A universality ansatz for the contact values of a multicomponent mixture of additive hard spheres is used to propose new formulae for the case of disparate-size binary mixtures. A comparison with simulation data and with a recent proposal by Alawneh and Henderson for binary mixtures shows reasonably good agreement with the predictions for the contact values of the large-large radial distribution functions. A discussion on the usefulness and limitations of the new proposals is also presented.
We report molecular dynamics results for the contact values of the radial distribution functions of binary additive mixtures of hard disks. The simulation data are compared with theoretical predictions from expressions proposed by Jenkins and Mancini [J. Appl. Mech. \textbf{54}, 27 (1987)] and Santos et al. [J. Chem. Phys. \textbf{117}, 5785 (2002)]. Both theories agree quantitatively within a very small margin, which renders the former still a very useful and simple tool to work with. The latter (higher-order and self-consistent) theory provides a small qualitative correction for low densitie…
Recent Monte Carlo simulation results for the contact values of polydisperse hard-sphere mixtures at a hard planar wall are considered in the light of a universality assumption made in approximate theoretical approaches. It is found that the data seem to fulfill the universality ansatz reasonably well, thus opening up the possibility of inferring properties of complicated systems from the study of simpler ones
The contact values $g_{ij}(σ_{ij})$ of the radial distribution functions of a $d$-dimensional mixture of (additive) hard spheres are considered. A `universality' assumption is put forward, according to which $g_{ij}(σ_{ij})=G(η, z_{ij})$, where $G$ is a common function for all the mixtures of the same dimensionality, regardless of the number of components, $η$ is the packing fraction of the mixture, and $z_{ij}$ is a dimensionless parameter that depends on the size distribution and the diameters of spheres $i$ and $j$. For $d=3$, this universality assumption holds for the contact values of the…
The problem of demixing in a binary fluid mixture of highly asymmetric additive hard spheres is revisited. A comparison is presented between the results derived previously using truncated virial expansions for three finite size ratios with those that one obtains with the same approach in the extreme case in which one of the components consists of point particles. Since this latter system is known not to exhibit fluid-fluid segregation, the similarity observed for the behavior of the critical constants arising in the truncated series in all instances, while not being conclusive, may cast seriou…
The spreading of a pure, volatile liquid on a wettable substrate has been studied in extensive detail. Here we show that the addition of a miscible, non-volatile liquid can strongly alter the contact line dynamics and the final liquid deposition pattern. We observe two distinct regimes of behavior depending on the relative strength of solutal Marangoni forces and surface wetting. Finger-like instabilities precede the deposition of a sub-micron thick film for large Marangoni forces and small solute contact angles, whereas isolated, pearl-like drops emerge and are deposited in quasi-crystalline …
A binary mixture made of heavy and light inelastic hard spheres in the free cooling state is considered. First, the regions in the parameter space where the partial granular temperature of the heavy species is larger (or smaller) than that of the light species are analyzed. Next, the asymptotic behavior of the mean square velocity ratio in the disparate-mass limit is investigated, assuming different scaling laws for the parameters of the mixture. It is seen that two general classes of states are possible: a "normal" state and an "ordered" state, the latter representing a strong breakdown of en…
Multiple distinct glass states occur in binary hard-sphere mixtures with constituents of very disparate sizes according to the mode-coupling theory of the glass transition (MCT), distinguished by considering whether small particles remain mobile or not, and whether small particles contribute significantly to perturb the big-particle structure or not. In the idealized glass, the four different glasses are separated by sharp transitions that give rise to higher-order transition phenomena involving logarithmic decay laws, and to anomalous power-law-like diffusion. The phenomena are argued to be e…
A method to obtain (approximate) analytical expressions for the radial distribution functions in a multicomponent mixture of additive hard spheres that was recently introduced is used to obtain the direct correlation functions and bridge functions in these systems. This method, which yields results practically equivalent to the Generalized Mean Spherical Approximation and includes thermodynamic consistency, is an alternative to the usual integral equation approaches and requires as input only the contact values of the radial distribution functions and the isothermal compressibility. Calculatio…
Monte Carlo simulations on the structural properties of ternary fluid mixtures of additive hard spheres are reported. The results are compared with those obtained from a recent analytical approximation [S. B. Yuste, A. Santos, and M. Lopez de Haro, J. Chem. Phys. 108, 3683 (1998)] to the radial distribution functions of hard-sphere mixtures and with the results derived from the solution of the Ornstein-Zernike integral equation with both the Martynov-Sarkisov and the Percus-Yevick closures. Very good agreement between the results of the first two approaches and simulation is observed, with a n…
We extend the Cahn-Landau-de Gennes mean field theory of binary mixtures to understand the wetting thermodynamics of a three phase system, that is in contact with an external surface which prefers one of the phases. We model the system using a phenomenological free energy having three minima corresponding to low, intermediate and high density phases. By systematically varying the \textit{(i)} depth of the central minimum, \textit{(ii)} the surface interaction parameters, we explore the phase behavior, and wetting characteristics of the system across the triple point corresponding to three phas…
A numerical model is used to simulate rheometer experiments at constant normal stress on dense suspensions of spheres. The complete model includes sphere-sphere contacts using a soft contact approach, short range hydrodynamic interactions defined by frame-invariant expressions of forces and torques in the lubrication approximation, and drag forces resulting from the poromechanical coupling computed with the DEM-PFV technique. Series of simulations in which some of the coupling terms are neglected highlight the role of the poromechanical coupling in the transient regimes. They also reveal that …
We present a Monte Carlo algorithm for selectively sampling radial distribution functions and effective interaction potentials in asymmetric liquid mixtures. We demonstrate its efficiency for hard-sphere mixtures, and for model systems with more general interactions, and compare our simulations with several analytical approximations. For interaction potentials containing a hard-sphere contribution, the algorithm yields the contact value of the radial distribution function.
A recently proposed rational-function approximation [Phys. Rev. E \textbf{84}, 041201 (2011)] for the structural properties of nonadditive hard spheres is applied to evaluate analytically (in Laplace space) the local density profiles of multicomponent nonadditive hard-sphere mixtures near a planar nonadditive hard wall. The theory is assessed by comparison with $NVT$ Monte Carlo simulations of binary mixtures with a size ratio 1:3 in three possible scenarios: a mixture with either positive or negative nonadditivity near an additive wall, an additive mixture with a nonadditive wall, and a nonad…
The Cassie-Wenzel transition of a symmetric binary liquid mixture in contact with a nano-corrugated wall is studied. The corrugation consists of a periodic array of nano-pits with square cross sections. The substrate potential is the sum over Lennard-Jones interactions, describing the pairwise interaction between the wall particles $C$ and the fluid particles. The liquid is composed of two species of particles, $A$ and $B$, which have the same size and equal $A - A$ and $B - B$ interactions. The liquid particles interact between each other also via $A - B$ Lennard-Jones potentials. We have emp…
Equal volume mixtures of small and large polytetrafluorethylene (PTFE) spheres are shaken in an atmosphere of controlled humidity which allows to also control their tribo-charging. We find that the contact numbers are charge-dependent: as the charge density of the beads increases, the number of same-type contacts decreases and the number of opposite-type contacts increases. This change is not caused by a global segregation of the sample. Hence, tribo-charging can be a way to tune the local composition of a granular material.
We study the influence of particle size asymmetry on structural evolution of randomly jammed binary sphere mixtures with varying large-sphere/small-sphere composition. Simulations of jammed packings are used to assess the transition from large-sphere dominant to small-sphere dominant mixtures. For weakly asymmetric particle sizes, packing properties evolve smoothly, but not monotonically, with increasing small sphere composition, $f$. Our simulations reveal that at high values of ratio $α$ of large to small sphere radii, ($α\geq α_c \approx 5.75$) evolution of structural properties such as pac…
An analysis of the direct correlation functions $c_{ij} (r)$ of binary additive hard-sphere mixtures of diameters $σ_s$ and $σ_b$ (where the subscripts $s$ and $b$ refer to the "small" and "big" spheres, respectively), as obtained with the rational-function approximation method and the WM scheme introduced in previous work [S.\ Pieprzyk \emph{et al.}, Phys.\ Rev.\ E {\bf 101}, 012117 (2020)], is performed. The results indicate that the functions $c_{ss}(r<σ_s)$ and $c_{bb}(r<σ_b)$ in both approaches are monotonic and can be well represented by a low-order polynomial, while the function $c_{sb}…
The depletion interactions between two colloidal plates or between two colloidal spheres, induced by interacting polymers in a good solvent, are calculated theoretically and by computer simulations. A simple analytical theory is shown to be quantitatively accurate for case of two plates. A related depletion potential is derived for two spheres; it also agrees very well with direct computer simulations. Theories based on ideal polymers show important deviations with increasing polymer concentration: They overestimate the range of the depletion potential between two plates or two spheres at all …
When a granular mixture involving grains of different sizes is shaken, sheared, mixed, or left to flow, grains tend to separate by sizes in a process known as size segregation. In this study, we explore the size segregation mechanism in granular chute flows in terms of pressure distribution and granular micro-structure. Therefore, 2D discrete numerical simulations of bi-disperse granular chute flows are systematically analysed. Based on the theoretical models by Gray and Thornton 2005 and Hill and Tan 2014, we explore the stress partition in the phases of small and large grains, discriminating…
The static and dynamic properties of binary mixtures of hard spheres with a diameter ratio of $σ_B/σ_A=0.1$ and a mass ratio of $m_B/m_A=0.001$ are investigated using event driven molecular dynamics. The contact value of the pair correlation functions are found to compare favourably with recently proposed theoretical expressions. The transport coefficients of the mixture, determined from simulation, are compared to the predictions of revised Enskog theory, using both a third-order Sonine expansion and direct simulation Monte Carlo. Overall, Enskog theory provides a fairly good description of t…
We study numerically the crystallization of a hard-sphere mixture with 8\% polydispersity. Although often used as a model glass former, for small system sizes we observe crystallization in molecular dynamics simulations. This opens the possibility to study the competition between crystallization and structural relaxation of the melt, which typically is out of reach due to the disparate timescales. We quantify the dependence of relaxation and crystallization times on density and system size. For one density and system size we perform a detailed committor analysis to investigate the suitability …
One versatile route to the creation of two-dimensional crystal structures on the nanometer to micrometer scale is the self-assembly of colloidal particles at an interface. Here, we explore the crystal phases that can be expected from the self-assembly of mixtures of spherical particles of two different sizes, which we map to (additive or non-additive) hard-disk mixtures. We map out the infinite-pressure phase diagram for these mixtures, using Floppy Box Monte Carlo simulations to systematically sample candidate crystal structures with up to 12 disks in the unit cell. As a function of the size …
Ion mixtures require an exclusion core to avoid collapse. The Debye Hueckel theory, where ions are point charges, is accurate only in the limit of infinite dilution. The MSA is the embedding of hard cores into DH, is valid for higher densities. In the MSA the properties of any ionic mixture can be represented by a single screening parameter $Γ$. For equal ionic size restricted model is obtained from the Debye parameter $κ$. This one parameter representation (BIMSA) is valid for complex and associating systems, such as the general n-polyelectrolytes. The BIMSA is the only theory that satisfies …
Explicit simulations of fluid mixtures of highly size-dispersed particles are constrained by numerical challenges associated with identifying pair-interaction neighbors. Recent algorithmic developments have ameliorated these difficulties to an extent, permitting more efficient simulations of systems with many large and small particles of disperse sizes. We leverage these capabilities to perform molecular dynamics simulations of binary sphere mixtures with elastically stiff particles approaching the hard sphere limit and particle size ratios of up to 50, approaching the colloidal limit. The sys…
We consider the Asakura-Oosawa model of hard sphere colloids and ideal polymers in contact with a porous matrix modeled by immobilized configurations of hard spheres. For this ternary mixture a fundamental measure density functional theory is employed, where the matrix particles are quenched and the colloids and polymers are annealed, i.e. allowed to equilibrate. We study capillary condensation of the mixture in a tiny sample of matrix as well as demixing and the fluid-fluid interface inside a bulk matrix. Density profiles normal to the interface and surface tensions are calculated and compare…
Using molecular dynamics simulation, we examine the dynamics of crystal, polycrystal, and glass in a Lennard-Jones binary mixture composed of small and large particles in two dimensions. The crossovers occur among these states as the composition c is varied at fixed size ratio. Shear is applied to a system of 9000 particles in contact with moving boundary layers composed of 1800 particles. The particle configurations are visualized with a sixfold orientation angle alpha_j(t) and a disorder variable D_j(t) defined for particle j, where the latter represents the deviation from hexagonal order. F…
The surface phase behavior of binary mixtures of colloidal hard rods in contact with a solid substrate (hard wall) is studied, with special emphasis on the region of the phase diagram that includes the smectic A phase. The colloidal rods are modelled as hard cylinders of the same diameter and different lengths, in the approximation of perfect alignment. A fundamental--measure density functional is used to obtain equilibrium density profiles and thermodynamic properties such as surface tensions and adsorption coefficients. The bulk phase diagram exhibits nematic-smectic and smectic-smectic demi…
