Mixture Of Spheres Research Articles

Alternative formulation of the induced surface and curvature tensions approach

We develop a novel method to analyze the excluded volume of the multicomponent mixtures of classical hard spheres in the grand canonical ensemble. The method is based on the Laplace–Fourier transform technique and allows one to account for the fluctuations of the particle number density for the induced surface and curvature tensions equation of state. As a result one can go beyond the Van der Waals (VdW) approximation by obtaining the suppression of the induced surface and curvature tensions coefficients at moderate and high packing fractions. In contrast to the standard induced surface and curvature tensions equation of state the suppression of these coefficients is not the exponential, but a power-like one. The obtained alternative equation of state is further generalized to account for higher virial coefficients. This result is straightforwardly generalized to the case of quantum statistics.

Experimental characterization of coupled sensible heat and moisture storage for dry cooling enhancement

Abstract A novel storage concept, based on the coupling of heat and humidity storages, is presented and experimentally characterized. This coupled storage is aiming at optimizing the cooling of the condenser for CSP power plant, and more broadly, for any thermodynamic cycles devoted to the production of electricity from heat. The global system consists in a dual-media thermocline-like TES using humid air as heat transfer fluid and filled with a mixture of glass spheres and sorbent pebbles. Experimental campaigns have confirmed the validity of the concept, i.e. cold temperature and humidity can be stored in a solid matrix during the night and can be used later, to cool ambient air during the day, thanks to heat convection and moisture desorption. Characterization and understanding of the behaviour of this coupled storage are provided through temperature profiles, steam molar fraction and mass of water sorbed/desorbed. Results highlight that such storage can be effective to reduce the drop of performances for air-cooled condenser under high temperatures ambient, which occurs typically for CSP power plant in arid regions.

Collisional dissipation rate for binary mixtures of aspherical particles

The homogeneous cooling process of binary mixtures of large aspherical particles and small spheres is modeled using DEM. The dissipation rate increases with the increasing total solid volume fraction of the mixture. For a specified total solid volume fraction of the mixture, the dissipation rate increases with the increasing fraction ratio of small spheres in the mixture. Energy equipartition analysis shows that the translational and rotational components of the granular temperature for the large aspherical particles are generally equivalent. Energy equipartition is also present between the translational granular temperature for the large and small particles. Both particle aspect ratio and shape irregularity affect the collisional dissipation rate. The collisional dissipation rate increases with the aspect ratio (AR) for the same particle shape. For the same AR, the collisional dissipation rate of more-irregular oval-like particles are larger than less-irregular rod-like particles. The collisional dissipation rate decreases with the increasing particle sphericity.

Effects of Polydispersity on the Phase Behavior of Additive Hard Spheres in Solution.

The ability to separate enzymes, nucleic acids, cells, and viruses is an important asset in life sciences. This can be realised by using their spontaneous asymmetric partitioning over two macromolecular aqueous phases in equilibrium with one another. Such phases can already form while mixing two different types of macromolecules in water. We investigate the effect of polydispersity of the macromolecules on the two-phase formation. We study theoretically the phase behavior of a model polydisperse system: an asymmetric binary mixture of hard spheres, of which the smaller component is monodisperse and the larger component is polydisperse. The interactions are modelled in terms of the second virial coefficient and are assumed to be additive hard sphere interactions. The polydisperse component is subdivided into sub-components and has an average size ten times the size of the monodisperse component. We calculate the theoretical liquid–liquid phase separation boundary (the binodal), the critical point, and the spinodal. We vary the distribution of the polydisperse component in terms of skewness, modality, polydispersity, and number of sub-components. We compare the phase behavior of the polydisperse mixtures with their concomittant monodisperse mixtures. We find that the largest species in the larger (polydisperse) component causes the largest shift in the position of the phase boundary, critical point, and spinodal compared to the binary monodisperse binary mixtures. The polydisperse component also shows fractionation. The smaller species of the polydisperse component favor the phase enriched in the smaller component. This phase also has a higher-volume fraction compared to the monodisperse mixture.

Particle shape-induced axial segregation of binary mixtures of spheres and ellipsoids in a rotating drum

Particles with different properties such as size and shape in rotating drums tend to segregate axially to different sections. In this work, we report an interesting phenomenon that for ellipsoid-sphere mixtures, spheres tend to segregate axially to the middle section of the drum. The axial segregation becomes severe and reaches a maximum at aspect ratios of 0.67 and 2.0. Further increasing the deviation leads to a lower segregation degree. It is observed that the acceleration effect on particles by the frictional end walls induces the axial flow of particles. Both ellipsoids and spheres in the outer region of the transverse slice tend to migrate to the middle section while particles in the inner region migrate to the end walls. Generally, the axial flow induced by the frictional end walls and the radial segregation are essential for the development of particle shape-induced axial segregation.

Navier–Stokes transport coefficients for a model of a confined quasi-two-dimensional granular binary mixture

The Navier–Stokes transport coefficients for a model of a confined quasi-two-dimensional granular binary mixture of inelastic hard spheres are determined from the Boltzmann kinetic equation. A normal or hydrodynamic solution to the Boltzmann equation is obtained via the Chapman–Enskog method for states near the local version of the homogeneous time-dependent state. The mass, momentum, and heat fluxes are determined to first order in the spatial gradients of the hydrodynamic fields, and the associated transport coefficients are identified. They are given in terms of the solutions of a set of coupled linear integral equations. In addition, in contrast to the previous results obtained for low-density granular mixtures, there are also nonzero contributions to the first-order approximations to the partial temperatures Ti(1) and the cooling rate ζ(1). Explicit forms for the diffusion transport coefficients, the shear viscosity coefficient, and the quantities Ti(1) and ζ(1) are obtained by assuming steady state conditions and by considering the leading terms in a Sonine polynomial expansion. The above transport coefficients are given in terms of the coefficients of restitution, concentration, and the masses and diameters of the components of the mixture. The results apply, in principle, for arbitrary degree of inelasticity and are not limited to specific values of concentration, mass, and/or size ratios. As a simple application of these results, the violation of the Onsager reciprocal relations for a confined granular mixture is quantified in terms of the parameter space of the problem.

Early stages of aggregation in fluid mixtures of dimers and spheres: a theoretical and simulation study.

We use Monte Carlo simulation and the Reference Interaction Site Model (RISM) theory of molecular fluids to investigate a simple model of colloidal mixture consisting of dimers, made up of two tangent hard monomers of different size, and hard spheres. In addition to steric repulsion, the two species interact via a square-well attraction only between small monomers and spheres. Recently, we have characterized the low-temperature regime of this mixture by Monte Carlo, reporting on the spontaneous formation of a wide spectrum of supramolecular aggregates [Prestipino et al., J. Phys. Chem. B, 2019, 123, 9272]. Here we focus on a regime of temperatures where, on cooling, the appearance of local inhomogeneties first, and the early stages of aggregation thereafter, are observed. In particular, we find signatures of aggregation in the onset of a low-wavevector peak in the structure factors of the mixture, as computed by both theory and simulation. Then, we link the structural information to the microscopic arrangement through a detailed cluster analysis of Monte Carlo configurations. In this regard, we devise a novel method to compute the maximum distance for which two spheres can be regarded as bonded together, a crucial issue in the proper identification of fluid aggregates. The RISM theory provides relatively accurate structural and thermodynamic predictions in comparison with Monte Carlo, but with slightly degrading performances as the fluid progresses inside the locally inhomogeneous phase. Our study certifies the efficacy of the RISM approach as a useful complement to numerical simulation for a reasoned analysis of aggregation properties in colloidal mixtures.

Magnetic assembly and manipulation of Janus photonic crystal supraparticles from a colloidal mixture of spheres and ellipsoids

Janus photonic crystal supraparticles with novel structures and properties were magnetically assembled from a colloidal mixture of nonmagnetic spheres and magnetic ellipsoids.

Energy characteristics of carbon spheres

The mixtures of template carbon foams and carbon spheres were synthesized by pyrolysis of hexane over Ni foam, followed by graphitization. All samples were analyzed by scanning and transmission electron microscopy, the BET method, thermogravimetry, Raman spectroscopy and X-ray diffraction. The standard enthalpy of formation of the presented material ( Δ f H 298 0 = 1.29 ± 0.35 kJ g−1) was determined for the first time.

Exploring an efficient manganese oxide catalyst for ozone decomposition and its deactivation induced by water vapor

A series of MnOx catalysts supported by carbon spheres were prepared by calcining mixtures of manganese acetate and carbon spheres under a nitrogen atmosphere, and their performance for ozone decomposition under high humidity conditions (RH = 90%) was evaluated.

Size-sieving separation of hard-sphere gases at low concentrations through cylindrically porous membranes.

Membranes are compelling devices for many industrial separation processes, which are all subject to the intrinsic permeability-selectivity tradeoff. A general strategy to enhance separation performance is to reduce the pore size distribution and, ideally, make the membrane isoporous. In this study, we focus on a minimal model for regularly porous membranes, which consists of hard spheres moving through cylindrical pores. The collision dynamics is solved exactly and implemented in nonequilibrium event-driven molecular dynamics simulations. For such size-sieving porous membranes, we show that the permeability P of hard spheres of size σ through cylindrical pores of size d follows the hindered diffusion mechanism due to size exclusion as P ∝ (1 - σ/d)2. According to this law, the separation of binary mixtures of large and small particles exhibits a linear relationship between α-1/2 and P-1/2, where α and P are the selectivity and permeability of the smaller particle, respectively. The mean permeability through polydisperse pores is the average of the permeabilities of individual pores, weighted by the fraction of the single pore area over the total pore area.

Congruent phase behavior of a binary compound crystal of colloidal spheres and dimpled cubes

Monte Carlo simulations were performed to study the phase behavior of equimolar mixtures of spheres and cubes having selective inter-species affinity. Such a selectivity was designed to promote the formation of the substitutionally ordered NaCl compound, the "C* phase," and to be driven not only by energetic bonds but also by entropic bonds generated by dimples on the cube facets. Nestling of the spheres in the cube indentations can promote negative nonadditive mixing and increase the C* phase packing entropy. The focus is on congruent phase behavior wherein the C* phase directly melts into, and can be conveniently accessed from, the disordered state. A specialized thermodynamic integration scheme was used to trace the coexisting curves for varying the values of the interspecies contact energy, ε*, the relative indentation size, λ, and the sphere-to-cube size ratio, ζ. By starting from a known coexistence point with ε* > 0 and λ = 0 (no indentation), it is found that increasing λ (at fixed ε* and ζ) reduces the free-energy and pressure of the C* phase at coexistence, indicative of stronger entropic bonding. Remarkably, it is demonstrated that a purely athermal C* phase (i.e., with ε* = 0) can be formed for λ ≥ 0.7 and suitable choices of ζ. A metric of nonadditive (excess) volume of mixing is also suggested as an approximate predictor of athermal C* phase stability. The principles used to engineer selective entropic bonds and compounds with congruent melting are expected to be applicable to other particle shapes and crystalline phases.

Phase Diagram for Ideal Diblock-Copolymer Micelles Compared to Polymerization-Induced Self Assembly.

In this work we constructed a detailed phase diagram for the solutions of ideal diblock-copolymers and compared such diagram with that obtained during polymerization-induced self-assembly (PISA); a wide range of polymer concentrations as well as chain compositions was studied. As the length of the solvophobic block nB increases (the length of the solvophilic block nA was fixed), the transition from spherical micelles to cylinders and further to vesicles (lamellae) occurs. We observed a rather wide transition region between the spherical and cylindrical morphology in which the system contains a mixture of spheres and short cylinders, which appear to be in dynamic equilibrium; the transition between the cylinders and vesicles was found to be rather sharp. Next, upon increasing the polymer concentration in the system, the transition region between the spheres and cylinders shifts towards lower nB/nA values; a similar shift but with less magnitude was observed for the transition between the cylinders and vesicles. Such behavior was attributed to the increased number of contacts between the micelles at higher polymer volume concentrations. We also found that the width of the stability region of the cylindrical micelles for small polymer volume concentrations is in good quantitative agreement with the predictions of analytical theory. The obtained phase diagram for PISA was similar to the case of presynthesized diblock copolymer; however, the positions of the transition lines for PISA are slightly shifted towards higher nB/nA values in comparison to the presynthesized diblock copolymers, which is more pronounced for the case of the cylinders-to-vesicles transition. We believe that the reason for such behavior is the polydispersity of the core-forming blocks: The presence of the short and long blocks being located at the micelle interface and in its center, respectively, helps to reduce the entropy losses due to the insoluble block stretching, which leads to the increased stability of more curved micelles.

Learning composition-transferable coarse-grained models: Designing external potential ensembles to maximize thermodynamic information.

Achieving thermodynamic faithfulness and transferability across state points is an outstanding challenge in the bottom-up coarse graining of molecular models, with many efforts focusing on augmenting the form of coarse-grained interaction potentials to improve transferability. Here, we revisit the critical role of the simulation ensemble and the possibility that even simple models can be made more predictive through a smarter choice of ensemble. We highlight the efficacy of coarse graining from ensembles where variables conjugate to the thermodynamic quantities of interest are forced to respond to applied perturbations. For example, to learn activity coefficients, it is natural to coarse grain from ensembles with spatially varying external potentials applied to one species to force local composition variations and fluctuations. We apply this strategy to coarse grain both an atomistic model of water and methanol and a binary mixture of spheres interacting via Gaussian repulsions and demonstrate near-quantitative capture of activity coefficients across the whole composition range. Furthermore, the approach is able to do so without explicitly measuring and targeting activity coefficients during the coarse graining process; activity coefficients are only computed after-the-fact to assess accuracy. We hypothesize that ensembles with applied thermodynamic potentials are more "thermodynamically informative." We quantify this notion of informativeness using the Fisher information metric, which enables the systematic design of optimal bias potentials that promote the learning of thermodynamically faithful models. The Fisher information is related to variances of structural variables, highlighting the physical basis underlying the Fisher information's utility in improving coarse-grained models.

Effect of hard particles on the ferromagnetic transition in dipolar fluids, a simulation study

We investigate by Monte Carlo simulation how the ferromagnetic ordering transition in a polar fluid is affected by the addition of nonpolar particles. To this end, we consider a mixture of dipolar and pure hard spheres of equal size. Using simulations in the Gibbs ensemble, we first determine the demixing domain in the region of high densities and mole fractions of the polar particles. Then, starting from a purely dipolar fluid at two different densities and monitoring the variation of the order parameter, it is shown that the addition of hard particles favours the alignment of the dipoles. The critical temperature of the transition is finally determined and we show how it is modified, depending on the vicinity of the demixing transition. The interplay of the orientational transition and the demixing transition is finally discussed.

Correlation functions in mixtures with energetically favoured nearest neighbours of different kind: a size-asymmetric case

Binary mixtures of hard spheres with different diameters and square-well attraction between different particles are studied by theory and Monte Carlo simulations. In our mesoscopic theory, local fluctuations of the volume fraction of the two components are taken into account. Semi-quantitative agreement between the simulation and theoretical results is obtained, except from very small distances. The correlation functions exhibit exponentially damped oscillations, with the period determined by the interaction potential, and both the amplitude and the correlation length increasing significantly with increasing diameter ratio. Increasing size asymmetry leads also to decreasing fluctuations of the number of the smaller particles in the attractive shell of the bigger ones. For small size asymmetry, the strongest correlations occur for comparable volume fraction of the two components. When the size ratio increases, the maximum of the structure factor moves to a larger volume fraction of the bigger particles, and for the size ratio as large as 4, the maximum goes beyond the accessible range of volume fractions. Our results show that when the neighbourhood of different particles is energetically favoured, the particles are much more uniformly distributed than in the random distribution even at relatively high temperature, especially for large size asymmetry.

Thermodynamic geometry for binary mixtures: A constrained approach

Thermodynamic geometry for binary mixtures is explored in a constrained version. In order to have an insight into the interpretation of the scalar curvature (R) for mixtures, we develop and discuss the thermodynamic geometry for binary mixtures of hard spheres and van der Waals fluids with a restriction in the total particle number. For the case of hard spheres we have an interaction which is exclusively repulsive and van der Waals fluids account for repulsive and attractive interactions, which is a more realistic model. From our analysis, it is seen that the physical interpretation of R given for monocomponent systems, is no longer satisfied for the case of mixture of ideal gases and hard spheres. For the constrained version of the mixture of van der Waals fluids, we have that the scalar curvature nicely reproduces the behavior observed for the monocomponent fluid, including the interpretation of R as an indicator of repulsive or attractive intermolecular interactions and phase transitions.

Discrete element modeling of boulder and cliff morphologies on comet 67P/Churyumov-Gerasimenko

Context.Even after the Rosetta mission, some of the mechanical parameters of comet 67P/Churyumov-Gerasimenko’s surface material are not yet well constrained. These parameters are needed to improve our understanding of cometary activity or for planning sample return missions.Aims.We study some of the physical processes involved in the formation of selected surface features and investigate the mechanical and geometrical parameters involved.Methods.Applying the discrete element method (DEM) in a low-gravity environment, we numerically simulated the surface layer particle dynamics involved in the formation of selected morphological features. The material considered is a mixture of polydisperse ice and dust spheres with inter-particle forces given by the Hertz contact model, translational friction, rolling friction, cohesion from unsintered contacts, and optionally due to bonds from ice sintering. We determined a working set of parameters that enables the simulations to be reasonably realistic and investigated morphological changes due to modifications thereof.Results.The selected morphological features are reasonably well reproduced using model materials with a tensile strength on the order of 1–10 Pa. Increasing the diameters of the spherical particles decreases the material strength, and increasing the friction leads to a more brittle but somewhat stronger material. High friction is required to make the material sufficiently brittle to match observations, which points to the presence of very rough, even angular particles. Reasonable seismic activity does not suffice to trigger the collapses of cliffs without material heterogeneities or structural defects.Conclusions.DEM modeling can be a powerful tool to investigate mechanical parameters of cometary surface material. However, many uncertainties arise from our limited understanding of particle shapes, spatial configurations, and size distributions, all on multiple length scales. Further numerical work, in situ measurements, and sample return missions are needed to better understand the mechanics of cometary material and cometary activity.

Perfect sampling for Gibbs point processes using partial rejection sampling

We present a perfect sampling algorithm for Gibbs point processes, based on the partial rejection sampling of Guo, Jerrum and Liu (In STOC’17 – Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing (2017) 342–355 ACM). Our particular focus is on pairwise interaction processes, penetrable spheres mixture models and area-interaction processes, with a finite interaction range. For an interaction range $2r$ of the target process, the proposed algorithm can generate a perfect sample with $O(\log(1/r))$ expected running time complexity, provided that the intensity of the points is not too high and $\Theta(1/r^{d})$ parallel processor units are available.

Modeling and experimental investigation of shear-induced particle percolation in diluted binary mixtures.

A polydispersed mixture of granular materials composed of different-sized particles segregates whenever it undergoes external actions such as shear. Predicting and controlling segregation pose a challenging problem of industrial interest. One of the most frequent and important causes of segregation is interparticle percolation that occurs when small particles fall down through the voids between large particles as a result of local shear in the presence of a gravitational field. In this paper, we present a theoretical model to predict the percolation velocity in sheared systems, and we validate it experimentally. The experiments were carried out in simple shear conditions. This type of flow was achieved in a shear box which allowed the quantitative study of particle percolation under constant shear conditions. The granular material inside the box was a binary mixture of cohesionless spheres differing only in size. The experiments allowed us to quantify the percolation speed for different size ratios and different shear rates. The collected data confirmed the validity of the proposed theoretical model; the latter can be implemented in a continuum framework to simulate more complex phenomena and geometries.