Rigid Sphere Research Articles

Migration of two rigid spheres translating within an infinite couple stress fluid under the impact of magnetic field

Migration of two rigid spheres translating within an infinite couple stress fluid under the impact of magnetic field

Study of Conducting Fluid Flow in Composite Regions Past an Impermeable Sphere in the Presence of Magnetic Field

A steady, two dimensional, incompressible, viscous and conducting fluid flow over a fixed rigid sphere has been considered under the effect of magnetic force applied normal to flow direction. The fluid flow occurs in three multiple regions namely fluid, porous and fluid region respectively. The governing equations are reduced into linear PDEs in terms of dimensionless parameters which intern converted into linear ODEs by similarity transformation method. The impact of Hartmann number and porosity on the fluid flow has been analyzed graphically. It is observed that as the Hartmann number increases for fixed porosity, the flow of fluid is well controlled in porous and non-porous regions. Further, as porosity increases for fixed Hartmann number, fluid flow over a porous region is observed. Also, diminishes the fluid velocity in the porous region due to the suppression of the fluid flow as ‘σ’ increases when magnetic field is fixed to finite constant. The same observation is made when the Hartmann number is intensified for the fixed porosity ‘σ’.

Elasticity and Viscoelasticity Imaging Based on Small Particles Exposed to External Forces

Particle-mediated elasticity/viscoelasticity imaging has the potential to expand the elasticity imaging field, as it can provide accurate and local tissue elastic properties as well as density and viscosity. Here, we investigated elasticity imaging based on small particles located within the tissue and at the tissue interface exposed to static/dynamic external loads. First, we discuss elasticity/viscoelasticity imaging methods based on the use of particles (bubbles and rigid spheres) placed within the tissue. Elasticity/viscoelasticity imaging techniques based on the use of particles (bubbles, rigid, and soft spheres) located at the tissue interface are then presented. Based on new advances, we updated some of the models for the responses of the particles placed within the tissue and at the tissue interface available in the literature. Finally, we compared the mathematical models for the particles located within the tissue and at the tissue interface and evaluated the elasticity/viscoelasticity imaging methods based on the use of small particles. This review summarized the methods for measuring the elasticity and viscosity of material using particles exposed to external forces. Remote viscoelasticity imaging can be used to improve material characterization in both medical and industrial applications and will have a direct impact on our understanding of tissue properties or material defects.

Electrosteric, van der Waals and elastic interaction of polyelectrolyte hydrogels

The electrosteric interaction energy for a charged hydrogel and hard plane, and between two charged hydrogels is derived in the Debye–Hückel approximation. This is combined with a van der Waals potential that explicitly addresses the Hamaker constant for the solvent-mediated hydrogel interactions. Then, in the Derjaguin approximation, DLVO-type interaction potentials are provided for hydrogel and hard/rigid spheres, accounting for elastic deformation that accompanies adhesion. As examples, this furnishes the energy for cohesion of soft polyelectrolyte microspheres, and provides a quantitative interpretation for the adhesion of rigid latex spheres to a soft deformable hydrogel, as reported by Sato et al. (Sato et al. 2017 Sci. Rep. 7 , 1–10 ( doi:10.1038/s41598-017-06257-1 )). The theory demonstrates that weak van der Waals attraction of hydrogels is readily balanced by electrosteric interactions, e.g. making colloidal hydrogel dispersions less stable than their rigid-particulate counterparts.

Generating, from scratch, the near-field asymptotic forms of scalar resistance functions for two unequal rigid spheres in low Reynolds number flow

The motion of rigid spherical particles suspended in a low Reynolds number fluid can be related to the forces, torques, and stresslets acting upon them by 22 scalar resistance functions, commonly notated X11A, X12A, Y11A, etc. Near-field asymptotic forms of these resistance functions were derived in Jeffrey and Onishi [“Calculation of the resistance and mobility functions for two unequal rigid spheres in low-Reynolds-number flow,” J. Fluid Mech. 139, 261–290 (1984)] and Jeffrey [“The calculation of the low Reynolds number resistance functions for two unequal spheres,” Phys. Fluids A 4, 16–29 (1992)]; these forms are now used in several numerical methods for suspension mechanics. However, the first of these important papers contains a number of small errors, which make it difficult for the reader to correctly evaluate the functions for parameters not explicitly tabulated. This short article comprehensively corrects these errors and adds formulas that were originally omitted from both papers, so that the reader can verify and implement the equations independently. The corrected expressions, rationalized and using contemporary nondimensionalization, are shown to match mid-field values of these scalars, which are calculated through an alternative method. A Python script to generate and evaluate these functions is provided.

Couple Stress Fluid Flow Through a Porous Media Past A Solid Sphere

A steady, two-dimensional, incompressible couple stress fluid flow over a rigid sphere of radius ‘a’ surrounded by infinite porous region specifying a constant velocity away from the boundary is considered. An exact solution is found for the governing equations which leads to the expression for the stream function and shearing stress. The impact of couple stress parameter and porosity on the flow patterns is examined through streamlines. Also shear stress is computed for various values of couple- stress parameter and porous parameter. The obtained results reveal that as coupling stress parameter increases for fixing the porosity, streamlines are symmetric and meandered near the rigid sphere. But for fixed coupling stress parameter and increase in porous parameter cause the streamlines to move away from the solid sphere. Also, the dimensionless shear stress increases as couple-stress parameter intensifies for fixed porous parameter and vanishes at two stagnation points. The amplitude of the shearing stress raises with raise in porous parameter for fixed coupling stress parameter.

An analysis of slippage effects on a solid sphere enclosed by a non-concentric cavity filled with a couple stress fluids

This investigation shows the effect of slippage on the slow spinning of a rigid sphere covered by a non-concentric spherical hollow full of an incompressible couple stress fluid. Moreover, the velocity slip conditions are employed on surfaces of both the rigid sphere and the cavity. In addition, the solid sphere and the cavity are rotating axially at various angular speeds. The solution is obtained semi-analytically at low Reynolds numbers utilizing the superposition with the numerical collocation approach. This paper discusses the hydrodynamic couple exerted by the fluid on the internal particle. The dimensionless torque increases as the slip and spin slip increase by 99%, the couple stress parameter by 49%, and the separation parameter by 79%. Additionally, the non-dimensional torque decreases with the increase of the size ratio by 89%. Consequently, it is found that all the results agreed with the corresponding numerical analysis in the traditional viscous liquids and the revolving of two eccentric rigid spheres with no slippage (Al-Hanaya et al. in J. Appl Mech Tech Phys 63(5):1–9, 2022).

Evaluation of virtual sensing with spherical array surrounding head for directional noise

Active noise control (ANC) is expected to be applicable to public transportation modalities such as airplanes and trains. In these application systems, passengers may need to avoid wearing devices such as earphones and ear microphones. However, in conventional ANC systems, it is necessary to locate a physical microphone at the ear positions as an error sensor. To overcome this problem, virtual sensing techniques have been studied for estimating sound pressures at ear positions using remote microphones. In this study, we investigated the performance of a virtual sensing method for interpolating the sound pressures at ear positions using a spherical microphone array surrounding the head, based on a spherical harmonic expansion. The experiments were conducted using a rigid sphere instead of a head and dodecahedral spherical microphone array surrounding the sphere. The estimation errors were evaluated for various noise directions at low frequencies (100, 300, 500, and 700 Hz). The experimental results showed that the estimation errors were less than -20 dB for almost all conditions below 500 Hz. By comparison with other virtual sensing methods using a few microphones in the vicinity of the ear positions, we confirmed that our proposed method was effective for any noise direction.

Fullerene Fragment Restructuring: How Spatial Proximity Shapes Defect-Rich Carbon Electrocatalysts.

Fullerene transformation emerges as a powerful route to construct defect-rich carbon electrocatalysts, but the carbon bond breakage and reformation that determine the defect states remain poorly understood. Here, we explicitly reveal that the spatial proximity of disintegrated fullerene imposes a crucial impact on the bond reformation and electrocatalytic properties. A counterintuitive hard-template strategy is adopted to enable the space-tuned fullerene restructuring by calcining impregnated C60 not only before but also after the removal of rigid silica spheres (∼300 nm). When confined in the SiO2 nanovoids, the adjacent C60 fragments form sp3 bonding with adverse electron transfer and active site exposure. In contrast, the unrestricted fragments without SiO2 confinement reconnect at the edges to form sp2-hybridized nanosheets while retaining high-density intrinsic defects. The optimized catalyst exhibits robust alkaline oxygen reduction performance with a half-wave potential of 0.82 V via the 4e- pathway. Copper poisoning affirms the intrinsic defects as the authentic active sites. Density functional theory calculations further substantiate that pentagons in the basal plane lead to localized structural distortion and thus exhibit significantly reduced energy barriers for the first O2 dissociation step. Such space-regulated fullerene restructuring is also verified by heating C60 crystals confined in gallium liquid and a quartz tube.

Edge effect and indentation depth-dependent contact behavior in contact of an elastic quarter-space

The edge effect in contact of an elastic quarter-space is numerically studied in this work. The extension of Hetényi’s approach of overlapping two elastic half-spaces is implemented in the boundary element method to obtain the solution of an elastic quarter-space whose top and side surfaces could be both loaded. In the study on the indentation test of a rigid sphere on an elastic quarter-space, the dependencies of the normal force, mean contact radius, and pressure distribution in contact area as well as the internal von Mises stress in relation to the position of the sphere from the side edge are obtained numerically and expressed by fitting the numerical results. These equations can be also used to interpret the indentation depth-dependent contact behavior: from Hertzian contact at the beginning of the indentation to the non-circular contact at large indentation depth.In addition, the results are compared with a contact case of a quarter-space in which the side surface of the quarter-space is not completely free: shear stresses on the side surface vanish but normal stress exists. The latter case generates very similar results, especially the contact area, but its solutions are much easier to achieve by applying a symmetrical loading on an elastic half-space, offering an effective way to approximate the solution of a quarter-space.

Numerical simulations of suspensions of rigid spheres in shear-thinning viscoelastic fluids

In multiphase flows, accurately modeling the interaction between the liquid phase of complex fluids and a porous medium of solid spheres poses a fundamental challenge. The dynamics of moderately dense non-colloidal suspensions constituted by static random arrays of mono-disperse spherical particles in non-linear viscoelastic fluids is studied numerically. This numerical study consists of about 9000 different systems, in which the volume fraction ϕ (0.04≤ϕ≤0.2) of the dispersed solid phase, the Reynolds number Re(5≤Re≤50), the solvent viscosity ratio β(0.05≤β≤0.9), the Weissenberg number Wi(0.5≤Wi≤4), and the mobility parameter of the Giesekus model α (0.1≤α≤0.5) were varied to understand the particle's interactions with the viscoelastic suspending fluid. We aim to investigate the relationship between the volume fraction of the dispersed solid phase and the non-linear rheology of shear-thinning viscoelastic fluids with the normalized average drag force ⟨F⟩. In addition, by assessing the flow patterns predicted numerically, we were able to provide a characterization of the velocity and stress fields as a function of the simulation parameters.

Exploring the interplay between memory effects and vesicle dynamics: A five‐dimensional analysis using rigid sphere models and mapping techniques

AbstractThe memory effect in vesicle dynamics refers to the persistence of shape changes in lipid vesicles, a type of lipid bilayer membrane that mimics some features of real cells, particularly red blood cells (RBCs). To study this effect, a fractional rigid sphere model in five dimensions has been investigated, which maps the dynamics of a vesicle using the Caputo operator. This model provides new insights into the mechanisms behind the memory effect as well as the emergence of two other motions, namely, tank‐treading with underdamped and tank‐treading with overdamped vesicle oscillations, in addition to the tank‐treading mode where the vesicle rotates about its axis while maintaining a constant shape. Overall, this work represents a significant advance in our understanding of vesicle dynamics and has important implications for understanding the behavior of RBCs.

Low frequency sound isolation by a metasurface of Helmholtz ping-pong ball resonators

We study both numerically and experimentally an acoustic metasurface based on coupled Helmholtz resonators to obtain broadband low-frequency spectral responses for acoustic insulation. A hierarchical approach is proposed, starting from single and coupled Helmholtz resonators, up to a periodic array of resonators. To this end, we performed numerical simulations using the finite element method, in which the resonators are modeled as drilled rigid spheres in airborne environment and experimental demonstrations based on ping-pong balls as Helmholtz resonators in an acoustic reverberation box. We showed the alteration of the low-frequency response of acoustic insulation resulting from inter-unit coupling in acoustic metasurfaces, and the apparition of additional attenuation by inserting a plexiglass board as support for the structure.

Out-of-contact peeling caused by elastohydrodynamic deformation during viscous adhesion.

We report on viscous adhesion measurements conducted in sphere-plane geometry between a rigid sphere and soft surfaces submerged in silicone oils. Increasing the surface compliance leads to a decrease in the adhesive strength due to elastohydrodynamic deformation of the soft surface during debonding. The force-displacement and fluid film thickness-time data are compared to an elastohydrodynamic model that incorporates the force measuring spring and finds good agreement between the model and data. We calculate the pressure distribution in the fluid and find that, in contrast to debonding from rigid surfaces, the pressure drop is non-monotonic and includes the presence of stagnation points within the fluid film when a soft surface is present. In addition, viscous adhesion in the presence of a soft surface leads to a debonding process that occurs via a peeling front (located at a stagnation point), even in the absence of solid-solid contact. As a result of mass conservation, the elastohydrodynamic deformation of the soft surface during detachment leads to surfaces that come closer as the surfaces are separated. During detachment, there is a region with fluid drainage between the centerpoint and the stagnation point, while there is fluid infusion further out. Understanding and harnessing the coupling between lubrication pressure, elasticity, and surface interactions provides material design strategies for applications such as adhesives, coatings, microsensors, and biomaterials.

Деформирование слоистых композитных пластин при низкоскоростном контакте с жестким индентором

The computational finite element model of contact between a steel sphere and a composite plate was developed in the ANSYS software package. The model includes geometric description of the contact, materials management, computational mesh generation using the SOLID186 and SOLID187 finite elements, as well as the surface-to-surface contact model using the CONTA174 and TARGET170 contact elements. The paper identifies influence of the rigid sphere radius on the woven composite structure and shows areas of the local composite destruction. Satisfactory compliance was obtained between the numerical calculation results and full-scale study of a contact between rigid indenter of different radii and the fiberglass laminate. The safety factor values are provided according to four criteria. The developed model of contact between the indenter and the composite plate made it possible to obtain stress fields in the carbon-plastic composite material with the laying layers [45°, –45°]n and [45°, 90°, –45°, 0°]n. Destruction in layers based on the numerical calculation results was analyzed using various stress criteria. Carbon composite had more destroyed layers due to low strength in the transverse direction. Destruction zone in the carbon composite was larger than in the fiberglass composite, and the pattern [45°, –45°]n had a smaller damage area compared to [45°, 90°, –45°, 0°]n.

Ice breaking by low-velocity impact with a rigid sphere

Penetrator–ice plate impact subjected to dynamic loading constitutes many scientific applications for ice, such as controlling ice disasters by penetrating the ice cover and then entering underwater to explosive ice breaking on Earth, and life detection and resource development under water ice sheet on outer space planets. We present experimental results of brittle damage induced by a small spherical projectile impacting an ice plate with a thickness of 6–50 mm using a drop ball test device or a vertical gas gun. The corresponding impact velocities vary from 2 to 74 m/s. Crater parameters, residual velocity and energy absorption are investigated and assessed. The main fracture patterns and crater formation are captured by two high-speed cameras. A dynamic recrystallization phenomenon of polycrystalline ice is observed, and its formation mechanism is preliminarily analysed. The effects of the impact velocity, ice sample thickness, and restriction conditions on dynamic fracture processes and failure modes are systematically explored. These results improve our understanding of dynamic fracturing mechanism in ice engineering applications.

Investigating projectile penetration into immersed granular beds via CFD-DEM coupling

Projectile penetration into an immersed granular bed is a common phenomenon in both geophysics and engineering, encompassing various scenarios such as immersed crater formation and offshore soil-structure interaction. It involves the complex physical interaction between the fluid and granular materials. In this study, we investigate the dynamics of projectile penetration into a granular bed immersed in a fluid using a coupled computational fluid dynamics and discrete element method (CFD-DEM). The granular bed is composed of polydisperse particles, and the projectile is modeled as a rigid sphere. The morphology of crater formation, the dynamics of the projectile, and the drag force characteristics in immersed cases were studied in detail and compared to the dry scenario. The numerical results show that the final penetration depth of the projectile follows an empirical relation derived from experimental observations, where the falling height and the drag force during penetration obey a power-law function and a modified generalized Poncelet law, respectively. The interstitial fluid not only provides direct drag force, but also enhances the effective drag force of the granular bed by improving its generalized friction and effective viscosity in different configurations. Micro-analyses of the velocity evolution and contact force network in different stages of the fluid–solid interaction were performed to clarify the penetration dynamics. This research provides insights into the mechanisms of projectile penetration and the effects of interstitial fluid on granular media, which are crucial in engineering applications such as offshore anchoring, ball penetration tests in soft sediments, and soil-structure interactions.Graphical

Occurrence state and enrichment mechanism of rhenium in molybdenite from Merlin Deposit, Australia

Rhenium (Re) is one of the critical metals, and molybdenite (MoS2) is the main host mineral for Re. Previous studies have shown that the distribution of Re in molybdenite is highly heterogeneous, and the occurrence state and enrichment mechanism of Re in molybdenite is not clear. The molybdenite of Merlin deposit has typical Re rich characteristics, which is an ideal object to study the occurrence state and enrichment mechanism of Re in molybdenite. Based on the geological research of the deposit, this study systematically investigated the Re-rich molybdenite of the Merlin deposit using LA-ICP-MS and STEM techniques. The LA-ICP-MS results showed that the content of Re in molybdenite ranged from 67 to 2726 ppm, and the distribution of Re content in molybdenite was extremely uneven and irregular. The STEM results showed that there was no independent Re mineral in molybdenite, and Re atoms were found to substitute molybdenum (Mo) atoms in situ in the Re-rich area of molybdenite. The substitution mechanism of Re was clarified at the atomic scale in a visual form, and a corresponding rigid sphere stacking model was established. Mo atoms are sandwiched between two layers of S atoms, while Re atoms enter the molybdenite lattice and substitute Mo atoms in situ, thus changing the lattice structure of the original molybdenite matrix. Rare lattice defects such as five-fold twinning were identified in the Re-rich area of molybdenite in high-resolution HAADF STEM images, which are related to plastic deformation caused by the low stacking fault energy and stress of hexagonal molybdenite. It is speculated that lattice defects such as five-fold twinning is an important mechanism for the enrichment of Re in molybdenite. The magmatic-hydrothermal fluids released from the intrusion of igneous rocks may have provided the main source of ore-forming materials for the Merlin deposit. The ore-forming fluids, which are rich in Mo4+ and Re4+, underwent redox reactions with carbonaceous shale, resulting in the decrease in temperature and oxygen fugacity, and the increase in S2- concentration. This ultimately led to the precipitation and enrichment of Re4+ and Mo4+ to form the Re-rich molybdenite in the Merlin deposit.

DEM analyses of mesoscopic failure mechanism and stress bearing mechanism of compacted snow subjected to unconfined compressive loading

In order to explore the mesoscopic failure mechanism and bearing mechanism of compacted snow under loading. First, the skeleton of dendritic snow crystal was constructed by 13 ice rigid sphere particles which are bonded together using a completed bond contact model. Second, a "falling snow method" was proposed and used to simulate the whole process of natural snowfall, i.e. snow generation, snow falling, snow deposition, and snow compaction. Third, the compacted snow sample was sintered at different temperatures with different times; in sintering process, the snow particles were bonded together by the completed bond contact model. Finally, after contact model parameter calibration by reported snow test results, the unconfined compression tests on the finished sintering snow were carried out and the mesoscopic failure mechanism and stress bearing mechanism were analyzed. Take the sintering temperature of −10 °C and finished sintering samples for example, the results show that the number of compacted snow bond breaks was mainly contributed by tension bond breaks. Meanwhile, with the increase of density, the ratio of bond breaks in tension and compression was higher. When the density was below 475 kg·m−3, the bond breakage was dominated by bending. While the density was above 475 kg·m−3, the bond breakage was mainly shearing. The contribution of the normal contact force to the total axial stress accounted for about 65% which was greater than that of the tangential contact force (ρ = 400 kg m−3). This study can provide support for the mesomechanical failure theory of compacted snow engineering, such as snow roads, compacted snow runways, and snow foundations.

Stiffness of Contacts between Adsorbed Particles and the Surface of a QCM‐D Inferred from the Adsorption Kinetics and a Frequency‐Domain Lattice Boltzmann Simulation

AbstractA simulation based on the frequency‐domain lattice Boltzmann method (FreqD‐LBM) is employed to predict the shifts of resonance frequency, Δf, and half bandwidth, ΔΓ, of a quartz crystal microbalance with dissipation monitoring (QCM‐D) induced by the adsorption of rigid spheres to the resonator surface. The comparison with the experimental values of Δf and ΔΓ allows to estimate the stiffness of the contacts between the spheres and the resonator surface. The contact stiffness is of interest in contact mechanics, but also in sensing because it depends on the properties of thin films situated between the resonator surface and the sphere. The simulation differs from previous implementations of FreqD‐LBM insofar, as the material inside the particles is not included in the FreqD‐LBM algorithm. Rather, the particle surface is configured to be an oscillating boundary. The amplitude of the particles' motions (displacement and rotation) is governed by the force balance at the surface of the particle. Because the contact stiffness enters this balance, it can be derived from experimental values of Δf and ΔΓ. The simulation reproduces experiments by the Krakow group. For sufficiently small spheres, a contact stiffness can be derived from the comparison of the simulation with the experiment.