Attractive Forces Research Articles

Casimir interaction driven by hyperbolic polaritons

Abstract Casimir interaction is an intriguing phenomenon that is induced by electromagnetic quantum fluctuations, which dominates the interaction between microstructures at small separations and is essential for micro- and nano-electromechanical systems (MEMS and NEMS). However, Casimir interaction driven by hyperbolic polaritons remains an unexplored frontier. In this work, we investigate the Casimir interaction between natural hyperbolic material hexagonal boron nitride from the perspective of force distribution with different optical axis orientations for the first time. The attractive Casimir force is remarkably enhanced due to the excitation of volume-confined hyperbolic polaritons (HPs). Furthermore, distinct repulsive contributions to the force are observed due to surface-confined HPs that only exist when the optical axis is in-plane. The HPs are associated with a striking thickness dependence of spectral force properties, suggesting that the discrete volume-confined HPs lead to the attractive-repulsive transition of Casimir force. This work sheds light on the relation between HPs and the vacuum fluctuation-induced force, which could offer new opportunities for the development of the MEMS and NEMS.

Study on the molecular interactions of binary mixtures of N-methyl benzyl amine with halo methane’s through thermodynamic properties and correlation with the Jouyban–Acree model

ABSTRACT The thermodynamic and transport properties of binary mixtures of N-methyl benzyl amine (NMBA) with halo methane compounds at temperatures from 303.15 K to 313.15 K were investigated. The study analysed the excess molar volume, excess isentropic compressibility, deviation in viscosity, and excess Gibbs free energy for activation of viscous flow using measured densities (ρ), viscosities (η), and speeds of sound (u). The research also examined the impact of the inductive effect on excess properties concerning intermolecular attractive forces between the respective constituents. Furthermore, the Jouyban–Acree model was employed to correlate density, speed of sound, and viscosity with composition and obtained good agreement.

Effect of temperature on the mechanical properties of aluminum polycrystal using molecular dynamics simulation

The initial temperature has a considerable effect on aluminum polycrystals' physical stability and mechanical performance, with the possibility to optimize their mechanical properties for practical applications. Thus, using a molecular dynamics technique, the effect of temperature on the mechanical properties of aluminum polycrystals is studied. Stress-strain curves, ultimate strength, and Young's modulus were all measured at temperatures of 300, 350, 400, and 450 K. The findings from MD simulations show that the initial temperature significantly affects the physical stability and mechanical performance of designed aluminum polycrystals. The aluminum polycrystal experiences a numerical increase in ultimate strength and Young's modulus from 6640 to 74.072 to 7.055 and 79.226 GPa, respectively, when subjected to the optimal initial conditions of 350 K. With further increasing temperature to 450 K, ultimate strength and Young's modulus decrease to 6.461 and 74.413 GPa, respectively. The observed decrease in ultimate strength and Young's modulus of the aluminum polycrystal as the temperature increased from the optimal condition of 350 K–450 K can be attributed to the weakening of interatomic attraction forces at higher temperatures. This reduction in interatomic bonding strength resulted in decreased material stiffness and resistance to deformation, leading to lower ultimate strength and Young's modulus values. This study's novelty lies in its comprehensive assessment of the initial temperature's effects on the mechanical performance of aluminum polycrystals, providing valuable insights for practical applications and advancing beyond previous efforts in the literature.

Numerical simulations of a coaxial bubble pair rising in a liquid metal column under horizontal magnetic fields

The motion and coalescence of a coaxial bubble pair rising in a liquid metal column under horizontal magnetic fields were numerically examined using the VOF method in this present paper. The MHD (Magnetohydrodynamics) effects on the characteristics of rise velocity, flow field, and coalescence process of bubble pair by considering various wall confinement ratios (Cr) were analyzed. The results indicate that the effects of magnetic field and wall confinement on the coalescence of the coaxial bubbles are non-monotonic. For smaller Cr, a higher initial rise velocity of the bubbles is generated by strengthening the counter-rotating toroidal vortices around bubbles in the initial stage, but the terminal rise velocity decreases in the stable stage. In the presence of the magnetic field, both the initial rise velocity and terminal rise velocity decrease. A horizontal magnetic field makes the flow field around the bubbles be anisotropic by weakening the toroidal vortices on both sides of the bubbles along the magnetic field direction, which also dampens the wake vortices of the leading bubble and thus reduces the attractive force of wake effect acting on the tailing bubble. On the other hand, the downward Lorentz force induced by the magnetic field on the top of the leading bubble suppresses its upward motion, which makes the tailing bubble collide with the leading bubble earlier. As the competition between the above two mechanisms varies with the magnetic field strength, the coalescence time of the bubble pair also changes accordingly. Particularly, a strong horizontal magnetic field tends to promote the bubbles coalescence under the wall effects and delay that when the wall effects are minor or negligible. For Ha=771, bubbles coalescence at Cr=2 is about 32 % earlier than that at Cr=4.

Agglomeration behaviors of different types of complex TiN inclusions in high titanium wear resistant steel

Large-sized titanium-containing inclusion clusters seriously affect the continuous casting and performance of high titanium wear-resistant steel. In the current work, thermodynamic calculations were firstly conducted to predict the formation of various complex TiN inclusions, viz, TiOx-TiN, Al2O3–TiN and LaAlO3–TiN. Based on that, laboratory-scale experiments were designed to prepare samples containing a single type of complex TiN inclusions. The agglomeration characterizes of different complex inclusions were compared by combing in-situ observation based on confocal laser scanning microscopy and Newtonian motion equation. Furthermore, the Kralchevsky-Paunov model was used to study the influences of density and size on the agglomeration behavior of complex TiN inclusions. The result shows that the attractive force between TiOx-TiN complex inclusions increases from 1.93 × 10−18 to 4.34 × 10−17 N, while it was 3.41 × 10−17 to 5.12 × 10−16 N for Al2O3–TiN complex inclusions and 6.42 × 10−18 to 1.14 × 10−16 N for LaAlO3–TiN inclusions. Based on the experimental results and theoretical calculation, the agglomeration tendency of Al2O3–TiN is the strongest due to the considered size and compared to the TiOx-TiN inclusions, the stronger agglomeration tendency of LaAlO3–TiN ones can be attributed to their higher density.

Cityphilia and cityphobia: A multi-scalar search for city love in Flanders

Cities, towns, and rural areas form a complex spatial system influenced by governance, economic factors, and the perceptions of their residents. This paper introduces the concepts of 'cityphilia' and 'cityphobia' as metaphors for the spatial attraction and repulsion forces that shape local quality of life. It aims to create and validate an operational framework for understanding citizens' appreciation and attachment to their living environment, often referred to as 'city love.' This framework considers two key components, 'body' and 'soul,' encompassing both physical and social aspects. Building upon Charles Tiebout's work on the competitive attractiveness of cities and aligning with contemporary research on the geography of happiness, a conceptual model is developed and applied to identify and assess the components of city love using various indicators. These indicators encompass local attractiveness, local public expenditures, and inter-urban interdependencies. The model is empirically tested in the context of Flanders, Belgium, a region comprising 300 distinct municipalities, both urban and rural. A Beta regression model is employed, which incorporates spatial dependencies to examine multi-scalar effects on residential satisfaction. The results affirm the soundness of the 'city love' framework and emphasize the significance of central place systems in providing tangible and intangible well-being services to citizens within a hierarchical spatial structure. These findings carry notable implications for urban policy and management, shedding light on how local attractiveness and interdependence shape the well-being of residents in diverse urban and rural settings.

Regulation research on weak co-adsorption and nonsteady-state capture for C6H6/CO2 over carbon materials

With the intention of capturing both benzene (C6H6) and carbon dioxide (CO2) from indoor air, it is assuring of getting both C6H6 and CO2 simultaneously adsorbed over activated carbon materials. Thus, in this study, how adsorption of C6H6 and CO2 performs over single-wall carbon materials is minutely investigated via density function theory (DFT). Specifically speaking, direct electronic interaction between C6H6 and CO2, co-adsorption features and nonsteady-state capture processes of C6H6/CO2 over single-wall carbon nanotube (CNT) as well as regulation of CNTs towards more stable adsorption are main contents in this study. According to results, C6H6 and CO2 are weakly mutually attracted because of limited electrostatic attraction forces and hydrogen-bond effects, which are also the major reason for consequent weak co-adsorption state over pure CNT. In the meantime, owing to repulsive forces of π-orbital electrons from pure CNT to C6H6, both of C6H6 and CO2 could be only captured by pure CNT in nonsteady state. However, with phosphorus (P) and aluminum (Al) embedded as dopants, surficial electron distribution is altered to a large degree and local electron-enriched centers of modified CNTs are formed to enhance connection with C6H6/CO2, especially stronger electrostatic positron–electron attraction and faster capture speeds from free-state to adsorption-state at relatively high temperatures. Overall, this study provides plentiful information of utilizing single-wall carbon materials for fast indoor air purification in a passive way.

Synthesis of aluminum alginate/graphene oxide/boehmite biopolymeric nanohybrid for the decontamination of Cu(II) and 2-chlorophenol

BackgroundSustainable biomaterials are crucial in wastewater treatment applications and are constantly in demand. Multifunctional nanohybrids can eliminate organic and inorganic pollutants from wastewater. MethodsHerein, aluminum alginate/graphene oxide/boehmite (Al-Alg/GO/AlOOH) has been synthesized and characterized using Fourier Transform Infrared Spectrophotometer (FT-IR), Transmission Electron Microscopy (TEM), and X-ray diffraction (XRD). The scavenging of 2-chlorophenol (2-CP) and copper (II)) onto synthesized hybrid biopolymer has been investigated as a function of reaction time, influence of pH, initial concentrations, and temperatures. Significant FindingsThe adsorption of Cu(II) onto Al-Alg/GO/AlOOH nanohybrid was more favorable than the 2-CP. The scavenging of Cu(II) and 2-CP was pH dependent and optimum adsorption capacity was found 83 mg/g for Cu(II) at pH 5.5 and 63 mg/g at pH 9.0 for 2-CP, respectively. The Cu(II) and 2-CP adsorption best fit the Redlich-Peterson (R-P) isotherm model. The equilibrium kinetic data for Cu(II) adsorption was fitted well to the Elovich model, and 2-CP adsorption was closely fitted to the pseudo-first-order (PFO) kinetic model. Cu(II) scavenging was spontaneous and endothermic, while, 2-CP adsorption was exothermic. Cu(II) and 2-CP adsorption mechanisms onto Al-Alg/GO/AlOOH have proposed mainly attraction forces, complexation, and hydrogen bonding. After five successive regenerations, Al-Alg/GO/AlOOH was considered a recyclable and promising adsorbent for removing organic and inorganic pollutants from the contaminated aquatic environment.

GraphT-T (V1.0Beta), a program for embedding and visualizing periodic graphs in 3D Euclidean space.

Following the work of Day & Hawthorne [Acta Cryst. (2022), A78, 212-233] and Day et al. [Acta Cryst. (2024), A80, 258-281], the program GraphT-T has been developed to embed graphical representations of observed and hypothetical chains of (SiO4)4- tetrahedra into 2D and 3D Euclidean space. During embedding, the distance between linked vertices (T-T distances) and the distance between unlinked vertices (T...T separations) in the resultant unit-distance graph are restrained to the average observed distance between linked Si tetrahedra (3.06±0.15 Å) and the minimum separation between unlinked vertices is restrained to be equal to or greater than the minimum distance between unlinked Si tetrahedra (3.713 Å) in silicate minerals. The notional interactions between vertices are described by a 3D spring-force algorithm in which the attractive forces between linked vertices behave according to Hooke's law and the repulsive forces between unlinked vertices behave according to Coulomb's law. Embedding parameters (i.e. spring coefficient, k, and Coulomb's constant, K) are iteratively refined during embedding to determine if it is possible to embed a given graph to produce a unit-distance graph with T-T distances and T...T separations that are compatible with the observed T-T distances and T...T separations in crystal structures. The resultant unit-distance graphs are denoted as compatible and may form crystal structures if and only if all distances between linked vertices (T-T distances) agree with the average observed distance between linked Si tetrahedra (3.06±0.15 Å) and the minimum separation between unlinked vertices is equal to or greater than the minimum distance between unlinked Si tetrahedra (3.713 Å) in silicate minerals. If the unit-distance graph does not satisfy these conditions, it is considered incompatible and the corresponding chain of tetrahedra is unlikely to form crystal structures. Using GraphT-T, Day et al. [Acta Cryst. (2024), A80, 258-281] have shown that several topological properties of chain graphs influence the flexibility (and rigidity) of the corresponding chains of Si tetrahedra and may explain why particular compatible chain arrangements (and the minerals in which they occur) are more common than others and/or why incompatible chain arrangements do not occur in crystals despite being topologically possible.

Surface Tension Estimation of Steel above Boiling Temperature

Surface tension is an important characteristic of materials. In particular at high temperatures, surface tension values are often unknown. However, for metals, these values are highly relevant in order to enable efficient industrial processing or simulation of material behavior. Plasma, electron or laser beam processes can induce such high energy inputs, which increase the metal temperatures to, and even above, boiling temperatures, e.g., during deep penetration welding or remote cutting. Unfortunately, both theoretical and experimental methods experience challenges in deriving surface tension values at high temperatures. Material models of metals have limitations in explaining complex ion interactions, and experimentally measuring temperature and surface tension at high temperatures is a challenge for methods and equipment. Therefore, surface wave analysis was conducted in this work to derive surface tension values around the boiling temperature of steel and identify trends. In addition, a simple ion interaction calculation was used to simulate the impacting parameters that define the surface tension. Since both the experimental values and simulation results indicate an increasing trend in surface tension above the boiling temperature, it is concluded that the dominating attractive forces above this temperature should increase with increasing temperature and lead to increasing surface tension forces in the surface layers of liquid metal.

Magnetic focusing sensor and its characterizations of defect non-destructive testing for ferromagnetic steel plate

The fast development in precision manufacturing and product quality inspection of ferromagnetic material desperately demands that the defect determining the performance, service life and reliability of the mechanical part should be accurately sensed, detected and evaluated. However, conventional defect detection methods and related magnetic induction sensors are usually characterized with low accuracy in small defect detection, which makes the non-destructive testing (NDT) for ferromagnetic material full of challenges. Thus, a new magnetic focusing sensor is proposed and designed for the precision defect detection of ferromagnetic steel plate here. First, the theoretical principle analysis of the magnetic focusing sensor is introduced, and the preliminary finite element modeling (FEM) is conducted to demonstrate the feasibility of the magnetic focusing sensor in tiny defect inspection. Then, both the static and coupling dynamic characterizations of the magnetic focusing sensor are investigated using the FEM method. The optimal structural parameters of the magnetic focusing (MF) sensor in static conditions are summarized. Furthermore, the effects of the dynamic movement of the MF sensor on the multi-physical fields of the magnetization field, electric field, electromagnetic attraction force field and thermal field are all revealed. Finally, experiments regarding the performance evaluation and comparison between the MF sensor and other two magnetic flux leakage (MFL) sensors are conducted, and the prominent capabilities of accurate and precise defect detection for the MF sensor is demonstrated through the defect detection with different sizes. The effectiveness and feasibility of the MF sensor in detecting tiny defects on ferromagnetic object, as well as its great potential for practical application is therefore validated. Additionally, the main conclusions, advantages of the MF sensor are summarized and the future work is discussed.

A diffused double-layer model of bulk nanobubbles in aqueous NaCl solutions

Bulk nanobubbles, known for their extraordinary stability due to their electrically charged surface, still have an elusive mechanism. This research examines the surface electrical properties of oxygen nanobubbles in various NaCl solution concentrations, utilizing a diffused double-layer model. The process involves the creation of nanobubbles through the hydrodynamic cavitation technique, followed by an assessment of their size and zeta potential. To quantify their influence on nanobubble stability, the thickness of the double layer, the density of surface charge, electrostatic repulsion and attractive force, and interaction energy between bubbles are evaluated. The results show that adding NaCl to nanobubble solutions increases bubble size while decreasing their negative zeta potential, minimizing repulsive electrostatic interactions among the bubbles. These findings are consistent with the diffused double-layer theory. Specifically, higher NaCl concentrations in solutions lead to thinner double layers and decreased energy barriers. Observing nanobubble stability in a 10 mM NaCl solution over six months reveals a decrease in bubble size accompanied by an increase in zeta potential. This rise in negative zeta potential correlates with changes in Debye length and ionic strength, inversely proportional to the solution's conductivity, likely due to reduced NaCl concentration over time. Furthermore, the pressure differential at the bubble interface is insufficient to overcome the pressure caused by the liquid's surface tension, indicating potential limitations in applying the diffused double-layer model. This highlights the need for further investigation to establish a more comprehensive understanding of the mechanical stability of bulk nanobubbles.

Thermal Expansion of Metal Oxides in Silicate Melts: A Simple Theoretical Analysis

The isobaric, isochemical coefficient of thermal expansion ( α) is the proportionality constant relating ∂V/V and ∂T. Noting that ∂V/V equals ∂lnV at constant pressure and composition (i.e., P and X): α=(∂VV∂T)P,X=(∂lnV∂T)P,X A polynomial expression for the temperature dependence of lnV yields direct and accurate calculation of α of melts and glasses. Using the approach, αG of Na-silicate glasses is shown to be constant between 300 and ∼650 K (P and X constant), but it increases linearly with Na2O content, indicating that α is controlled mostly by Na behaviour. Values of α for a melt or glass are necessarily (thermodynamically) related to the coefficients of thermal expansion of its ‘N’ melt components ( αN) by: α=α1θ1+α2θ2+α3θ3+⋯+αNθN where θ represents volume fraction of a component. Calculated αNa2O and αSiO2 values compare satisfactorily with reported values for melts containing ∼40–60 mole% Na2O but are less satisfactory for highly siliceous melts, implying need for refinement of α values. The Coulombic force of attraction between cation and anion is the primary determinant of the magnitude of α values of alkali and alkaline earths oxides. Their values represent a lower bound on α of 3d and 4f modifier oxides. Values larger than this lower bound likely result from a change in coordination number (CN) from higher to lower CN values of modifier cations. Experimental and molecular dynamics studies indicate that partial charges on NBO (O of Si-O-M moieties) and BO (O of Si-O-Si moieties) are about −0.96 and −0.64 respectively, thus NBOs should be incorporated into the first coordination spheres of modifier cations in preference to BOs. A simple mechanism is proposed whereby NBO-BO exchange occurs and CN of the modifier cation decreases with minimal topological adjustment or energetic cost to the melt.

Heteroaggregation and sedimentation of natural goethite and artificial Fe3O4 nanoparticles with polystyrene nanoplastics in water

Iron oxide nanomaterials play important roles in biogeochemical processes. This study investigates the effects of representative natural carbonaceous materials (humic acid [HA] and extracellular polymeric substances [EPS]) and cations on the heteroaggregation and sedimentation of engineered and natural iron oxide nanomaterials with montmorillonite and sulfate- and amine-modified polystyrene (PS) nanoparticles (NPs) (S- and N-PS NPs, respectively) in water, assessing their environmental behavior and differences in colloidal stability parameters. In addition, a novel extended Derjaguin–Landau–Verwey–Overbeek theory (XDLVO) was developed to describe the mechanism of colloidal behavior that concurrently considers gravitational and magnetic attraction forces. In CaCl2 solution and most natural water samples, negatively charged S-PS NPs promoted heteroaggregation with goethite and iron oxide (Fe3O4) NPs more than positively charged N-PS NPs with increased nanoplastic particle concentration. In seawater, the introduction of S- and N-PS NPs increased the maximum net energy (barrier) (ΦMAX) of heteroaggregation and sedimentation with goethite and Fe3O4 NPs, facilitating dispersal and suspension of the system. The X-ray photoelectron spectroscopy (XPS) and molecular dynamics simulation results suggested that Ca2+ forms bridging interactions between Fe3O4 and S-PS NPs to promote aggregation, while competitive adsorption occurs between the N atoms of N-PS NPs and Ca2+ on the surface of Fe3O4 NPs. The study findings will help to improve the understanding of interfacial processes affecting ions at nanomaterial/water interfaces and assessments of the geochemical behavior and ecological risks of nanoplastics.

New dynamical system for circular satellites relative motion

In this work, a new perturbed dynamical system to describe the satellites relative motion is derived considering that the gravitational attractive force is generated by the continued fraction potential. In this context, the parameter of continuation fraction creates an additional force which is the source of perturbation for motion. Aiming to find a simple and precise mathematical model to characterize this motion while maintaining high accuracy results, a new circular linear perturbed system is also derived under the effect of this parameter. Furthermore, the perturbed linear dynamical system of satellites relative motion is studied, along with finding the conditions of stable and periodic solutions. Finally, these solutions are calculated and their graphical simulation is introduced. We emphasize that the new proposed system could be applied in space rendezvous missions aiming at getting precise descriptions of satellites relative motion.

Modeling of novel cross-type hybrid 4-pole carrier system and experimental air gap control

PurposeThe purpose of this paper is to introduce a novel cross (+) type yoke with hybrid electromagnets and new reluctance modeling to precisely calculate attraction force is given.Design/methodology/approachThe comparison of attraction force and torque analyses between the proposed formulation and the existing formulation in the literature is comparatively presented. For the correctness of the force and torque values calculated in the model created, the system was created in ANSYS Maxwell and its accuracy was proved by making analyses. The maglev carrier system is inherently unstable from the point of view of control engineering. For that, it needs an active controller to eliminate this instability. For the levitation of the carrier system, it is necessary to design a controller in three axes (z, α and β). I-PD controller was designed for the air gap control of the carrier system in three axes and the controller parameters were determined by the canonical method.FindingsWhile the new formulation proposed in the modeling of the carrier system has a maximum error of 1.03%, the existing formula in the literature has an error of 16.83% in the levitation distance point.Originality/valueA novel cross-type hybrid carrier system has been proposed in the literature. With the double integral used in modeling the system, it takes a long time to solve symbolically, and it is difficult to simulate dynamic behavior in control validation. To solve this problem, attraction force and inclination torque values are easily characterized by new formulation and besides the simulations are conducted easily. The experimental setup was manufactured and assembled, and the carrier system was successfully levitated, and reference tracking was performed without overshoot.

Synthesis of porous carbon/zeolite composites by low-temperature acid-alkaline leaching from coal gasification fine slag for adsorption of dye wastewater

The conversion and utilization of coal gasification slag is considered one of the key issues in the development of the modern coal chemical industry. In this work, porous carbon/Na-P1 zeolite composites were successfully prepared by a simple and easy-to-operate acid-alkali leaching method on the basis of the composition of coal gasification fine slag. The synthesized CZ-10 possessed a honeycomb-like porous carbon structure and a typical flower-cluster zeolite structure, with the specific surface area and pore volume reaching 195.68 m2/g and 0.257 m3/g, respectively. CZ-10 showed excellent adsorption performance, with an equilibrium adsorption capacity of 175.93 mg/g on methylene blue (MB) at 300 K. CZ-10 can effectively adsorb MB in a wide pH range, and the increase in pH was favorable for adsorption. According to the results of adsorption kinetics and isothermal adsorption experiments, the adsorption process was in good agreement with PSO model and Sips model. According to the characterization results and adsorption experiments, it was speculated that the adsorption of CZ-10 on MB was mainly chemisorption, and may be affected by various factors such as ion-exchange, electrostatic attraction, hydrogen bonding, π-π bonding and van der Waals forces.

Homogeneous crystallization in four-dimensional Lennard-Jones liquids.

We observe homogeneous crystallization in simulated high-dimensional (d>3) liquids that follow physically realistic dynamics and have system sizes that are large enough to eliminate the possibility that crystallization was induced by the periodic boundary conditions. Supercooled four-dimensional (4D) Lennard-Jones (LJ) liquids maintained at zero pressure and constant temperatures 0.59<T<0.63 crystallized within ∼2×10^{4}τ, where τ is the LJ time unit. Weeks-Chandler-Andersen (WCA) liquids that were maintained at the same densities and temperatures at which their LJ counterparts nucleated did not crystallize even after 2.5×10^{5}τ, showing that the presence of long-ranged attractive interactions dramatically speeds up 4D crystallization, much as it does in 3D. On the other hand, the overlap of the liquid and crystalline phases' local-bond-order distributions is smaller for LJ systems than for WCA systems, which is the opposite of the 3D trend. This implies that the widely accepted hypothesis that increasing geometrical frustration rapidly suppresses crystallization as the spatial dimension d increases is only generally valid in the absence of attractive interparticle forces.

Attractive carbon black dispersions: Structural and mechanical responses to shear

The rheological behavior of colloidal dispersions is of paramount importance in a wide range of applications, including construction materials, energy storage systems, and food industry products. These dispersions consistently exhibit non-Newtonian behaviors, a consequence of intricate interplays involving colloids morphology, volume fraction, and interparticle forces. Understanding how colloids structure under flow remains a challenge, particularly in the presence of attractive forces leading to cluster formation. In this study, we adopt a synergistic approach, combining rheology with ultra small-angle x-ray scattering, to probe the flow-induced structural transformations of attractive carbon black (CB) dispersions and their effects on the viscosity. Our key findings can be summarized as follows. First, testing different CB volume fractions, in the high shear rate hydrodynamic regime, CB particles aggregate to form fractal clusters. Their size conforms to a power law of the shear rate, ξc∝γ˙−m, with m≃0.5. Second, drawing insights from the fractal structure of clusters, we compute an effective volume fraction ϕeff and find that microstructural models adeptly account for the hydrodynamic stress contributions. We identify a critical shear rate γ∗˙ and a critical volume fraction ϕeff∗, at which the clusters percolate to form a dynamical network. Third, we show that the apparent yield stress measured at low shear rates inherits its properties from the percolation point. Finally, through data scaling and the integration of Einstein’s viscosity equation, we revisit and discuss the Caggioni–Trappe–Spicer model, revealing a significant connection between its empirical parameters and the structural properties of CB dispersions under flow.

Forces Between Pair of Rings Made of a Magnetically Soft Ferromagnet in an Axial External Field

Purpose. Demonstration of the way to enhance the attraction force between coaxial rings made of a magnetically soft ferromagnet by way of profiling their edges facing each other.Methods. In the framework of magnetostatics numerical calculation is carried out for a system of two coaxial rings made of a magnetically soft ferromagnet under conditions when the system is subjected to a uniform magnetic field directed along the rings’ axis. Such a design prototypes a soft gripper for robotics. On the basis of the found out field distribution, the force of mutual attraction is evaluated. Using a particular example, the advantages of a system where the ring edges facing each other are profiled (tapered) are considered in comparison with the its analog where the rings have rectangular edges.Results. In is shown that tapering of the edges enables one to acquire a notable gain with respect to the attraction strength. The dependences of the force of the force are calculated on the inter-ring distance and on extent of tapering of the edges: replacement of the rectangular shape by a trapezoid one. It is found that the advantages of the tapered system take place only in certain intervals of the respective parameters. For example, tapering entails an order of magnitude enhancement provided that inter-ring gap is sufficiently narrow (much smaller than the thickness of the ring wall) but it loses to a standard system all its advantage when the rings are separated by a distance of the order of their radius or greater. The dependence of the attraction force on the extent of tapering (the ratio of the upper and lower bases of the trapezium) is non-monotonic. Under a weak tapering, this function grows rapidly, then it passes a maximum (its position depends on the magnetic susceptibility of the ring material) and afterwards goes down when the profile of the edge approaches triangular shape.Conclusions. The obtained results enable one to optimize the force interaction in the system under consideration. It is worth noting that the profiling not only augments the mutual attraction force but as well reduces that amount of magnetic material required for the construction.