Rough Spheres Research Articles

Hydrodynamics of granular gases of inelastic and rough hard disks or spheres. I. Transport coefficients.

The transport coefficients for dilute granular gases of inelastic and rough hard disks or spheres with constant coefficients of normal (α) and tangential (β) restitution are obtained in a unified framework as functions of the number of translational (d_{t}) and rotational (d_{r}) degrees of freedom. The derivation is carried out by means of the Chapman-Enskog method with a Sonine-like approximation in which, in contrast to previous approaches, the reference distribution function for angular velocities does not need to be specified. The well-known case of purely smooth d-dimensional particles is recovered by setting d_{t}=d and formally taking the limit d_{r}→0. In addition, previous results [G. M. Kremer, A. Santos, and V. Garzó, Phys. Rev. E 90, 022205 (2014)10.1103/PhysRevE.90.022205] for hard spheres are reobtained by taking d_{t}=d_{r}=3, while novel results for hard-disk gases are derived with the choice d_{t}=2,d_{r}=1. The singular quasismooth limit (β→-1) and the conservative Pidduck's gas (α=β=1) are also obtained and discussed.

Scattering cross section of rough metallic spheres at terahertz frequencies

At terahertz frequencies, the detailed fine structures on target’s surface can be compared with the wavelength, and the dispersive dielectric property of metals becomes obvious. Then, it is naturally thought that scattering characteristics of metallic spheres will exhibit a special phenomenon when compared with the situation in microwave band or infrared. Thus, a novel method of scattering modeling and calculation is proposed based on a full-wave approach for rough spheres at terahertz frequencies. The influence of the surface roughness and dielectric parameters of metal spheres on the scattering characteristics is evaluated by the proposed calculation method. With the further analyzing, it is clarified that the backscattering characteristics of metallic sphere can be depicted by Rayleigh region, resonant region, optical region, rough attenuation region, scattering enhancement region and ultraviolet transparent region with the increase of frequencies. Both the frequency dispersion and the rough surface decide the scattering characteristics of the metallic sphere, and also determine the frequency positions and amplitude levels of the rough attenuation region and scattering enhancement region.

Hydrodynamics of wet particles in liquid-solid fluidized beds using kinetic theory of rough spheres model

To actually describe the flow behaviors of particles in the liquid-solid fluidized bed, the effects of liquid film covered on the particles surface and the sphericity of particles need to be considered for quasi-spherical wet particles. Liquid-solid fluidization characteristics are predicted using a two-fluid model incorporating with the kinetic theory of rough spheres (KTRS) model. Simulation results show that the normal restitution coefficient for wet particles covered liquid film increases with an increase of the particles diameter. As for the sphericity of particles, a higher sphericity of particles gives rise to a lower granular temperature and higher solids pressure and viscosity. Also, the normal restitution coefficient of quasi-spherical particles is relatively small, compared with completely sphere. The simulation results obtained by the kinetic theory of rough spheres model for quasi-spherical wet particles are in satisfactory agreement with the experimental data from Lu et al.

Adhesion enhancement in a dimpled surface with axisymmetric waviness and rate-dependent work of adhesion

ABSTRACT Surfaces showing macroscopic adhesion are rare in industry but are abundant in Nature. Adhesion enhancement has been discussed mostly with geometrical systems (e.g. patterned surfaces), more rarely with viscoelasticity, and has the goal of increasing hysteresis and the detachment force at separation. Soft materials are common, and these have viscoelastic properties that result in a rate-dependent increase in toughness. Here the detachment of two half-spaces is studied, one being flat and the other having a dimple in the limit of short-range adhesion and rate-dependent work of adhesion, in the presence of axisymmetric single-scale waviness, which itself results in adhesion enhancement, similarly to the Guduru model of rough spheres. The dimpled surface shows pressure-sensitive adhesion, and when waviness is added, the roughness-induced toughening is enhanced. It is shown that when a rate-dependent work of adhesion is also accounted for, as in the present paper, assuming a power-law dependence of the effective work of adhesion on the crack tip velocity, the two enhancements are not completely multiplicative, as the “viscoelastic” one tends to prevail and indicates a new avenue of research for pressure-sensitive adhesion.

Synthesis of Rough Colloidal SU-8 Rods and Bananas via Nanoprecipitation

Surface roughness plays an important role in determining the mechanical properties, wettability, and self-assembly in colloidal systems. In this work, we develop a simple and fast method to produce rough colloidal SU-8 rods, bananas, and spheres, via the nanoprecipitation of SU-8 in water. During this process, SU-8 nanospheres are absorbed onto the surface of the colloidal SU-8 particles and then cross-linked using UV-light. The size of the spherical asperities and the asperity density are controlled by the concentration of SU-8 used during the nanoprecipitation reaction. Fluorescent labeling of the rough SU-8 colloidal particles allows for their confocal imaging, which demonstrates their stability at high packing fractions. With these newly developed rough particles, we provide a colloidal model system that allows for studies addressing the impact of surface roughness on materials composed of anisotropic particles.

Influences of acid catalysts on the microstructure, bioactivity and cytotoxicity of bioactive glass nanoparticles prepared by spray pyrolysis

Bioactive glasses (BGs) have received considerable attention in the fields of medical and material science and have been applied in various applications due to their superior properties. Although studies have demonstrated the fabrication of BG by various approaches, the effects of acid catalysts in the synthesis of spray pyrolyzed BG remain unclear. Therefore, in this study, we aim to synthesize BG nanoparticles using spray pyrolysis technique and treated them with different acid catalysts of hydrochloric acid, lactic acid and acetic acid. By characterizing the phase information and morphologies of the BG specimens, three morphologies of smooth, rough, and porous spheres were found and their corresponding formation mechanisms were discussed. Finally, evaluations of both bioactivity and cytotoxicity were carried out, and the results suggested that all BG specimens are bioactive while BG treated with hydrochloric acid was associated with greater cell viability than the lactic acid- and acetic acid-treated specimens.

Porous yolk-shell structured Na3(VO)2(PO4)2F microspheres with enhanced Na-ion storage properties

Na3(VO)2(PO4)2F (NVPOF) has been considered as one potential candidate for sodium-ion batteries because of its high operating voltage and theoretical capacity. However, the poor intrinsic electronic conductivity significantly restricts its widespread application. In response to this drawback, we adopt the optimization strategy of tuning the morphology and structure to boost the electrical conductivity and mitigate the capacity fading. In this paper, NVPOF microspheres with unique porous yolk-shell structure were fabricated via a facile one-step solvothermal method for the first time. By monitoring the morphological evolution with time-dependent experiments, the self-sacrifice and Ostwald ripening mechanism from rough spheres to yolk-shell structure was revealed. Benefited from the favorable interwoven nanosheets shell, inner cavity and porous core structure, the resulting NVPOF electrode exhibits superior rate capability of 63 mA h g−1 at 20 C as well as outstanding long-cycling performance with the capacity retention up to 92.1% over 1000 cycles at 5 C.

Production of NiMn2O4 hollow spheres and CoFe2O4 bowl-like structures by using block copolymer stabilized polystyrene spheres as a hard template.

The aim of this study is to highlight the use of polystyrene (PS) latexes stabilized with block copolymers as a hard template in the production of metal oxide hollow spheres. PS latexes produced by dispersion polymerization by stabilizing with tertiary amine methacrylate-based diblock copolymer were used as a hard template in the preparation of nickel manganese oxide (NiMn2O4) hollow spheres and cobalt iron oxide (CoFe2O4) bowl-like structures. Thanks to the diblock copolymer stabilizer with tertiary amine functional groups on the PS surface, precursor salts of CoFe2O4 and NiMn2O4 were first homogeneously deposited on the surface of PS latexes with a controlled precipitation technique. Then, metal oxide hollow spheres and bowl-like structures were produced by calcination. XRD results showed that CoFe2O4 and NiMn2O4 structures were successfully obtained after calcination. The thermogravimetric analysis results showed that the CoFe2O4 and NiMn2O4 contents of the hybrid PS spheres were in the range of 26.0-28.6 wt%. SEM images showed that the inorganic-polymer spheres fused with each other after calcination to form larger magnetic CoFe2O4 bowl-like structures. SEM images also indicated successful production of highly rough NiMn2O4 hollow spheres with nanosheets on the surface.

Using Molecular Simulation to Compute Transport Coefficients of Molecular Gases.

The existing kinetic theory of gases is based on an analytical approach that becomes intractable for all but the simplest molecules. Here we propose a simple numerical scheme to compute the transport properties of molecular gases in the limit of infinite dilution. The approach that we propose is approximate, but our results for the diffusivity D, the viscosity η, and the thermal conductivity λ of hard spheres, Lennard-Jones particles, and rough hard spheres agree well with the standard (lowest order) Chapman-Enskog results. We also present results for a Lennard-Jones-dimer model for nitrogen, for which no analytical results are available. In the case of polyatomic molecules (we consider n-octane), our method remains simple and gives good predictions for the diffusivity and the viscosity. Computing the thermal conductivity of polyatomic molecules requires an approximate treatment of their quantized internal modes. We show that a well-known approximation that relates λ to D and η yields good results. We note that our approach should yield a lower limit to the exact value of D, η, and λ. Interestingly, the most sophisticated (higher-order) Chapman-Enskog results for rough hard spheres seem to violate this bound.

Non-Newtonian rheology in inertial suspensions of inelastic rough hard spheres under simple shear flow

Non-Newtonian transport properties of an inertial suspension of inelastic rough hard spheres under simple shear flow are determined by the Boltzmann kinetic equation. The influence of the interstitial gas on rough hard spheres is modeled via a Fokker–Planck generalized equation for rotating spheres accounting for the coupling of both the translational and rotational degrees of freedom of grains with the background viscous gas. The generalized Fokker–Planck term is the sum of two ordinary Fokker–Planck differential operators in linear v and angular ω velocity space. As usual, each Fokker–Planck operator is constituted by a drag force term (proportional to v and/or ω) plus a stochastic Langevin term defined in terms of the background temperature Tex. The Boltzmann equation is solved by two different but complementary approaches: (i) by means of Grad’s moment method and (ii) by using a Bhatnagar–Gross–Krook (BGK)-type kinetic model adapted to inelastic rough hard spheres. As in the case of smooth inelastic hard spheres, our results show that both the temperature and the non-Newtonian viscosity increase drastically with an increase in the shear rate (discontinuous shear thickening effect) while the fourth-degree velocity moments also exhibit an S-shape. In particular, while high levels of roughness may slightly attenuate the jump of the viscosity in comparison to the smooth case, the opposite happens for the rotational temperature. As an application of these results, a linear stability analysis of the steady simple shear flow solution is also carried out showing that there are regions of the parameter space where the steady solution becomes linearly unstable. The present work extends previous theoretical results (H. Hayakawa and S. Takada, “Kinetic theory of discontinuous rheological phase transition for a dilute inertial suspension,” Prog. Theor. Exp. Phys. 2019, 083J01 and R. G. González and V. Garzó, “Simple shear flow in granular suspensions: Inelastic Maxwell models and BGK-type kinetic model,” J. Stat. Mech. 2019, 013206) to rough spheres.

Contact behaviour of simulated rough spheres generated with spherical harmonics

Normal contact behaviour between non-adhesive fractal rough particles is studied using a finite element method (FEM). A series of spherical grain surfaces with distinguished roughness features are generated by means of Spherical Harmonics. These surfaces are described by two roughness descriptors, namely, relative roughness (Rr) and fractal dimension (FD). The contact behaviour of rough spheres with a rigid flat surface is simulated using FEM to quantify the influences of surface structure and sphere morphology by focusing on contact stiffness and true contact area. The dependence of normal contact stiffness (k) on applied normal force (F) is found to follow a power law (k = αFβ) over four orders of magnitude, with both α and β being highly correlated with Rr and FD. With increasing load, the power exponent converges to that of Hertzian contact, e.g., 1/3, independent of Rr. Regions of true contact evolve through the formation of new microcontacts and their progressive merging, meanwhile the area distributions of contact island induced by various forces tend to obey similar Weibull distributions due to fractal nature in their surfaces. Contacts with larger values of Rr are found to produce contact contours with higher fractal dimension as calculated by a 2D box-counting method. Our results suggest that the correlation between radial lengths in a quasi-spherical particle should be considered in studying contact behaviour.

Application of the kinetic theory of rough spheres to the simulation of the hydrodynamics of particles and liquid phases in a fluidized bed

The flow behaviors of liquid and particles in a fluidized bed are simulated using a liquid-solid two-fluid model, coupling with the kinetic theory of rough spheres. The expressions for the energy dissipation and viscosities of particles are adopted as functions of the tangential restitution coefficient and the restitution coefficient of particles, which consider the effects of particle rotation on the exchange and dissipation of particle energy. The simulated bed expansion height, particle concentration, particle velocity and total granular temperature differ from those not considering particle rotation. According to the simulation results, particle rotation enhances particle aggregation and decreases the bed expansion height, particle axial velocity and total granular temperature. The energy dissipation that is produced by particle rotation constitutes approximately 25% of the total energy dissipation in a liquid-solid system. In addition, two factors that affect particle rotation are explored by changing the tangential restitution coefficient of the particles and the liquid velocity. The simulation results demonstrate that the particle rotation effect is the most significant at β = −0.2, and the particle rotation is enhanced with the increase in the liquid velocity.

Effect of Roughness and Elasticity on Interactions between Charged Colloidal Spheres.

The effects of realistic roughness and elasticity on the interactions between charged silica spheres are studied as a function of surface potential, screening length, interfacial energy, and roughness. The repulsive force Frep that must be overcome to bring charged spheres into contact is relatively insensitive to elasticity unless spheres are hundreds of times softer than silica. Frep is also insensitive to roughness and interfacial energy. In contrast, roughness has a large effect on the binding energy of spheres and the force Fsep to separate them. Both are lowered by 1 to 2 orders of magnitude by the measured surface roughness of less than 1 nm on 1 μm silica spheres. The reason is that interactions between rigid spheres are dominated by the highest surface peaks rather than the entire spherical surface. Elasticity can increase the pull-off force of rough spheres by a factor of 2 or more because additional surface area can be brought into contact. The implications of these results for shear-thickening transitions are discussed.

A critical comparison of two-fluid model, discrete particle method and direct numerical simulation for modeling dense gas-solid flow of rough spheres

Interphase drag coefficient is a critical input in two-fluid model (TFM) and discrete particle method (DPM). In this study, extensive TFM and DPM simulations were carried out to study of the hydrodynamics of gas-solid flows of monodisperse, rough particles in a dense fluidized bed using fourteen drag coefficient correlations available in literature, the simulation results were then compared to the direct numerical simulation (DNS) and experimental data of Tang et al. (2016). It was shown that (i) all TFM and DPM simulations result in a lower bed expansion rate than those of DNS and experiment, which indicates that the true interphase drag force is underestimated by all fourteen drag coefficient correlations; (ii) all DPM simulations can correctly capture, at least in a qualitative sense, the main hydrodynamic features obtained from DNS, but some TFM simulations with the exactly same drag coefficients show anomalous phenomena. This is not an indicator of the failure of the used drag coefficients but might be a sign of the deficiency of the used particle phase stress model in this specific situation; (iii) the time-averaged differential pressure drops of DPM and TFM simulations agree well with DNS results, but the characteristic frequency of pressure fluctuation found in DNS is overestimated by a factor of 2–3 by all DPM and TFM simulations; and (iv) the magnitude of local and global granular temperatures of TFM, DPM and DNS are all in a fair agreement, but the degree of the anisotropy of both local and global granular temperature found in DNS is systematically underestimated by DPM and TFM, especially, the local granular temperature in TFM simulations is inherently isotropic due to the fundamental assumption of the used kinetic theory. This study highlights the need of a better interphase drag coefficient and a better particle phase stress model for modeling dense gas-solid flow.

Sulphur-Doped Ordered Mesoporous Carbon Hollow Spheres with High Catalytic Activity for the Oxygen Reduction Reaction and Exceptional Electrochemical Stability

We reported the synthesis and characterization of the novel and less explored methanol-functionalized Sulphur-Doped Ordered Mesoporous Carbon Hollow Spheres (S-HWf) as metal-free electrocatalyst for the Oxygen Reduction Reaction (ORR) in alkaline media. The S-HWf was synthetized by the silica template-based method, using resorcinol and formaldehyde as carbon source. The doping was made in situ using 2-thiophenemethanol as sulphur source. The functionalization was carried out with methanol solution (0.5 mol L-1) with the aid of intermittent microwave heating. The catalytic activity of S-HWf was compared with that of non-doped Ordered Mesoporous Carbon Hollow Spheres (HW) synthetized by the same method. The morphology of S-HWf and HW analyzed in a Field Emission-Scanning Electron Microscope (FE-SEM) resulted in rough hollow spheres. The diameter and wall thickness were ~304 and ~90 nm for HW, while for S-HWf were ~248 and ~50 nm, respectively. The use of 2-thiophenemethanol as dopant, had an important effect in the morphology. The chemical surface composition determined by X-ray Photoelectron Spectroscopy (XPS) included the presence of C, O, and Si for HW. In addition to these elements, S was also detected at S-HWf (0.4 at. %). The textural properties were determined by N2 adsorption/desorption measurements. S-HWf and HW showed a surface area of 1007 and 505 m2 g-1, respectively, with micro-mesoporosity. Analysis of the electrocatalysts by X-Ray Diffraction (XRD) showed their amorphous structure with low-intensity crystalline phases. Meanwhile, from Raman spectroscopy S-HWf exhibited better ordering in its structure due to a lower value in ID/IG the intensity ratio compared to HW. The catalytic activity of the electrocatalysts for the ORR was evaluated by Rotating-Ring Disc Electrode (RRDE) technique. S-HWf showed a higher performance than HW, with an onset potential of 0.88 V half-wave potential 0.81 V and a current density (j) of -1.49 mA cm-2 at 0.8 V (all potentials vs. RHE). Moreover, its electron transfer number was n= 3.9 with a H2O2 production of ~3%. Furthermore, after accelerated degradation tests (3000 cycles, between 0.6 and 1.0 V), S-HWf showed an improvement in catalytic activity with onset potential of 0.88 V, half-wave potential of 0.82 V and j= -1.69 mA cm-2 at 0.8 V. Also, its n was 3.9 with a production of H2O2 of ~2%. In this study it was found that doping with sulphur and functionalizing with methanol have a positive effect on the catalytic activity for the ORR and the electrochemical stability of Ordered Mesoporous Carbon Hollow Spheres. The electrochemical behavior of the S-HWf electrocatalyst indicated that it is a potential candidate for Anion Exchange Membrane Fuel Cells (AEMFC) cathode applications.

Morphological mapping of high-pressure solvothermal synthesis of BaTiO3 particles

Abstract In this paper BaTiO3 particles were synthesized by an additive-free solvothermal technique. Different combinations of temperature, holding time and, especially, pressure by gas injection were studied to evaluate the effect of the synthesis parameters on particle morphology. Powders were obtained by using titanium(IV) isopropoxide, barium nitrate and potassium hydroxide as reactants and water/ethanol as solvent. The results showed that from 80 °C to 180 °C and 6 h to 24 h at inherent pressure, amorphous rough spheres, assembled nanocubes and irregular particles were formed. Dendritic and flower-like particles were synthesized at high pressures (20–80 bar). Oriented agglomeration and Ostwald ripening were the main crystal growth mechanisms observed.

Two-fluid modelling for cylindrical fluidized beds using kinetic theory for rough spheres

Recently, we have extended the kinetic theory of granular flow (KTGF) to include friction between the spherical particles and tested it in rectangular geometries. In this study, the extended KTGF implemented in cylindrical coordinates is used to model the more-commonly employed cylindrical bubbling fluidized beds. Special attention is paid to the anti-symmetric part of the velocity gradient in the solids stress tensor. For verification of the implementation, a comparison of the present model in the limit of zero friction with the original (frictionless) KTGF model was made. Subsequently, simulations of bubbling fluidized beds of inelastic particles were performed using our extended KTGF and an effective KTGF model for inelastic particles of Jenkins and Zhang. The simulation results show good agreement for the time-averaged solids volume fraction distribution and solids circulation patterns. Finally, our model is validated by predicting the individual bubble behavior in dense bubbling fluidized beds containing different granular materials in a comparison with experimental data from Verma et al. (2014). The extended KTGF leads to an improved agreement with experimental bubble data. Compared to previous work (Yang et al., 2016b, 2017c), and by introducing cylindrical coordinates, the current work demonstrates that the extended KTGF improves predictions for the temporal bubble behavior of cylindrical fluidized beds.

Design of Hierarchical Beads for Efficient Label-Free Cell Capture.

Defined hierarchical materials promise cell analysis and call for application-driven design in practical use. The further issue is to develop advanced materials and devices for efficient label-free cell capture with minimum instrumentation. Herein, the design of hierarchical beads is reported for efficient label-free cell capture. Silica nanoparticles (size of ≈15 nm) are coated onto silica spheres (size of ≈200 nm) to achieve nanoscale surface roughness, and then the rough silica spheres are combined with microbeads (≈150-1000 µm in diameter) to assemble hierarchical structures. These hierarchical beads are built via electrostatic interaction, covalent bonding, and nanoparticle adherence. Further, after functionalization by hyaluronic acid (HA), the hierarchical beads display desirable surface hydrophilicity, biocompatibility, and chemical/structural stability. Due to the controlled surface topology and chemistry, HA-functionalized hierarchical beads afford high cell capture efficiency up to 98.7% in a facile label-free manner. This work guides the development of label-free cell capture techniques and contributes to the construction of smart interfaces in bio-systems.

Large Mpemba-like effect in a gas of inelastic rough hard spheres.

We report the emergence of a giant Mpemba effect in the uniformly heated gas of inelastic rough hard spheres: The initially hotter sample may cool sooner than the colder one, even when the initial temperatures differ by more than one order of magnitude. In order to understand this behavior, it suffices to consider the simplest Maxwellian approximation for the velocity distribution in a kinetic approach. The largeness of the effect stems from the fact that the rotational and translational temperatures, which obey two coupled evolution equations, are comparable. Our theoretical predictions agree very well with molecular dynamics and direct simulation Monte Carlo data.

Driven and undriven states of multicomponent granular gases of inelastic and rough hard disks or spheres

Starting from a recent derivation of the energy production rates in terms of the number of translational and rotational degrees of freedom, a comparative study on different granular temperatures in gas mixtures of inelastic and rough disks or spheres is carried out. Both the homogeneous freely cooling state and the state driven by a stochastic thermostat are considered. It is found that the relaxation number of collisions per particle is generally smaller for disks than for spheres, the mean angular velocity relaxing more rapidly than the temperature ratios. In the asymptotic regime of the undriven system, the rotational-translational nonequipartition is stronger in disks than in spheres, while it is hardly dependent on the class of particles in the driven system. On the other hand, the degree of component-component nonequipartition is higher for spheres than for disks, both for driven and undriven systems. A study of the mimicry effect (whereby a multicomponent gas mimics the rotational-translational temperature ratio of a monocomponent gas) is also undertaken.