Event-driven Molecular Dynamics Research Articles

Hydrodynamics of granular gases of inelastic and rough hard disks or spheres. II. Stability analysis.

Conditions for the stability under linear perturbations around the homogeneous cooling state are studied for dilute granular gases of inelastic and rough hard disks or spheres with constant coefficients of normal (α) and tangential (β) restitution. After a formally exact linear stability analysis of the Navier-Stokes-Fourier hydrodynamic equations in terms of the translational (d_{t}) and rotational (d_{r}) degrees of freedom, the transport coefficients derived in the companion paper [A. Megías and A. Santos, "Hydrodynamics of granular gases of inelastic and rough hard disks or spheres. I. Transport coefficients" Phys. Rev. E 104, 034901 (2021)10.1103/PhysRevE.104.034901] are employed. Known results for hard spheres [Garzó, Santos, and Kremer, Phys. Rev. E 97, 052901 (2018)10.1103/PhysRevE.97.052901] are recovered by setting d_{t}=d_{r}=3, while novel results for hard disks (d_{t}=2,d_{r}=1) are obtained. In the latter case, a high-inelasticity peculiar region in the (α,β) parameter space is found, inside which the critical wave number associated with the longitudinal modes diverges. Comparison with event-driven molecular dynamics simulations for dilute systems of hard disks at α=0.2 shows that this theoretical region of absolute instability may be an artifact of the extrapolation to high inelasticity of the approximations made in the derivation of the transport coefficients, although it signals a shrinking of the conditions for stability. In the case of moderate inelasticity (α=0.7), however, a good agreement between the theoretical predictions and the simulation results is found.

Tethered-particle model: The calculation of free energies for hard-sphere systems

Two methods for computing the entropy of hard-sphere systems using a spherical tether model are explored, which allow the efficient use of event-driven molecular-dynamics simulations. An intuitive derivation is given, which relates the rate of particle collisions, either between two particles or between a particle and its respective tether, to an associated hypersurface area, which bounds the system's accessible configurational phase space. Integrating the particle-particle collision rates with respect to the sphere diameter (or, equivalently, density) or the particle-tether collision rates with respect to the tether length then directly determines the volume of accessible phase space and, therefore, the system entropy. The approach is general and can be used for any system composed of particles interacting with discrete potentials in fluid, solid, or glassy states. The entropies calculated for the liquid and crystalline hard-sphere states using these methods are found to agree closely with the current best estimates in the literature, demonstrating the accuracy of the approach.

Separation of a binary gas mixture outflowing into vacuum through a micronozzle

The present paper studies the separation phenomenon for argon–helium mixture outflowing through a convergent–divergent micronozzle into a vacuum. We numerically investigate the effect of the geometrical parameters of the micronozzle and gas rarefaction (Knudsen number is varied in range ≈0.01−100). Simulations were performed using the event-driven molecular dynamics method. Performed analysis revealed several interesting and important features of the separation process. First, it was shown that separation in the present problem results mainly from a lateral component, which appears when significant curvature of gas streamlines is present. Second, it was demonstrated how the fine-tuning of micronozzle geometry can enhance separation efficiency. At the same time, the simplest microslit arrangement (a microchannel without converging and diverging parts) was shown to provide results comparable to micronozzles and may be preferable due to its manufacturing simplicity. Then, it was shown that the position of the product gas selector is crucial for effective separation and its proper placement brings more influence than the geometry of the micronozzle itself. Finally, it was shown that maximal purity of product gas can be obtained in a peripheral area in transitional and slip flow regimes inside the micronozzle. Therefore, for effective separation, there is no need to achieve high rarefaction levels inside the micronozzle.

Self-diffusivity of dense confined fluids

Molecular transport through tight porous media is crucial to shale gas exploration, but deeper insights of the elemental physics are still required, particularly under high pressures and nanoscale confinements, where Navier–Stokes and Boltzmann solutions are no longer valid. In this work, we carry out a fundamental and systematic study of self-diffusion using event-driven molecular dynamics simulations, varying fluid rarefaction, confinement, and surface friction. We differentiate between fluid–fluid and fluid-wall collisions to identify the interplay of the underpinning diffusive mechanisms, namely, molecular and Knudsen diffusion. We find that the Bosanquet formula, which has been used for describing rarefied gases, is also able to provide a good semi-analytical description of self-diffusivities in confined dense fluids, as long as the pore height is not smaller than five molecular diameters. Importantly, this allows us to predict the self-diffusion coefficient, regardless of the fluid rarefaction, confinement state, and surface roughness, in a wide range of Knudsen numbers that were not possible before. Often as a source of debate, we prove here that despite strong fluid inhomogeneities arising in these conditions, the Einstein self-diffusivity can still be used within Fick's law, provided boundary effects are considered when using Fick's setup. Finally, we notice that a previously identified linear scaling of self-diffusivities with confinement is only valid in the limit of low densities and frictionless walls, which is not representative of shale reservoirs. This work will serve as a foundation for investigating the anomalous gas transport behavior observed in the recent work of dense, confined fluids.

Tagged-particle motion in quasi-confined colloidal hard-sphere liquids

We investigate the tagged-particle motion in a strongly interacting quasi-confined liquid using periodic boundary conditions along the confining direction. Within a mode-coupling theory of the glass transition we calculate the self-nonergodicity parameters and the self-intermediate scattering function and compare them with event-driven molecular dynamics simulations. We observe non-monotonic behavior for the in-plane mean-square displacement and further correlation functions which refer to higher mode indices encoding information about the perpendicular motion. The in-plane velocity-autocorrelation function reveals persistent anti-correlations with a negative algebraic power-law decay t −2 at all packing fractions.

An Investigation of Transition Flow in Porous Media by Event Driven Molecular Dynamics Simulation

Aim of this study is to investigate the properties of mono-atomic gas flow through the porous medium by using Event-Driven Molecular Dynamics (EDMD) simulation in the transition regime. The molecules and the solid particles forming the porous structure were modelled as hard spheres hence molecule trajectories, collision partners, interaction times and post-collision velocities were calculated deterministically. The porous medium is formed of spherical particles suspended in the middle of the channel and these particles are distributed into the channel in a regular cubic array. Collisions of gas molecules with porous medium were provided by means of the specular reflection boundary condition. A negative pressure boundary condition was applied to the inlet and outlet of the porous media to ensure gas flow. Porosity, solid sphere diameter and Knudsen number (Kn) were initially input to the simulation for different Cases. Thus, the effects of these parameters on mass flow rate, dynamic viscosity, tortuosity and permeability were calculated by EDMD simulation. The results were compared with the literature and were found to be consistent.

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.

Non-equilibrium response and slow equilibration in hard disk systems

The relaxation from a non-equilibrium state to the equilibrium depends on the methodologies and initial conditions. To investigate the microscopic mechanisms of equilibration systematically, we focus on the non-equilibrium response during the equilibration process induced by a disturbance of the homogeneous expansion of the simple hard disk systems. Large scale simulations by event-driven molecular dynamics revealed that an anomalous slow equilibration toward the liquid states emerges when starting from the co-existence phase. The origin of the slow decay mechanism is investigated using the probability distribution of local density and orientational order parameter.Their inhomogeneities seem to cause the anomalous slow equilibration.

Dependence of cluster growth on the coefficient of restitution in a cooling granular fluid

Starting from configurations having homogeneous spatial density, we study kinetics in a two-dimensional system of inelastically colliding hard particles, a popular model for cooling granular matter. Following an initial time period, the system exhibits a crossover to an inhomogeneous regime that is characterized by the formation and growth of particle-rich clusters. We present results on the time dependence of average mass of the clusters and that of average kinetic energy, obtained via event-driven molecular dynamics simulations, for a wide range of values for the coefficient of restitution (e), by fixing the overall density of particles in the system to a constant number. The time of onset of crossover from homogeneous to the inhomogeneous regime, as is well known, strongly increases as one moves towards the elastic limit. Nevertheless, our presented results suggest that the asymptotic growth is independent of e, for uniform definition of cluster, onset of which has a different e-dependence than the onset of above-mentioned crossover. In other words, not only the exponent but also the amplitude of the power-law growth, which is widely believed to be the form of the evolution, is at the most very weakly sensitive to the choice of e. While it is tempting to attribute this fact to the similar feature in the decay of energy, we caution that our current understanding is not matured enough to draw such a connection between cluster growth and energy decay in a meaningful manner.

Rotational relaxation model for nitrogen and its application in free jet expansion problem

This paper studies a rotational relaxation process in nitrogen. A series of more than 200 × 106 classical trajectory calculations (CTCs) of collisions of nitrogen molecules were carried out. Based on the CTC results, a collision model accounting for rotational relaxation was proposed and used for three-dimensional event-driven molecular dynamics simulation of a free jet expansion. It was shown that the collision model parameterized by the CTCs can produce results in good agreement with the existing experimental measurements.

Dense gas flow simulations in ultra-tight confinement

Modeling dense gas flows inside channels with sections comparable to the diameter of gas molecules is essential in porous medium applications, such as in non-conventional shale reservoir management and nanofluidic separation membranes. In this paper, we perform the first verification study of the Enskog equation by using particle simulation methods based on the same hard-sphere collisions dynamics. Our in-house Event-Driven Molecular Dynamics (EDMD) code and a pseudo-hard-sphere Molecular Dynamics (PHS-MD) solver are used to study force-driven Poiseuille flows in the limit of high gas densities and high confinements. Our results showed (a) very good agreement between EDMD, PHS-MD, and Enskog solutions across density, velocity, and temperature profiles for all the simulation conditions and (b) numerical evidence that deviations exist in the normalized mass flow rate vs Knudsen number curve compared to the standard curve without confinement. While we observe slight deviations in the Enskog density and velocity profiles from the MD when the reduced density is greater than 0.2, this limit is well above practical engineering applications, such as in shale gas. The key advantages of promoting the Enskog equation for upscaling flows in porous media lie in its ability to capture the non-equilibrium physics of tightly confined fluids while being computationally more efficient than fundamental simulation approaches, such as molecular dynamics and derivative solvers.

Anomalous transport due to retroreflection

The magnetotransport of an electron gas in a two-dimensional, random arrangement of overlapping retroreflective crosses is studied using a combination of experiment and classical event-driven molecular dynamics simulation. The experimentally measured magnetoconductivity ${\ensuremath{\sigma}}_{xx}$ as a function of the magnetic field $B$ displays an anomalous behavior at low $B$ fields, accompanied with an increase of ${\ensuremath{\sigma}}_{xx}$ with increasing temperature at $B=0$. The simulations show that at $B=0$ the magnetoconductivity does not exist and is associated with anomalous diffusion in the asymptotic long-time limit that depends on the orientational order of the obstacles. At any finite $B$ field, the motion of the tracer particle is asymptotically diffusive but the diffusion coefficient vanishes with a power law in the limit $B\ensuremath{\rightarrow}0$.

Dynamical properties of densely packed confined hard-sphere fluids.

Numerical solutions of the mode-coupling theory (MCT) equations for a hard-sphere fluid confined between two parallel hard walls are elaborated. The governing equations feature multiple parallel relaxation channels which significantly complicate their numerical integration. We investigate the intermediate scattering functions and the susceptibility spectra close to structural arrest and compare to an asymptotic analysis of the MCT equations. We corroborate that the data converge in the β-scaling regime to two asymptotic power laws, viz. the critical decay and the von Schweidler law. The numerical results reveal a nonmonotonic dependence of the power-law exponents on the slab width and a nontrivial kink in the low-frequency susceptibility spectra. We also find qualitative agreement of these theoretical results to event-driven molecular dynamics simulations of polydisperse hard-sphere systems. In particular, the nontrivial dependence of the dynamical properties on the slab width is well reproduced.

Temperature relaxation in binary hard-sphere mixture system: Molecular dynamics and kinetic theory study.

Computational schemes to describe the temperature relaxation in the binary hard-sphere mixture system are given on the basis of molecular dynamics (MD) simulation and renormalized kinetic theory. Event-driven MD simulations are carried out for three model systems in which the initial temperatures and the ratios of diameter and mass of two components are different to study the temporal evolution of each component temperature in nanoscale molecular conditions mimicking those in living cells. On the other hand, the temperature changes of the two components are also described in terms of a mean-field kinetic theory with the correlation functions calculated in the Percus-Yevick approximation. The calculated results by both the computational approaches have shown fair agreement with each other, whereas slight deviations have been found in the temporal range of femto- to picoseconds when the initial temperatures of the two components are significantly different, such as 300 K vs 1000 K. This discrepancy can be ascribed to the fast intra-component temperature relaxation assumed in the kinetic theory, and its violation in the MD simulations can be evaluated in terms of the Kullback-Leibler divergence between the equilibrated Maxwell-Boltzmann distribution at each temperature and the actual non-equilibrium velocity distribution realized in the MD. Thus, the present analysis provides a quantitative basis for addressing the temperature inhomogeneities experimentally observed in nanoscale crowding conditions.

Spontaneous Crystallization in Systems of Binary Hard Sphere Colloids.

Computer simulations of the fluid-to-solid phase transition in the hard sphere system were instrumental for our understanding of crystallization processes. But while colloid experiments and theory have been predicting the stability of several binary hard sphere crystals for many years, simulations were not successful to confirm this phenomenon. Here, we report the growth of binary hard sphere crystals isostructural to Laves phases, AlB_{2}, and NaZn_{13} in simulation directly from the fluid. We analyze particle kinetics during Laves phase growth using event-driven molecular dynamics simulations with and without swap moves that speed up diffusion. The crystallization process transitions from nucleation and growth to spinodal decomposition already deep within the fluid-solid coexistence regime. Finally, we present packing fraction-size ratio state diagrams in the vicinity of the stability regions of three binary crystals.

Dynamical coexistence in moderately polydisperse hard-sphere glasses.

We perform extensive numerical simulations of a paradigmatic model glass former, the hard-sphere fluid with 10% polydispersity. We sample from the ensemble of trajectories with fixed observation time, whereby single trajectories are generated by event-driven molecular dynamics. We show that these trajectories can be characterized in terms of the local structure, and we find a dynamical-structural (active-inactive) phase transition between two dynamical phases: one dominated by liquidlike trajectories with a low degree of local order and one dominated by glassylike trajectories with a high degree of local order. We show that both phases coexist and are separated by a spatiotemporal interface. Sampling exceptionally long trajectories allows us to perform a systematic finite-size scaling analysis. We find excellent agreement with Binder's scaling theory for first-order transitions. Interestingly, the coexistence region narrows at higher densities, supporting the idea of a critical point controlling the dynamic arrest. Scaling of the susceptibility suggests that the critical behavior falls into the universality class of directed percolation in 3 + 1 dimensions.

Tracer transport in attractive and repulsive supercooled liquids and glasses.

The transport of small penetrants through disordered materials with glassy dynamics is encountered in applications ranging from drug delivery to chemical separations. Nonetheless, understanding the influence of the matrix structure and fluctuations on penetrant motions remains a persistent challenge. Here, we use event-driven molecular dynamics to investigate the transport of small, hard-sphere tracers embedded in matrices of square-well particles. Short-range attractions between matrix particles give rise to reentrant dynamics in the supercooled regime, in which the liquid's relaxation time increases dramatically upon heating or cooling. Heating results in a "repulsive" supercooled liquid where relaxations are frustrated by steric interactions between particles, whereas cooling produces an "attractive" liquid in which relaxations are hindered by long-lived interparticle bonds. Further cooling or heating, or compression, of the supercooled liquids results in the formation of distinct glasses. Our study reveals that tracer transport in these supercooled liquids and glasses is influenced by the matrix structure and dynamics. The relative importance of each factor varies between matrices and is examined in detail by analyzing particle mean-square displacements, caging behavior, and trajectories sampled from the isoconfigurational ensemble. We identify features of tracer dynamics that reveal the spatial and temporal heterogeneity of the matrices and show that matrix arrest is insufficient to localize tracers.

Generalization of the Wall theorem to out-of-equilibrium conditions.

The well-known Wall theorem states a simple and precise relation among temperature, pressure, and density of a fluid at contact with a confining hard wall in thermodynamic equilibrium. In this Communication, we develop an extension of the Wall theorem to out-of-equilibrium conditions, providing an exact relation between pressure, density, and temperature at the wall, valid for strong nonequilibrium situations. We derive analytically this nonequilibrium Wall theorem for stationary states and validate it with nonequilibrium event-driven molecular-dynamics simulations. We compare the analytical expression with simulations by direct evaluation of temperature, density, and pressure on the wall of a nanoconfined liquid under stationary flow. This is done for linear regime, medium and very strong out-of-equilibrium conditions, presenting viscous heating and heat transport. The agreement between theory and simulation is excellent, allowing for a conclusive verification. In addition, we explore the degree of accuracy of using the equilibrium Wall theorem and different expressions for the local temperature, employed in nonequilibrium molecular-dynamics simulations.

A new principle of separation of gas mixtures in non-stationary transitional flows

The paper studies non-stationary gas flow in a transitional regime in a region with a moving boundary. Interest in this problem is due to the search for new principles of gas separation, which can be implemented in practice as a microelectromechanical system (MEMS). The diminutiveness of such systems makes them relevant for aerospace applications. To solve the problem, the method of event-driven molecular dynamics (EDMD) was used, which was extended by the authors to the case of computational domain with moving boundaries (simulating moving elements of the device). A new principle of operation of the separation device was proposed and investigated. It was obtained that the separation coefficient of proposed device can be significantly higher than that of the diffusion method.

Efficient equilibration of hard spheres with Newtonian event chains.

An important task in the simulation of hard spheres and other hard particles is structure prediction via equilibration. Event-driven molecular dynamics is efficient because its Newtonian dynamics equilibrates fluctuations with the speed of sound. Monte Carlo simulation is efficient if performed with correlated position updates in event chains. Here, we combine the core concepts of molecular dynamics and event chains into a new algorithm involving Newtonian event chains. Measurements of the diffusion coefficient, nucleation rate, and melting speed demonstrate that Newtonian event chains outperform other algorithms. Newtonian event chains scale well to large systems and can be extended to anisotropic hard particles without approximations.