Dense Binary Mixtures Research Articles

Discrete Element Method Investigation of Binary Granular Flows with Different Particle Shapes

The effects of particle shape differences on binary mixture shear flows are investigated using the Discrete Element Method (DEM). The binary mixtures consist of frictionless rods and disks, which have the same volume but significantly different shapes. In the shear flows, stacking structures of rods and disks are formed. The effects of the composition of the mixture on the stacking are examined. It is found that the number fraction of stacking particles is smaller for the mixtures than for the monodisperse rods and disks. For binary mixtures with small particle shape differences, the mixture stresses are bounded by the stresses of the two corresponding monodisperse systems. However, for binary mixtures with large particle shape differences, the stresses of the mixtures can be larger than the stresses of the monodisperse systems at large solid volume fractions because larger differences in particle shape cause geometrical interference in packing, leading to stronger particle–particle interactions in the flow. The stresses in dense binary mixtures are found to be exponential functions of the order parameter, which is a measure of particle alignment. Based on the simulation results, an empirical expression for the bulk friction coefficient (ratio of the shear stress to normal stress) for dense binary flows is proposed by accounting for the effects of particle alignment and solid volume fraction.

Effective one-component model of binary mixture: molecular arrest induced by the spatially correlated stochastic dynamics

Spatially correlated noise (SCN), i.e. the thermal noise that affects neighbouring particles in a similar manner, is ubiquitous in soft matter systems. In this work, we apply the over-damped SCN-driven Langevin equations as an effective, one-component model of the dynamics in dense binary mixtures. We derive the thermodynamically consistent fluctuation-dissipation relation for SCN to show that it predicts the molecular arrest resembling the glass transition, i.e. the critical slow-down of dynamics in the disordered phases. We show that the mechanism of singular dissipation is embedded in the dissipation matrix, accompanying SCN. We are also able to identify the characteristic length of collective dissipation, which diverges at critical packing. This novel physical quantity conveniently describes the difference between the ergodic and non-ergodic dynamics. The model is fully analytically solvable, one-dimensional and admits arbitrary interactions between the particles. It qualitatively reproduces several different modes of arrested disorder encountered in binary mixtures, including e.g. the re-entrant arrest. The model can be effectively compared to the mode coupling theory.

Local structure, thermodynamics, and phase behavior of asymmetric particle mixtures: Comparison between integral equation theories and simulation.

We study the structural pair correlations, thermodynamics, and fluid-fluid demixing phase behavior of dense binary sphere mixtures as predicted by integral equation theories with diverse closure approximations. The focus is on mixtures with a large size asymmetry over a wide range of compositions and strengths of interparticle attractive interactions with an emphasis on the nonperturbative strong bridging or network forming regime. Quantitative comparisons with simulations are carried out. At high volume fractions of the larger species, we find that all studied closures are reasonably good. However, large quantitative or even qualitative discrepancies compared with simulations emerge when the large species is the volumetrically minority component, under both entropic depletion and strong enthalpic bridging conditions. Overall, we find that using the modified-Verlet (MV) closure approximation for all three correlation functions leads to good predictions for structure, phase behavior, and the equation-of-state, along with assuring pair correlation functions which are rigorously positive. This symmetric or "triple MV" approximation has the advantage that the same closure can be used for any size ratio in all thermodynamic state regimes, in contrast to asymmetric closures. The good accuracy of the triple MV closure for particle mixtures provides as basis for developing improved theoretical descriptions of polymer nanocomposites and will serve as a crucial input to microscopic theories of slow dynamics in glass and gel forming systems.

Glassy swirls of active dumbbells.

Is an active glass different from a conventional passive glass? To address this, we study the dynamics of a dense binary mixture of soft dumbbells, each subject to an active propulsion force and thermal fluctuations. This dense assembly shows dynamical arrest, first to a translational and then to a rotational glass, as one reduces temperature T or the self-propulsion force f. We monitor the dynamics along an iso-relaxation-time contour in the (T-f) plane. We find dramatic differences both in the fragility and in the nature of dynamical heterogeneity, which characterize the onset of glass formation-the activity-induced glass exhibits large swirls or vortices, whose scale is set by activity, and it appears to diverge as one approaches the glass transition. This large collective swirling movement should have implications for collective cell migration in epithelial layers. We construct continuum hydrodynamic equations for the simulated system, and we show that the observed behavior of this growing dynamic length scale can be understood from these equations.

Turbulent channel flow of a dense binary mixture of rigid particles

We study turbulent channel flow of a binary mixture of finite-sized neutrally buoyant rigid particles by means of interface-resolved direct numerical simulations. We fix the bulk Reynolds number and total solid volume fraction, $Re_{b}=5600$ and $\unicode[STIX]{x1D6F7}=20\,\%$, and vary the relative fraction of small and large particles. The binary mixture consists of particles of two different sizes, $2h/d_{l}=20$ and $2h/d_{s}=30$ where $h$ is the half-channel height and $d_{l}$ and $d_{s}$ the diameters of the large and small particles. While the particulate flow statistics exhibit a significant alteration of the mean velocity profile and turbulent fluctuations with respect to the unladen flow, the differences between the mono-disperse and bi-disperse cases are small. However, we observe a clear segregation of small particles at the wall in binary mixtures, which affects the dynamics of the near-wall region and thus the overall drag. This results in a higher drag in suspensions with a larger number of large particles. As regards bi-disperse effects on the particle dynamics, a non-monotonic variation of the particle dispersion in the spanwise (homogeneous) direction is observed when increasing the percentage of small/large particles. Finally, we note that particles of the same size tend to cluster more at contact whereas the dynamics of the large particles gives the highest collision kernels due to a higher approaching speed.

Describing diffusion in fluid mixtures at elevated pressures by combining the Maxwell–Stefan formulation with an equation of state

Many operations of interest to chemical engineers require proper modeling of diffusion in fluid mixtures at operating pressures ranging to several megapascals. Examples include supercritical extraction, fractionation of natural gas liquids, enhanced oil recovery and exploitation of shale gas reserves. The Maxwell–Stefan (M–S) formulation, in combination with the Peng–Robinson equation of state, affords a convenient framework for modeling mixture diffusion. The primary objective of this article is to highlight a number of important and distinguishing diffusional characteristics of mixture diffusion at elevated pressures. For dense binary gas mixtures, the pressure-dependence of the M–S diffusivity Ðij requires additional correction for the compressibility factor, Z; this correction introduces a composition dependence for the Ðij that is absent for ideal gas mixtures. Also significant are influences of the thermodynamic correction factors Γij, that are related to the derivatives of the fugacity coefficients with respect to the compositions. For operations near critical pressures, or close to vapor/liquid and solid/liquid phase transition regions, the thermodynamic factor for binary mixtures tend to reduce to near-zero values; this reduction has a direct and proportional impact on the Fick diffusivities. For ternary fluid mixtures, the Γij cause the individual diffusion fluxes to be strongly coupled. Such coupling effects can be of significant importance even for hydrocarbon mixtures; this conclusion is not intuitively obvious. Strongly coupled diffusion leads to curvilinear equilibration trajectories, and may cause uphill diffusion of species.

Instabilities in granular binary mixtures at moderate densities.

A linear stability analysis of the Navier-Stokes (NS) granular hydrodynamic equations is performed to determine the critical length scale for the onset of vortices and clusters instabilities in granular dense binary mixtures. In contrast to previous attempts, our results (which are based on the solution to the inelastic Enskog equation to NS order) are not restricted to nearly elastic systems since they take into account the complete nonlinear dependence of the NS transport coefficients on the coefficients of restitution α(ij). The theoretical predictions for the critical length scales are compared to molecular dynamics (MD) simulations in flows of strong dissipation (α(ij) ≥ 0.7) and moderate solid volume fractions (ϕ ≤ 0.2). We find excellent agreement between MD and kinetic theory for the onset of velocity vortices, indicating the applicability of NS hydrodynamics to polydisperse flows even for strong inelasticity, finite density, and particle dissimilarity.

Experimentally Validated Computational Fluid Dynamics Simulations of Multicomponent Hydrodynamics and Phase Distribution in Agitated High Solid Fraction Binary Suspensions

The mixing of dense (5–40 wt %) binary mixtures of glass particles in water has been studied in a stirred vessel at the “just-suspended” speed and at speeds above it, using a Eulerian–Eulerian computational fluid dynamics (CFD) model. For each phase component, numerical predictions are compared to 3-dimensional distributions of local velocity components and solid concentration measured by an accurate technique of positron emission particle tracking. For the first time, it has been possible to conduct such a detailed “pointwise” validation of a CFD model within opaque, dense multicomponent slurries of this type. Predictions of flow number and mean velocity profiles of all phase components are generally excellent. The spatial solid distribution is well-predicted except near the base of the vessel and underneath the agitator where it is largely overestimated; however, predictions improve significantly with increasing solid concentration. Other phenomena and parameters such as particle slip velocities and homogeneity of suspension are analyzed.

Theory and simulations of crystalline control via salinity and pH in ionizable membranes

Many amphiphilic molecules with ionizable charged groups self-assemble into membranes. Their degree of ionization is a function of the pH and salt concentration in the solution, and it can also be suppressed or enhanced depending on the local crystalline structure on the membrane, which must be computed self-consisitently via the competition of short range and electrostatic interactions. We consider here a dense two-dimensional binary mixture consisting of positive and negative species of equal concentration. Each particle may be either charged according to its type or neutral, specifying its ionization state. We analyze this co-assembled system by numerically exact optimization and by continuum Monte Carlo simulations including short range and electrostatic interactions among all the particles. We find the optimal structure to be a triangular lattice for high salt concentrations, a face-centered rectangular lattice for intermediate salt concentrations, and a square lattice for low salt concentrations. At neutral pH, this crossover occurs gradually over a wide range of salt concentrations, while for highly acidic or basic solutions, it is much more abrupt. At intermediate values of pH, the unit cells become more complicated, causing the dissociation curve to follow a staircase function.

Theory of kinetic arrest, elasticity, and yielding in dense binary mixtures of rods and spheres

We extend the quiescent and stressed versions of naïve mode coupling theory to treat the dynamical arrest, shear modulus, and absolute yielding of particle mixtures where one or more species is a nonrotating nonspherical object. The theory is applied in detail to dense isotropic "chemically matched" mixtures of variable aspect ratio rods and spheres that interact via repulsive and short range attractive site-site pair potentials. A remarkably rich ideal kinetic arrest behavior is predicted with up to eight "dynamical phases" emerging: an ergodic fluid, partially localized states where the spheres remain fluid but the rods can be a gel, repulsive glass or attractive glass, doubly localized glasses and gels, a porous rod gel plus sphere glass, and a narrow window where a type of rod glass and gel localization coexist. Dynamical complexity increases with rod length and the introduction of attractive forces between all species which both enhance gel network formation. Multiple dynamic reentrant features and triple points are predicted, and each dynamic phase has unique particle localization characteristics and mechanical properties. Orders of magnitude variation of the linear shear modulus and absolute yield stress are found as rod length, mixture composition and the detailed nature of interparticle attractions are varied. The interplay of total (high) mixture packing fraction and composition at fixed temperature is also briefly studied. The present work provides a foundation to study more complex rod-sphere mixtures of both biological and synthetic interest that include physical features such as interaction site size asymmetry, rod-sphere specific attractions, and/or Coulomb repulsion.

Dynamics of dense granular flows of small-and-large-grain mixtures in an ambient fluid

Dense grain flows in nature consist of a mixture of solid constituents that are immersed in an ambient fluid. In order to obtain a good representation of these flows, the interaction mechanisms between the different constituents of the mixture should be considered. In this article, we study the dynamics of a dense granular flow composed of a binary mixture of small and large grains immersed in an ambient fluid. In this context, we extend the two-phase approach proposed by Meruane et al. [J. Fluid Mech. 648, 381 (2010)] to the case of flowing dense binary mixtures of solid particles, by including in the momentum equations a constitutive relation that describes the interaction mechanisms between the solid constituents in a dense regime. These coupled equations are solved numerically and validated by comparing the numerical results with experimental measurements of the front speed of gravitational granular flows resulting from the collapse, in ambient air or water, of two-dimensional granular columns that consisted of mixtures of small and large spherical particles of equal mass density. Our results suggest that the model equations include the essential features that describe the dynamics of grains flows of binary mixtures in an ambient fluid. In particular, it is shown that segregation of small and large grains can increase the front speed because of the volumetric expansion of the flow. This increase in flow speed is damped by the interaction forces with the ambient fluid, and this behavior is more pronounced in water than in air.

Geometrical aspects of the glass-forming ability of dense binary hard-sphere mixtures

Non-crystalline dense binary hard-sphere mixtures are generated where the size ratio of the spheres and the fraction of small spheres are varied from 1.0 to 2.0 in steps of 0.1 and from 0 to 100% in steps of 10%, respectively. A confined region within this parameter space is defined where non-crystalline structures are stabilized. Comparison of the present results with experimental data for binary bulk metallic glasses supports the validity of geometrical arguments regarding glass-forming ability of binary metallic melts.

Modeling phase behavior for quantifying micro-pervaporation experiments

We present a theoretical model for the evolution of mixture concentrations in a micro-pervaporation device, similar to those recently presented experimentally. The described device makes use of the pervaporation of water through a thin PDMS membrane to build up a solute concentration profile inside a long microfluidic channel. We simplify the evolution of this profile in binary mixtures to a one-dimensional model which comprises two concentration-dependent coefficients. The model then provides a link between directly accessible experimental observations, such as the widths of dense phases or their growth velocity, and the underlying chemical potentials and phenomenological coefficients. It shall thus be useful for quantifying the thermodynamic and dynamic properties of dilute and dense binary mixtures.

Transient ordering in a quasi-two-dimensional binary liquid near freezing

We report the results of a theoretical study of locally ordered fluctuations in a quasi-two-dimensional (quasi-2D) binary hard sphere mixture as monitored by the aperture cross-correlation function. Systems with thickness less than two large hard sphere diameters were studied, over a range of large hard sphere density and relative concentration of large and small hard spheres in the liquid state, for two ratios of sphere diameters, 0.2 and 0.3. In several major respects the occurrence and character of the structured fluctuations in a quasi-2D binary hard sphere mixture have similarities with those in a quasi-2D one-component hard sphere fluid, as reported by Sheu and Rice [J. Chem. Phys. 128, 244517 (2008)]. Specifically, our studies establish that structured fluctuations with both hexagonal and square symmetries can be found in the liquid phase well below the freezing density and that the occurrence of particular structured fluctuations is correlated with the symmetry of the solid to which the liquid freezes. However, there is also a major difference, specifically, the presence of the smaller spheres in the binary mixture can suppress the occurrence of all structured fluctuations. We attribute the affect of a small volume fraction of small spheres in a dense binary mixture of small and large spheres on the occurrence of structured fluctuations to the unfavorable entropy change associated with demixing of the small and large spheres.

Crystallization of Dense Binary Hard-Sphere Mixtures with Marginal Size Ratio

Molecular dynamics simulations are performed for binary hard-sphere mixtures with a size ratio of gamma =0.9 and a volume fraction of phi=0.58 over a range of compositions. We show how, at this high volume fraction, crystallization depends sensitively on the composition. Evidence is presented that crystallization in these mixtures does not proceed by the standard nucleation and growth paradigm. Rather, some crystallite forms almost immediately and then an interplay between compositional fluctuations and crystal growth is able to dramatically extend the time scale on which further crystallization occurs. This can be seen as a form of geometric frustration.

Segregation induced by inelasticity in a vibrofluidized granular mixture

We investigate the segregation of a dense binary mixture of granular particles that only differ in their restitution coefficient. The mixture is vertically vibrated in the presence of gravity. We find a partial segregation of the species, where most dissipative particles submerge in the less dissipative ones. The segregation occurs even if one type of the particles is elastic. In order to have a complete description of the system, we study the structure of the fluid at microscopic scale (few particle diameters). The density and temperature pair distribution functions show strong enhancements with respect to the equilibrium ones at the same density. In particular, there is an increase in the probability that the more inelastic particles group together in pairs (microsegregation). Microscopically the segregation is buoyancy driven, by the appearance of a dense and cold region around the more inelastic particles.

Hydrodynamic theory for reverse brazil nut segregation and the non-monotonic ascension dynamics

Based on the Boltzmann–Enskog kinetic theory, we develop a hydrodynamic theory for the well known (reverse) Brazil nut segregation in a vibrofluidized granular mixture. Under strong shaking conditions, the granular mixture behaves in some ways like a fluid and the kinetic theory constitutive models are appropriate to close the continuum balance equations for mass, momentum and granular energy. Using this analogy with standard fluid mechanics, we have recently suggested a novel mechanism of segregation in granular mixtures based on a competition between buoyancy and geometric forces: the Archimedean buoyancy force, a pseudo-thermal buoyancy force due to the difference between the energies of two granular species, and two geometric forces, one compressive and the other-one tensile in nature, due to the size-difference. For a mixture of perfectly hard-particles with elastic collisions, the pseudo-thermal buoyancy force is zero but the intruder has to overcome the net compressive geometric force to rise. For this case, the geometric force competes with the standard Archimedean buoyancy force to yield a threshold density-ratio, R ρ 1 = ρ l /ρ s < 1, above which the lighter intruder sinks, thereby signalling the onset of the reverse buoyancy effect. For a mixture of dissipative particles, on the other hand, the non-zero pseudo-thermal buoyancy force gives rise to another threshold density-ratio, R ρ 2 (> R ρ 1), above which the intruder rises again. Focussing on the tracer limit of intruders in a dense binary mixture, we study the dynamics of an intruder in a vibrofluidized system, with the effect of the base-plate excitation being taken into account through a 'mean-field' assumption. We find that the rise-time of the intruder could vary nonmonotonically with the density-ratio. For a given size-ratio, there is a threshold density-ratio for the intruder at which it takes the maximum time to rise, and above(/below) which it rises faster, implying that the heavier (and larger) the intruder, the faster it ascends. The peak on the rise-time curve decreases in height and shifts to a lower density-ratio as we increase the pseudo-thermal buoyancy force. The rise (/sink) time diverges near the threshold density-ratio for reverse-segregation. Our theory offers a unified description for the (reverse) Brazil-nut segregation and the nonmonotonic ascension dynamics of Brazil-nuts.

Mass-Transfer Coefficients in Dense Binary Mixtures

A modified elementary kinetic theory of gases is generalized to arbitrary densities of mixtures (from the gaseous to the solid state). Derived expressions for the mass-transfer coefficients are based on the lattice gas model, which is applicable to all the three aggregation states. For a rarefied gas, the expression for the mutual diffusion coefficient that is derived in terms of the modified theory is consistent with that obtained in terms of the rigorous kinetic theory of gases. The migration of particles is described in terms of transition state theory. The theory takes into account the role of thermal fluctuations in surmounting the activation barrier in dense phases. The label diffusion coefficient, pressure diffusion coefficient, thermal diffusion coefficient, and forced diffusion coefficient are discussed.

Finite-difference-based lattice Boltzmann model for dense binary mixtures

We propose a finite-difference-based lattice Boltzmann model for dense binary mixtures based on the Enskog theory. The model is applicable to a mixture composed of two dense fluids with different shear viscosities. The macroscopic hydrodynamic and diffusion equations are derived from the model through the Chapmann-Enskog procedure. The model is also validated numerically.

Reaching large lengths and long times in polymer dynamics simulations

A lattice model is presented for the simulation of dynamics in polymeric systems. Each polymer is represented as a chain of monomers, residing on a sequence of nearest-neighbor sites of a face-centered-cubic lattice. The polymers are self- and mutually avoiding walks: no lattice site is visited by more than one polymer, nor revisited by the same polymer after leaving it. The dynamics occurs through single-monomer displacements over one lattice spacing. To demonstrate the high computational efficiency of the model, we simulate a dense binary polymer mixture with repelling nearest-neighbor interactions between the two types of polymers, and observe the phase separation over a long period of time. The simulations consist of a total of 46 080 polymers, 100 monomers each, on a lattice with 13 824 000 sites, and an interaction strength of 0.1kBT. In the final two decades of time, the domain-growth is found to be d(t)∼t1/3, as expected, since the lattice model shows the dynamical scaling of “Model B,” once the domains are bigger than the radius of gyration.