Smooth Spheres Research Articles

Mean square displacement of intruders in freely cooling multicomponent granular mixtures.

The mean square displacement (MSD) of intruders (tracer particles) immersed in a multicomponent granular mixture made up of smooth inelastic hard spheres in a homogeneous cooling state is explicitly computed. The multicomponent granular mixture consists of s species with different masses, diameters, and coefficients of restitution. In the hydrodynamic regime, the time decay of the granular temperature of the mixture gives rise to a time decay of the intruder's diffusion coefficient D_{0}. The corresponding MSD of the intruder is determined by integrating the corresponding diffusion equation. As expected from previous works on binary mixtures, we find a logarithmic time dependence of the MSD which involves the coefficient D_{0}. To analyze the dependence of the MSD on the parameter space of the system, the diffusion coefficient is explicitly determined by considering the so-called second Sonine approximation (two terms in the Sonine polynomial expansion of the intruder's distribution function). The theoretical results for D_{0} are compared with those obtained by numerically solving the Boltzmann equationby means of the direct simulation Monte Carlo method. We show that the second Sonine approximation improves the predictions of the first Sonine approximation, especially when the intruders are much lighter than the particles of the granular mixture. In the long-time limit, our results for the MSD agree with those recently obtained by Bodrova [Phys. Rev. E 109, 024903 (2024)2470-004510.1103/PhysRevE.109.024903] when D_{0} is determined by considering the first Sonine approximation.

Back interface engineering by designing core–shell structured mesoporous carbon spheres counter electrode in thin–film solar cells

Exploration of economical and highly effective counter electrodes is crucial for both fundamental research into and the commercial application of dye-sensitized solar cells (DSCs) and perovskite solar cells (PSCs). Herein, a new type of core–shell structured mesoporous carbon spheres (Ag@MCSs) was meticulously designed and synthesized as a low-cost counter electrode to optimize back interface. The tailored mesoporous core–shell structure and metal nanoparticle core can optimize the energy level alignment and improve the conductivity of the counter electrode. These improvements facilitate charge carrier extraction and transport processes and inhibit recombination at the back interface of the counter electrode/perovskite. The hole transport layer–free PSCs using Ag@MCSs counter electrode obtains a power conversion efficiency (PCE) of 12.36 %, surpassing the parallel PSCs based on smooth surface carbon spheres (SSCSs) and micro/mesoporous carbon spheres (MMCSs) counter electrodes. Additionally, Ag@MCSs provide numerous catalytically active sites, smooth mass transfer channels, and improved conductivity, resulting in superior catalytic activity for iodide redox couple regeneration in DSCs, generating a high PCE of 8.25 %. This study is expected to offer a feasible pathway for exploring cheap counter electrodes and back interface engineering to accelerate mass and carrier transport processes in the back interface of PSCs and DSCs.

Thermal analysis of packed bed thermal energy storage system with dimpled spherical capsules

The thermal storage potential of a packed bed filled with paraffin wax capsules was examined. Heat transfer fluid (HTF) at 70 °C inlet temperature for dimpled and plain stainless-steel capsules was compared for three different flow rates, 1 L/min, 3 L/min and 5 L/min. In general, dimpled spherical capsules sustain more heat than plain spherical capsules at the same flow rate, according to instantaneous and cumulative heat stored. Spherical capsules with dimples exhibited a 30 % improvement in charging rate compared to smooth spheres, particularly at elevated flow rates. Specifically, at a flow rate of 5 L/min, dimpled capsules achieved faster charging and sustained higher temperature compared to plain capsules. Higher flow rates (3 and 5 L/min) result in steeper temperature increases and an earlier peak temperature phase compared to the lower flow rate (1 L/min). Key dimensionless heat transfer numbers were examined. The Stefan number was found to be 0.1966 for an HTF inlet temperature of 70 °C and a latent heat of fusion (Lm) of 213 kJ/kg. Heat transfer increases when Reynolds numbers increased from laminar (123.8 at 1 L/min) to turbulent (619.1 at 5 L/min). Rayleigh number decreased over time but increased for dimpled capsules, indicating improved convection. Dimpled capsules had higher Nusselt numbers and increases with flow rate, indicating better convective heat transfer. Dimpled capsules absorbed heat faster and stored more energy, giving them a viable and efficient Packed Bed Latent Thermal Energy Storage system design.

Frictional Contacts Between Rough Grains With Fractal Morphology

AbstractSurface morphology plays a crucial role in friction between two contacting geomaterial surfaces, yet many questions remain unanswered regarding how detailed frictional responses deviate from analytical solutions for smooth surfaces due to the presence of roughness. In this study, we revisit the Cattaneo‐Mindlin problem for contacts between two fractally rough elastic or elasto‐plastic spheres generated based on ultra‐high degree (e.g., up to 2,000) spherical harmonics with the corresponding wavelength less than a thousandth of the mean grain diameter. Transverse contacts are simulated by finite element method, validated by the extended Cattaneo‐Mindlin solution to full slide regime for smooth sphere contacts. Extensive simulations are conducted to study contacts between two rough spheres with various surface geometries, micro friction coefficients, normal contact distances, relative roughness, fractal dimensions, and wavelength ranges. Out results indicate that: (a) the new analytical solution can approximately predict the macro contact response except for extremely high relative roughness and narrow wavelength range; (b) deviations induced by roughness from smooth sphere contacts can be neutralized by plasticity, high normal contact interference, and high micro friction coefficient; and (c) fractal dimension impacts frictional contacts less than relative roughness. The main cause of these phenomena can be credited to the underlying microscale contact information. Contact area and stress distributions and their evolutions provide concrete evidence of these observed behavior. This work provides a pathway for applying computational contact mechanics to many geophysical fields, such as the asperity model in earthquake science and the mechanics of granular materials.

Terminal velocity and drag coefficient of a smooth steel sphere moving in the water-filled vertical and inclined glass pipe (Newton regime)

This paper aimed to determine new data on terminal velocities and drag coefficients of single spheres moving inside a vertical and inclined glass pipe filled with water using the Particle Image Shadowgraph technique in the range of Reynolds numbers from 1420 to 12,740. The inclination angle α of the pipe varied from 0° to 30° relative to the vertical position. In the experiment, smooth steel spheres with diameters ranging from 3 to 9.5 mm were used, and the pipe had a fixed inner diameter of 40 mm. For verification, the experimental results of the drag coefficients were compared with known data from other authors for a free-settling sphere and a sphere rolling down a pipe wall or plane. Finally, the paper presents a new regression model describing the relationship between the sphere drag coefficient and Reynolds number when the cosine of the pipe inclination angle is varied.

Effects of surface roughness on the drag coefficient of spheres freely rolling on an inclined plane

An experimental investigation identifying the effects of surface roughness on the drag coefficient ( $C_{D}$ ) of freely rolling spheres is reported. Although lubrication theory predicts an infinite drag force for an ideally smooth sphere in contact with a smooth wall, finite drag coefficients are obtained in experiments. It is proposed that surface roughness provides a finite effective gap ( $G$ ) between the sphere and panel, resulting in a finite drag force while also allowing physical contact between the sphere and plane. The measured surface roughnesses of both the sphere and panel are combined to give a total relative roughness ( $\xi$ ). The measured $C_{D}$ increases with decreasing $\xi$ , in agreement with analytical predictions. Furthermore, the measured $C_{D}$ is also in good agreement with the combined analytical and numerical predictions for a smooth sphere and wall, with a gap approximately equal to the root-mean-square roughness ( $R_q$ ). The accuracy of these predictions decreases for low mean Reynolds numbers ( $\overline {Re}$ ), due to the existence of multiple scales of surface roughness that are not effectively captured by $R_{q}$ . Experimental flow visualisations have been used to identify critical flow transitions that have been previously predicted numerically. Path tracking of spheres rolling on two panels with different surface roughnesses indicates that surface roughness does not significantly affect the sphere path or oscillations. Analysis of sphere Strouhal number ( $St$ ) highlights that wake shedding and sphere oscillations are coupled at low $\overline {Re}$ but with increasing $\overline {Re}$ , the influence of wake shedding on the sphere path diminishes.

The combined influence of spin and roughness frequency on sphere aerodynamics

AbstractThe lift and drag of spinning spheres roughened with macro-roughness elements are examined. The velocity field of these same spheres in flight is measured with particle image velocimetry (PIV). Several spheres with varying roughness are examined at various spin rates and fixed Reynolds number. Unlike previous studies, where the roughness height is varied, in the present work, the number of roughness elements is varied. The PIV datasets are used to determine the boundary layer separation points for each case. Comparing the lift and drag to the separation points reveals that (1) the separation points become more asymmetric with spin (the Magnus effect), (2) The drag increases with the size of the wake, and (3) the drag increases with the asymmetry of the separation points, meaning that lift on spheres is accompanied by increased drag. Scant evidence of this third effect has been reported previously. Additionally, it is shown that, counter to smooth spheres, the force transmitted to the surface through the roughness elements leads to significant drag. The drag is shown to increase with the number of roughness elements while the lift decreases. Results have implications for understanding aerodynamic forces on bluff bodies with roughness and passive control of aerodynamic forces through roughness element frequency rather than the traditional roughness height.

Photocatalytic degradation of persistent antibiotic pollutants by MOF-derived bird-nest ferric molybdate

A photocatalyst (PC) with an optimized morphology exhibits better pollutant photodegradation because of the augmentation of the surface area available for redox reactions and light harvesting. Here, we synthesized a Fe2(MoO4)3 (FMO) PC from a coordinated Fe metal-organic framework (MOF) precursor. During this process, FMOMOF was pyrolyzed to rearrange the organic structure of the Fe-MOF precursor. This synthesis strategy resulted in a unique PC made of stacked nanosheets (NSs) organized in a bird-nest structure. Compared to smooth FMOFC spheres synthesized from uncoordinated Fe ions, FMOMOF exhibited a 3.6-time larger surface. In addition, FMOMOF NSs were accompanied by smaller nanoparticle and quantum dot satellites, which expedited charge separation. FMOMOF was evaluated for the photodegradation of the polluting antibiotics tetracycline hydrochloride (TCH) and oxytetracycline hydrochloride (OTCH). The PC readily photodegraded above 90 % of both antibiotics and completely mineralized a large fraction. Illuminated FMOMOF oxidized TCH and OTCH 1.6 to 3.0 times faster than FMOFC and was also reusable. A larger surface exposing more redox sites and a better charge separation efficiency were responsible for the improved photooxidation performance of FMOMOF. Thus, these results describe how a MOF precursor can be employed to develop a promising FMO PC capable of removing recalcitrant antibiotics.

Dissolution of CaO in SiO2-CaO-Al2O3 Slag in Si Production

This work investigates the dissolution of CaO into three different compositions of SiO2-CaO-Al2O3 slag similar to those found in industrial Si furnaces. It was found that CaO dissolution into the slag is fast. During the dissolution process, a layer containing 35–42% CaO was formed between the CaO particle and the slag, which corresponded to the phases CaO·Al2O3·2SiO2 or 2CaO·Al2O3·SiO2 in this study. Two models were investigated to determine the dissolution rate of the three slags. In the first model, the CaO particle is assumed to be a smooth shrinking sphere, and the rate controlled by the chemical reaction rate. The second model assumes that the rate is controlled by mass transport and depends on the diffusion rate of CaO through a boundary layer on the surface of the CaO. Both models gave similar accuracy to the experimental values, and a proportional relationship between the rate constants and the viscosities was obtained. At 1500 °C, the diffusion coefficients were found to be in the order of 10−6 cm2/s.

PREPARATION AND IN-VITRO ESTIMATION FOR GASTRORETENTIVE FLOATING HOLLOW – MICROSPHERES OF FAMOTIDINE

Objective: The present study’s objectives were to prepare and evaluate gastroretentive floating hollow-microspheres (HM) of the selected Famotidine (FM) to enhance its retention time within the stomach. Methods: HM was prepared by solvent emulsion diffusion technique utilizing various polymers such as ethyl cellulose, eudragit L100, eudragit S100 as polymers, and Dichloromethane and methanol as solvents. The formulated HM was estimated for their particle-size, entrapment efficiency, floating ability, scanning electron microscopy, and in vitro drug release of drug. Results: The average particle-size of the formulated HM was within the range of 262.3±3.5 to 323.1±2.1μm. The SEM confirmed the smooth surface, sphere shape, and hollow cavity within it. The formulated microspheres showed good floating behavior for up to 8 h because of their low particle size. The invitro release profile of the HM displayed a controlled-release of FM microspheres in pH1.2 for up to 8 h. Conclusion: The result depicts that the formulated HM of FM by virtue of good floating time and sustained release properties is likely to improve the retention time within the stomach and thereby the oral bioavailability.

Passive control of flow-induced vibration of a sphere using a trip wire

We experimentally investigated the potential of a trip wire as a passive control mechanism for controlling flow-induced vibration (FIV) of a three-dimensional bluff body. The effect of a surface trip wire was investigated for varying diameter ratio in the range 1.3×10−2⩽k/D⩽6.7×10−2, where k is the wire diameter and D is the sphere diameter, and trip-wire location in the range 20∘≤ϕ≤60∘, where the angle ϕ was measured from the leading stagnation point. The FIV response of the sphere is characterised for a wide range of reduced velocities 3⩽U∗⩽20, defined as U∗=U/fnwD, where U is the free stream velocity and fnw is the natural frequency of the system in water. It was found that for a fixed trip-wire diameter ratio, the vibration amplitude decreased progressively with increasing ϕ. Furthermore, the synchronisation regime became narrower, and the mode II and the plateau branches of the FIV response occurred for lower reduced velocities, compared to those for a smooth sphere. The control was highly effective for high reduced velocities (U∗>10) with a maximum reduction of up to 97.8% for ϕ=60∘. Interestingly, thicker trip wires (k/D>1.3×10−2) were effective in disrupting Mode I, but induced a galloping-like response for higher reduced velocities. Tripping proved to be an effective passive control strategy for spheres, with the optimal trip-wire size varying across Mode I to Mode III.

Implementation of the Hybrid ADI-FDTD Scheme to Maxwell Equation for Mathematical Modeling of Breast Tumor

Breast cancer is the most common cancer in women, and non-destructive detection of the tumor is vital. The interaction of electromagnetic waves with breast tissue and the behavior of waves after interaction are used to model tumor detection mathematically. The behavior of electromagnetic waves in a medium is described using Maxwell's equations. Electromagnetic waves propagate according to the electrical properties of a medium. Since the electrical properties of tumor tissue are different from those of normal breast tissue, it is assumed that the tumor is a lossy dielectric sphere, and the breast is a lossy dielectric medium. Under this assumption, Maxwell's equations are used to calculate the scattered field from the tumor. The field scattered by the tumor is different from other tissues because their dielectric properties are different. The location and size of the tumor can be determined by utilizing the difference in scattering from the tissues. While the scattering field from the tumor in spherical geometric form is analytically calculated, it is not analytically possible to calculate the scattering field from the tumor in different geometric shapes. In addition to non-destructive detection of the tumor, an efficient numerical method, the finite difference time domain method (FDTD), is used to simulate the field distribution. After the location of the tumor is determined, the Alternating Direction Implicit (ADI) FDTD method, which gives simulation results by dividing the computation domain into smaller sub-intervals, can be used. Scattered fields are calculated analytically in the geometry where the tumor is in the form of a smooth sphere, and in more complex geometry, the field distributions are successfully obtained with the help of MATLAB using FDTD and ADI-FDTD algorithms.

A Pressure Drop and Particle Image Velocimetry Investigation into Depressurized Loss-of-Coolant Accident Parameters Applied to Packed Beds with an Aspect Ratio of D/dp = 4.4

New developments in porous media modeling have allowed for a new opportunity to implement experimental data for validation and verification. This includes velocity measurements using particle image velocimetry and global pressure drop measurements that are used to produce pressure drop correlations. We conducted such experiments on two very similar facilities of packed spheres by the authors of this paper. The results from the measurements are presented in this paper as a complete experimental study of a packed bed of smooth spheres through a two-prong approach. First, a set of global pressure drop correlations are validated with experimental data and presented as a function of porous Reynolds numbers. Second, the local velocity measurements from three depths spanning 2.4 sphere diameters are presented and further analyzed through the use of a normalized probability distribution function of the time-resolved velocity field. The conclusion of this paper is a suggestion for the results to be used in the creation or validation of computational fluid dynamics porous media models in the measured flow regimes for a packed bed of smooth spheres with an aspect ratio between the sphere diameter and the empty column diameter of 4.4.

Photochromic performance optimization of polyurethane microcapsules by interfacial polymerization method

AbstractSpiropyran photochromic materials have been widely studied in military camouflage, optical data storage, information encryption, and fashion ornaments. The non‐photochromism and low endurance of solid spiropyran make the challenges of their application. Photochromic microcapsules with a butyl acetate solution of spiropyran as core and polyurethane as shell are synthesized via interfacial polymerization. The optimized polyurethane photochromic microcapsules are prepared with a Tween 20 concentration of 4 wt%, core–shell ratio of 16:5, and spiropyran concentration of 0.40 wt%. Polyurethane photochromic microcapsules with a mean particle diameter of 0.33 μm are obtained. The morphology shows smooth spheres, and the core–shell structure is observed. Butyl acetate in the microcapsule core does not evaporate at a temperature lower than 218.01°C as the microcapsule shell insulates heat. The polyurethane photochromic microcapsules are mixed with adhesive, thickener, and water into a paste and screen‐printed on cotton fabric. The printed fabric shows the ΔE of 17.56, 11.93, and 6.96 after 80s irradiation with the xenon lamp intensity of 102, 68, and 34 mW cm−2. The light stability of the photochromic fabric is excellent as ΔE decreases about 8.28% after 20 cycles of UV‐Vis irradiation.

Artificial intelligence-based analysis of time-lapse images of sphere formation and process of plate adhesion and spread of pancreatic cancer cells.

Background: Most pancreatic cancers are pancreatic ductal adenocarcinomas (PDAC). Spherical morphology formed in three-dimensional (3D) cultures and the effects of anticancer drugs differ between epithelial and mesenchymal PDAC cell lines. In the human pancreas, cancer cells form 3D tumors, migrate to adjacent tissues, and metastasize to other organs. However, no effective methods exist to examine the ability of the tumor mass to migrate to surrounding tissues in vitro. We used spheres formed in 3D culture to investigate whether the migratory ability of tumors of PDAC cell lines, including epithelial and mesenchymal cell lines, varies. Methods: Sphere formation and adhesion and spread on culture plates were examined by artificial intelligence-based analysis of time-lapse imaging using five epithelial and three mesenchymal PDAC cell lines. Fused and non-fused areas of the sphere surface during sphere formation on low-attachment plates, the adhesion area to normal culture plates, and the sphere area maintaining its original form during adhesion to plates were measured. Results: Immunocytochemical staining confirmed that E-cadherin was highly expressed in epithelial PDAC spheres, as was vimentin in mesenchymal PDAC spheres, in 2D culture. When forming spheres using low-attachment plates, most epithelial PDAC cell lines initially showed decreased sphere area, and then the covering cells fused to form a smooth surface on the sphere. Mesenchymal PANC-1 and MIA PaCa-2 cells showed little reduction in sphere area and few areas of sphere surface fusion. When formed PDAC spheres were seeded onto normal culture plates, spheres of epithelial PK-8 cells-which have the highest E-cadherin expression, form numerous cysts, and have smooth sphere surfaces-did not adhere to normal plates even after 60h, and epithelial PK45-P and T3M-4 spheres hardly adhered. Conversely, the area of adhesion and spread of mesenchymal PANC-1 and KP4 cell spheres on normal plates markedly increased from early on, forming large areas of attachment to plates. Conclusion: Seeding spheres formed in 3D culture onto culture plates can clarify differences in tumor migration potential to surrounding areas. The masses formed by each PDAC cell line varied in migratory ability, with mesenchymal PDAC masses being more migratory than epithelial PDAC masses.

The contact mechanics of a UK railway ballast

A newly developed apparatus was used to investigate the contact mechanics between particles of a common UK railway ballast. The data were then compared with the models currently and commonly used in geotechnical discrete-element method (DEM) analyses, but the discrepancy between the predictions and measurements is large even at small loads. The first contact behaviour was much softer than the Hertz–Mindlin model for smooth spheres, both in normal and shear. Even if the normal loading could be fitted better with a model that accounted for roughness, the elastic nature of these models could not capture the plasticity that is evident on unloading. Large displacement shear cycles caused not only an increase of inter-particle friction, as discussed previously, but also a significant degree of particle interlock arising from the wear of the contacts. While there were no rate effects for sliding shearing, contact ageing displacements could be observed at pre-failure loads, although these stabilised after a few days. Pre-failure cyclic loading resulted in stiffnesses that increased in lateral loading but decreased in normal loading; in both cases, however, this stabilised after a few tens of cycles, while the stiffnesses at the reversals of the large displacement cycles did not evolve with continued cycling. The presence of water did not affect the lateral stiffness and the influence of the normal load was consistent with Hertz–Mindlin, even if the absolute values were much softer. It can be concluded that the current commonly used models for DEM analyses are not applicable for ballast/crushed rock and alternative models should also focus on plasticity at the asperity scale.

Diffusion of intruders in granular suspensions: Enskog theory and random walk interpretation.

The Enskog kinetic theory is applied to compute the mean square displacement of impurities or intruders (modeled as smooth inelastic hard spheres) immersed in a granular gas of smooth inelastic hard spheres (grains). Both species (intruders and grains) are surrounded by an interstitial molecular gas (background) that plays the role of a thermal bath. The influence of the latter on the motion of intruders and grains is modeled via a standard viscous drag force supplemented by a stochastic Langevin-like force proportional to the background temperature. We solve the corresponding Enskog-Lorentz kinetic equationby means of the Chapman-Enskog expansion truncated to first order in the gradient of the intruder number density. The integral equationfor the diffusion coefficient is solved by considering the first two Sonine approximations. To test these results, we also compute the diffusion coefficient from the numerical solution of the inelastic Enskog equationby means of the direct simulation Monte Carlo method. We find that the first Sonine approximation generally agrees well with the simulation results, although significant discrepancies arise when the intruders become lighter than the grains. Such discrepancies are largely mitigated by the use of the second Sonine approximation, in excellent agreement with computer simulations even for moderately strong inelasticities and/or dissimilar mass and diameter ratios. We invoke a random walk picture of the intruders' motion to shed light on the physics underlying the intricate dependence of the diffusion coefficient on the main system parameters. This approach, recently employed to study the case of an intruder immersed in a granular gas, also proves useful in the present case of a granular suspension. Finally, we discuss the applicability of our model to real systems in the self-diffusion case. We conclude that collisional effects may strongly impact the diffusion coefficient of the grains.

Formation of whey protein isolate–dextran conjugates by Maillard reaction with ethanol-water pretreatment

A simple, efficient, and low-cost Maillard reaction method was developed through ethanol-water pretreatment. The formation of whey protein isolate (WPI)–dextran conjugates was confirmed using the degree of glycosylation, ultraviolet absorbance, browning intensity, color, and sodium dodecyl sulfate-polyacrylamide gel electrophoresis. The significant conformational changes were illuminated because of the higher wavenumber shift of absorption peaks of FTIR amide I, II, and III bands, the reduction of fluorescent signal, and the decrease of surface hydrophobicity. Scanning electron microscopy revealed the morphological transition of WPI from a smooth sphere to an inhomogeneous block structure with rough and uneven surface before and after covalent grafting of dextran. The strong steric hindrance and abundant hydrophilic hydroxyl groups from covalently conjugated dextran dramatically inhibited the aggregation between conjugate molecules which exhibited low turbidity and good solubility in a wide pH range from 2.0 to 10.0. Emulsifying activity and emulsifying stability of WPI were significantly improved after glycosylation. This work will be beneficial to control the formation of light-colored Maillard reaction products under high substrate concentration, high reaction rate, and low water content at mild temperatures for short processing time, and to facilitate the large-scale preparation of glycosylated protein with desirable physicochemical properties.

Nickel-based tungstate supported with different forms of SnS2 to achieve improved photocatalytic performance

Semiconductor materials have been applied in many research directions such as photoelectrocatalysis, and shortening the electron transport pathway by coupling semiconductors is an effective path to promote the capability of photocatalytic hydrogen-producing. The crystalline SnS2 and amorphous SnS2 were combined with NiWO4 respectively, in the respective optimal hydrogen-producing conditions, it was 298.6 μmol for SnS2/NiWO4 (amorphous J-SnS2 and NiWO4) and 228.5 μmol for J-SnS2 NiWO4 (crystalline SnS2 and NiWO4). A series of characterization results showed that SnS2/NiWO4 showed better photocatalytic hydrogen-producing performance than J-SnS2/NiWO4 under the same test conditions. The catalysts SnS2 and NiWO4 were constructed into p-n type heterojunction SnS2/NiWO4 by electrostatic self-recombination. SEM, XRD and electrochemical tests demonstrate that the high hydrogen-producing performance of SnS2/NiWO4 is due to the establishment of p-n heterojunction, which enhances the electron transport efficiency. The experimental data were used to test the photocatalytic hydrogen-producing activity of SnS2/NiWO4 with the control variable method, then it was proved that the photocatalytic hydrogen-producing volume of SnS2/NiWO4 reached 298.6 μmol in 5 h, which was 3.51 times that of NiWO4 at 5 h hydrogen-producing of 85 μmol. The morphology of nanoparticles NiWO4 attached to a smooth surface sphere SnS2 provides a larger specific surface area and more reactive sites for the photocatalytic eosin hydrogen-producing system, in addition the establishment of p-n type heterojunction structure effectively improves the utilization rate of the sacrificial TEOA and photosensitizer EY, thereby improving the hydrogen-producing performance of SnS2/NiWO4, which offers a feasible policy for photocatalytic efficient hydrogen-producing technology.

The effect of surface geometry on the aerodynamic behaviour of a football

Several studies have investigated the effect of surface features on the aerodynamic behaviour of a sphere or a football. Research on footballs typically compare real footballs with highly complex seam geometry and surface texture, making it difficult to identify which features influence the aerodynamic behaviour. This study commissioned many 3D printed footballs with regularly increasing seam length and surface texture to undertake a designed experiment to study these changes in a controlled fashion. Each ball was tested in a wind tunnel in non-spinning cases, or spinning about a vertical axis, at a range of speeds and key aerodynamic parameters were extracted from the data. Several methods were employed to characterise the roughness of each ball, and these roughness metrics were statistically tested for correlations with selected aerodynamic parameters. Using these relationships provides design guidance to football manufacturers to understand how modifying their surface geometry would influence the ball’s aerodynamic behaviour. In general, increasing the volume of roughness of the ball, measured as the change in volume of the ball introduced through seams or texture compared to a smooth sphere, decreased the critical Reynolds number. Balls with larger texture elements, particularly those with protrusive texture, had a much lower critical Reynolds number than other balls with the same absolute volumes of roughness. The post-critical drag coefficient did not significantly correlate with any of the roughness features of the balls. In a spinning case, the balls with high roughness generated a higher side force, this relationship plateaued at a certain level of roughness. The reverse Magnus behaviour changed significantly with the surface roughness; as the overall roughness volume of the ball increased, the Reynolds number at which the reverse Magnus changed to a conventional Magnus effect decreased. The large protrusive texture elements were effective at preventing a reverse Magnus effect from occurring at all in the tested Reynolds number range.