of the asymmetry vector, which is the key quantity in the calculation of photophoretic force, are given using the adjoint boundary value method. Numerical simulations are performed to analyze the influences of polarization, the half-cone angle, and the beam order of the incident beam, particle size, and absorptivity of the particle on the asymmetry vector for both on-axis and off-axis illuminations. Longitudinal and transverse photophoretic forces on a homogeneous sphere are displayed for the slip-flow regime of gaseous media. The results offer important insights into the working mechanism underpinning the development of heat-mediated optical manipulation techniques and the measurement of the refractive index of particles.

Ion Imprinted Sodium Alginate Hydrogel Beads Enhanced with Carboxymethyl Cellulose and β-Cyclodextrin to Improve Adsorption for Cu2+

To achieve efficient adsorption and recycling of Cu2+ in wastewater, using Cu2+ as template ion, glutaraldehyde as crosslinker, three sodium alginate hydrogel beads including SA, SAC, and SAB beads were prepared by imprinting sol–gel method using sodium alginate (SA) with carboxymethyl cellulose (CMC) and β-cyclodextrin (β-CD) as different precursors, respectively. Scanning electron microscopy and Fourier transform infrared spectroscopy were used to characterize and analyze morphology and composition change of the hydrogel beads, respectively. When the mass ratio of SA to CMC or SA to β-CD reach 1:1, the SAC beads or SAB beads are nearly homogeneous sphere. Then the effects of pH, adsorption time, initial concentration of Cu2+, adsorbent dosage, and coexisting ions on the adsorption efficiency of three hydrogel beads were investigated. The results indicated that adding carboxymethyl cellulose and β-cyclodextrin into skeleton of beads increased the toughness of the beads and improved the adsorption capacity of Cu2+. Compared to the saturated adsorption capacity 510 mg/g of Cu2+ on SA, the saturated adsorption capacity of Cu2+ on SAB and SAC reached 817 mg/g and 822 mg/g, respectively. And their adsorption efficiency for Cu2+ are over 95% at 25 °C with pH of 7, contact time within 350 min, adsorbent dosage of 4 mg/50 mL, and initial concentration of 5 mg/L. Thus, SAC and SAB beads could be used as adsorption material for detecting and removing Cu2+ from wastewater.

A Stochastic Transport Model for the Cumulative Number of Fissions and Deposited Fission Energy

The stochastic theory of neutron transport is extended to describe the cumulative distribution of fission numbers and deposited fission energy in a subvolume of a multiplying assembly. Solutions for the probability distributions are obtained using analytical approximations and Monte Carlo simulation in lumped geometry and in symmetric homogeneous and heterogeneous spheres. The results show the development of a power-law tail in the steady-state fission number and deposited energy distributions when the medium is critical, independent of the fission neutron multiplicity distribution and domain heterogeneity. In contrast, the asymptotic decay is faster than exponential in subcritical media due to rapid chain extinction and in supercritical media due to the increasing probability of chain divergence. A formal asymptotic analysis of the problem in lumped geometry with an arbitrary fission neutron multiplicity confirms the existence of power-law tails at critical.

Ideal Kerker scattering by homogeneous spheres: the role of gain or loss.

We investigate how the optical gain or loss (characterized by isotropic complex refractive indexes) influence the ideal Kerker scattering of exactly zero backward scattering. It was previously shown that, for non-magnetic homogeneous spheres with incident plane waves, either gain or loss prohibit ideal Kerker scattering, provided that only electric and magnetic multipoles of a specific order are present and contributions from other multipoles can all be made precisely zero. Here we reveal that, when two multipoles of a fixed order are perfectly matched in terms of both phase and magnitude, multipoles of at least the next two orders cannot possibly be tuned to be all precisely zero or even perfectly matched, and consequently cannot directly produce ideal Kerker scattering. Moreover, we further demonstrate that, when multipoles of different orders are simultaneously taken into consideration, loss or gain can serve as helpful rather than harmful contributing factors, for the elimination of backward scattering.

Debye-series expansion of T-matrix for light scattering by non-spherical particles computed from Riccati-differential equations.

A new formulation of the Debye series based on the Riccati-differential equations was developed to compute electromagnetic wave scattering by non-spherical particles. In this formulation, the T-matrix was expanded in terms of the Debye series. The zeroth-order term, which corresponds to a combination of diffraction and external reflection, is given by unity minus the external reflection matrix. The higher-order terms are generated from the transmission matrix from the medium to the particle, the internal reflection matrix within the particle and the transmission matrix from the particle to the medium. We demonstrate that the aforementioned four reflection-transmission matrices satisfy the Riccati-differential equations, which can be numerically solved by the fourth-order Runge-Kutta method. The present algorithm can be applied to generalized convex non-spherical particles. The differential equations were analytically validated in the case of a homogeneous sphere. Representative results were given in the case of spheroids. The impacts of the Debye series with various orders on the optical properties of spheroids were revealed with significant details.

Inelastic light scattering from a dielectric sphere with a time-varying radius

This work reports on light scattering by a homogeneous dielectric sphere with a periodically time-varying radius. The off-shell inelastic scattering $T$ matrix, which describes the dynamically changing particle, is evaluated using the Floquet method, and some remarkable phenomena, emerging in the strong- and weak-coupling regimes, are discussed. In particular, the limits of validity of the approximate quasistatic solution are established through comparison with the results of fully dynamic calculations, and the scattering in the strong-coupling regime is analyzed in terms of the general behavior of parametrically driven oscillators. Additionally, the influence of damping of the sphere vibrations on the optical spectra is also investigated.

Effect of Multilayered Structure on the Static and Dynamic Properties of Magnetic Nanospheres.

The development of flexible and lightweight electromagnetic interference (EMI)-shielding materials and microwave absorbers requires precise control and optimization of core–shell constituents within composite materials. Here, a theoretical model is proposed to predict the static and dynamic properties of multilayered core–shell particles comprised of exchange-coupled layers, as in the case of a spherical iron core coupled to an oxide shell across a spacer layer. The theory of exchange resonance in homogeneous spheres is shown to be a limiting special case of this more general theory. Nucleation of magnetization reversal occurs through either quasi-uniform or curling magnetization processes in core–shell particles, where a purely homogeneous magnetization configuration is forbidden by the multilayered morphology. The energy is minimized through mixing of modes for specific interface conditions, leading to many inhomogeneous solutions, which grow as 2n with increasing layers, where n represents the number of magnetic layers. The analytical predictions are confirmed using numerical simulations.

Contribution of Submicron Particles to the Unpolarized and Linearly Polarized Angular Scattering

The scattering by suspended particles is being measured with increasing frequency in the global oceans. Yet, little is known of size fractioned contribution, particularly from submicron particles and to the polarized scattering. In this study, three Mueller scattering matrix elements, P11, P12, and P22, for the bulk particles and for size fractions <0.2 μm and <0.7/0.8 μm were measured using a commercial instrument LISST-VSF in the North Pacific Ocean in 2018 (NPO-18) and in the North Atlantic Ocean in 2021 (NAO-21). We found that P11 and P12 by particles <0.2 μm each had median value that was very similar between the two sites, even though the variability was greater in the NAO-21 than in the NPO-18. Relatively, particles <0.2 µm accounted for the same fraction of total particle scattering in P11 and P12, approximately 20% at near surface water and 40–60% at deeper depths. In contrast, P11 and P12 by particles <0.7/0.8 μm differed between the two sites, which we found was because particles of sizes 0.25–1.0 µm had greater concentration in the NAO-21 than in the NPO-18. P22 normalized to P11 indicated that the sphericity of particles was the same between submicron and bulk particles in the NPO-18 site, but bulk particles deviated more from sphericity than submicron particles in the NAO-21 site where the experiment took place during a phytoplankton spring bloom. Simulations were conducted using three particle models including homogenous spheres, mix of homogenous/coated spheres, and homogenous asymmetric hexahedra to account for the effects of particle shapes or internal structures on the polarized scattering. Using the size distribution that was measured, each of the models can reproduce some of the scattering features measured in this study, but neither of them can reproduce all. Our results suggest that accurate simulation of the polarized scattering by oceanic particles needs to account for both their nonsphericity and heterogeneity, in addition to the concentration and size distribution of the particles.

A Spherical “Earth–Ionosphere” Model for Deep Resource Exploration Using Artificial ELF-EM Field

Fully coupled lithosphere, atmosphere, and ionosphere theory has demonstrated that extremely low-frequency electromagnetic (ELF-EM) fields present a broad application prospect in deep resource exploration, but previous studies have ignored the contribution of the Earth’s curvature. This study extends the theory of ELF-EM over a stratified Earth to the case where the Earth’s curvature must be taken into account, and presents an analytical solution of the ELF-EM field excited by a grounded horizontal antenna in a spherical Earth–ionosphere model, whose theoretical approach and solution method are notably different from the flat Earth–ionosphere model. Additionally, the Earth is treated as a concentric-layered sphere rather than an ideal homogeneous sphere. We aim to investigate the effects of the Earth’s curvature on the surface field, so as to broaden the coverage of the ELF wave in resource exploration. The solution is mathematically accurate and physically reasonable, since it reflects the sphericity and radially stratified structure of the Earth. We first verify the correctness and reliability of the proposed method by comparing the results with FDTD in a full-space spherical model. Additionally, we then compared the spherical results with the conventional controlled-source electromagnetic method and flat Earth–ionosphere results. The results show that when the distance between the transmitter and the receiver is comparable to the Earth radius, the spherical model better reflects the resonance of the wave in the cavity, suggesting that the effect of the Earth’s curvature is not negligible. Then, the numerical simulations conducted to investigate the properties of the EM fields and their sensitivities to the conductivity at depth in the Earth are discussed. Finally, the EM responses of some simple electrical conductivity structures models are modeled to illustrate their prospects in future resource exploration.

Temperature Variation in a Homogeneous Sphere Induced by the Tide-Generating Force

In this paper, we present a semi-coupled theory to compute the temperature variation due to the tide-generating force. The tidal volume strain is first derived in a pure elastic homogeneous sphere, in terms of the classic Love’s solution. Then the temperature variation is obtained by solving the inhomogeneous heat conduction equation by considering both the isothermal and adiabatic conditions on the surface. The results show that the magnitude of the tidal temperature variation can be more than 1 mK, which is detectable by the current precision thermometer.

Optimization of an information system module for solving a direct gravimetry problem using a genetic algorithm

Optimal approaches to solving many problems are required in many areas. One of these areas is the determination of the occurrence of gravity anomalies in oil and gas fields. In this paper is proposed a new approach for determining the source of gravity anomalies in an oil and gas fields by estimating the gravity parameters associated with simple-shaped bodies such as a homogeneous sphere, a horizontal prism, and a vertical step. The approach was implemented in the computational module of the GeoM information system for optimizing the solution of a series of direct gravimetry problems using a genetic algorithm (GA). Approach is based on solving the direct gravimetry problem to minimize the discrepancy of gravity variations by the genetic algorithm. The method allows to select values simultaneously for several parameters of the studied environment. The task is realized through successive approximations based on a given initial approximation of the medium. The paper indicates the initial calculation parameters and criteria for finding optimal solutions for models of the geological environment. The calculations were carried out for such models of the environment as a homogeneous sphere, a horizontal prism and a vertical ledge. For calculations, the results of gravimetric monitoring at one of the Kazakh oil and gas fields were used. The paper demonstrates the operation of the algorithm and presents the results of modeling for three available field profiles. The obtained results of the system showed an acceptable accuracy of the algorithm up to 10-11. The genetic algorithm made it possible to significantly increase the reliability of the model and reduce the working time for analyzing the measured gravitational field

Full Laplace spectrum of distance spheres in symmetric spaces of rank one

We use Lie-theoretic methods to explicitly compute the full spectrum of the Laplace--Beltrami operator on homogeneous spheres which occur as geodesic distance spheres in (compact or noncompact) symmetric spaces of rank one, and provide a single unified formula for all cases. As an application, we find all resonant radii for distance spheres in the compact case, i.e., radii where there is bifurcation of embedded constant mean curvature spheres, and show that distance spheres are stable and locally rigid in the noncompact case.

Critical parameters and decay constants for one-speed neutrons in slabs and spheres with anisotropic scattering

Abstract Time-dependent, one-speed neutron transport equations with strong forward and backward scattering together with isotropic scattering are studied in homogeneous slabs and spheres. First, a simple formal equivalence between the transport equations for a critical and for a time-decaying system is established. Then, the transport equation is converted into a more conventional one. The FN method of solving the resulting transport equation is applied to the calculation of the critical parameters and decay constants for the fundamental mode of the flux distribution and one-speed neutrons in spheres and infinite slabs. Numerical results are given for a number of significant figures and compared with those already available in the literature.

Cobalt oxyhydroxide decorating hollow carbon sphere: A high-efficiency multi-functional material for Li-S batteries and alkaline electrocatalysis

Materials with excellent electrocatalytic properties play an important role in the field of electrochemistry. In this work, a multi-function electrocatalyst of cobalt oxyhydroxide decorating homogeneous porous hollow carbon sphere (CoOOH-PHCS) was designed and fabricated. The CoOOH-PHCS can not only be used as an electrocatalyst to inhibit the shuttle effect in Li-S batteries (LSBs), but also can effectively accelerate the reaction kinetics in oxygen reduction/evolution reactions (ORR/OER). Meanwhile, density functional theory (DFT) calculations were performed to investigate the electrocatalytic activity of the CoOOH-PHCS. Benefiting from the synergy effect of CoOOH and PHCS, the CoOOH-HPC/S electrode exhibits a low capacity decay of 0.04% per cycle in 450 cycles at 1C. Meanwhile, the CoOOH-PHCS demonstrates excellent OER and ORR activity in the alkaline electrolyte. This work explores and reveals the application potential of CoOOH in electrocatalytic field.

Optimal Finite Homogeneous Sphere Approximation

The two-dimensional sphere can’t be approximated by finite homogeneous spaces. We describe the optimal approximation and its distance from the sphere. We compare this distance to the distance achieved by all Platonic and Archimedean solids.