Overrelaxation in a diffusive integer lattice gas.

One of the most striking drawbacks of standard lattice gas methods over lattice Boltzmann methods is a much more limited range of transport parameters that can be achieved. It is common for lattice Boltzmann methods to use over-relaxation to achieve arbitrarily small transport parameters in the hydrodynamic equations. Here, we show that it is possible to implement over-relaxation for integer lattice gases. For simplicity, we focus here on lattice gases for the diffusion equation. We demonstrate that adding a flipping operation to lattice gases results in a multirelaxation time lattice Boltzmann scheme with over-relaxation in the Boltzmann limit.

Integer lattice gas with a sampling collision operator for the fluctuating diffusion equation.

We developed an integer lattice gas method for the fluctuating diffusion equation. Such a method is unconditionally stable and able to recover the Poisson distribution for the microscopic densities. A key advance for integer lattice gases introduced in this paper is a sampling collision operator that replaces particle collisions with sampling from an equilibrium distribution. This can increase the efficiency of our integer lattice gas by several orders of magnitude.

Shaping the equation of state to improve numerical accuracy and stability of the pseudopotential lattice Boltzmann method.

It has recently been shown that altering the shape of the metastable and unstable branches of an equation of state (EOS) can substantially improve the numerical accuracy of liquid and vapor densities in the pseudopotential lattice Boltzmann method [Peng et al., Phys. Rev. E 101, 063309 (2020)2470-004510.1103/PhysRevE.101.063309]. We found that this approach reduces stability of the method in nonequilibrium conditions and is unstable for bubbles at low reduced temperatures. Here we present an improved method for altering the shape of the metastable and unstable branches of the EOS which remains stable for both equilibrium and nonequilibrium situations and has no issues with bubbles. We also performed a detailed study of the stability of the methods for a droplet impact on a liquid film for reduced temperatures down to 0.35 with Reynolds number of 300. Our approach remained stable for a density ratio of up to 3.38×10^{4}.

Molecular dynamics lattice gas equilibrium distribution function for Lennard-Jones particles.

The molecular dynamics lattice gas (MDLG) method maps a molecular dynamics (MD) simulation onto a lattice gas using a coarse-graining procedure. This is a novel fundamental approach to derive the lattice Boltzmann method (LBM) by taking a Boltzmann average over the MDLG. A key property of the LBM is the equilibrium distribution function, which was originally derived by assuming that the particle displacements in the MD simulation are Boltzmann distributed. However, we recently discovered that a single Gaussian distribution function is not sufficient to describe the particle displacements in a broad transition regime between free particles and particles undergoing many collisions in one time step. In a recent publication, we proposed a Poisson weighted sum of Gaussians which shows better agreement with the MD data. We derive a lattice Boltzmann equilibrium distribution function from the Poisson weighted sum of Gaussians model and compare it to a measured equilibrium distribution function from MD data and to an analytical approximation of the equilibrium distribution function from a single Gaussian probability distribution function. This article is part of the theme issue 'Progress in mesoscale methods for fluid dynamics simulation'.

Nonuniqueness of fluctuating momentum in coarse-grained systems.

Coarse-grained descriptions of microscopic systems often require a mesoscopic definition of momentum. The question arises as to the uniqueness of such a momentum definition at a particular coarse-graining scale. We show here that particularly the fluctuating properties of common definitions of momentum in coarse-grained methods like lattice gas and lattice Boltzmann do not agree with a fundamental definition of momentum. In the case of lattice gases, the definition of momentum will even disagree in the limit of large wavelength. For short times we derive analytical representations for the distribution of different momentum measures and thereby give a full account of these differences.

Non-Gaussian distribution of displacements for Lennard-Jones particles in equilibrium.

Most mesoscale simulation methods assume Gaussian distributions of velocity-like quantities. These quantities are not true velocities, however, but rather time-averaged velocities or displacements of particles. We show that there is a large range of coarse-graining scales where the assumption of a Gaussian distribution of these displacements fails, and a more complex distribution is required to adequately express these distribution functions of displacements.

Force approach for the pseudopotential lattice Boltzmann method.

One attractive feature of the original pseudopotential method consists on its simplicity of adding a force dependent on a nearest-neighbor potential function. In order to improve the method, regarding thermodynamic consistency and control of surface tension, different approaches were developed in the literature, such as multirange interactions potential and modified forcing schemes. In this work, a strategy to combine these enhancements with an appropriate interaction force field using only nearest-neighbor interactions is devised, starting from the desired pressure tensor. The final step of our procedure is implementing this external force by using the classical Guo forcing scheme. Numerical tests regarding static and dynamic flow conditions were performed. Static tests showed that current procedure is suitable to control the surface tension and phase densities. Based on thermodynamic principles, it is devised a solution for phase densities in a droplet, which states explicitly dependence on the surface tension and interface curvature. A comparison with numerical results suggest a physical inconsistency in the pseudopotential method. This fact is not commonly discussed in the literature, since most of studies are limited to the Maxwell equal area rule. However, this inconsistency is shown to be dependent on the equation of state (EOS), and its effects can be mitigated by an appropriate choice of Carnahan-Starling EOS parameters. Also, a droplet oscillation test was performed, and the most divergent solution under certain flow conditions deviated 7.5% from the expected analytical result. At the end, a droplet impact test against a solid wall was performed to verify the method stability, and it was possible to reach stable simulation results with density ratio of almost 2400 and Reynolds number of Re=373. The observed results corroborate that the proposed method is able to replicate the desired macroscopic multiphase behavior.

Large Fluctuations in Nonideal Coarse-Grained Systems.

Using the recently introduced molecular dynamics lattice gas approach, we test fluctuations of coarse-grained quantities. We show that as soon as the system can no longer be considered an ideal gas fluctuations fail to diminish upon coarse graining as is usually expected. These results suggest that current approaches to simulating fluctuating hydrodynamics may have to be augmented to achieve quantitative results for systems with a nonideal equation of state. The molecular dynamics lattice gas method gives a guidance to the exact nature of the fluctuation in such systems.

Multicomponent flow on curved surfaces: A vielbein lattice Boltzmann approach.

We develop and implement a finite difference lattice Boltzmann scheme to study multicomponent flows on curved surfaces, coupling the continuity and Navier-Stokes equations with the Cahn-Hilliard equation to track the evolution of the binary fluid interfaces. The standard lattice Boltzmann method relies on regular Cartesian grids, which makes it generally unsuitable to study flow problems on curved surfaces. To alleviate this limitation, we use a vielbein formalism to write the Boltzmann equation on an arbitrary geometry, and solve the evolution of the fluid distribution functions using a finite difference method. Focusing on the torus geometry as an example of a curved surface, we demonstrate drift motions of fluid droplets and stripes embedded on the surface of the torus. Interestingly, they migrate in opposite directions: fluid droplets to the outer side while fluid stripes to the inner side of the torus. For the latter we demonstrate that the global minimum configuration is unique for small stripe widths, but it becomes bistable for large stripe widths. Our simulations are also in agreement with analytical predictions for the Laplace pressure of the fluid stripes, and their damped oscillatory motion as they approach equilibrium configurations, capturing the corresponding decay timescale and oscillation frequency. Finally, we simulate the coarsening dynamics of phase separating binary fluids in the hydrodynamics and diffusive regimes for tori of various shapes, and compare the results against those for a flat two-dimensional surface. Our finite difference lattice Boltzmann scheme can be extended to other surfaces and coupled to other dynamical equations, opening up a vast range of applications involving complex flows on curved geometries.

Integer lattice gas with Monte Carlo collision operator recovers the lattice Boltzmann method with Poisson-distributed fluctuations.

We examine a new kind of lattice gas that closely resembles modern lattice Boltzmann methods. This new kind of lattice gas, which we call a Monte Carlo lattice gas, has interesting properties that shed light on the origin of the multirelaxation time collision operator, and it derives the equilibrium distribution for an entropic lattice Boltzmann. Furthermore these lattice gas methods have Galilean invariant fluctuations given by a Poisson statistics, giving further insight into the properties that we should expect for fluctuating lattice Boltzmann methods.

Fourth-order analysis of a diffusive lattice Boltzmann method for barrier coatings.

We examine the applicability of diffusive lattice Boltzmann methods to simulate the fluid transport through barrier coatings, finding excellent agreement between simulations and analytical predictions for standard parameter choices. To examine more interesting non-Fickian behavior and multiple layers of different coatings, it becomes necessary to explore a wider range of parameters. However, such a range of parameters exposes deficiencies in such an implementation. To investigate these discrepancies, we examine the form of higher-order terms in the hydrodynamic limit of our lattice Boltzmann method. We identify these corrections to fourth order and validate these predictions with high accuracy. However, it is observed that the validated correction terms do not fully explain the bulk of observed error. This error was instead caused by the standard finite boundary conditions for the contact of the coating with the imposed environment. We identify a self-consistent form of these boundary conditions for which these errors are dramatically reduced. The instantaneous switching used as a boundary condition for the barrier problem proves demanding enough that any higher-order corrections meaningfully contribute for a small range of parameters. There is a large parameter space where the agreement between simulations and analytical predictions even in the second-order form are below 0.1%, making further improvements to the algorithm unnecessary for such an application.

Publisher's Note: Fluctuating lattice Boltzmann method for the diffusion equation [Phys. Rev. E 94, 033302 (2016)].

This corrects the article DOI: 10.1103/PhysRevE.94.033302.

Determination of the Absolute Configuration of ß-Chiral Primary Alcohols Using the Competing Enantioselective Conversion Method.

A method for determining the absolute configuration of ß-chiral primary alcohols has been developed. Enantioenriched alcohols were acylated in the presence of either enantiomer of the enantioselective acylation catalyst HBTM, and the faster reaction was determined by measuring product conversion using 1H NMR spectroscopic analysis. An empirical mnemonic was developed that correlates the absolute configuration of the alcohol to the faster reacting catalyst. Successful substrates for this method include primary alcohols that bear a "directing group" on the stereogenic center; directing groups include arenes, heteroarenes, enones, and halides.

Chiral Sugars Drive Enantioenrichment in Prebiotic Amino Acid Synthesis.

Chiral pentose sugars mediate the enantioselective synthesis of amino acid precursors, with the magnitude of the chiral induction dictated by a subtle cooperativity between sugar hydroxyl groups. Ribose and lyxose give opposite chiral preferences, and theoretical calculations reveal the pseudoenantiomeric nature of transition state structures from the two sugars. Prebiotically plausible mixtures of natural d-sugars lead to enantioenrichment of natural l-amino acid precursors. Temporal monitoring and kinetic modeling of the reaction reveal an unusual dynamic kinetic resolution that shifts toward an enantioselective pathway over time, providing an amplification mechanism for the transfer of chiral information. This work adds to growing evidence for synergy in the etiology of the single chirality of the two most important classes of biological molecules, the sugars that make up DNA and RNA and the amino acids that form proteins.

Lattice gas with molecular dynamics collision operator.

We introduce a lattice gas implementation that is based on coarse-graining a molecular dynamics (MD) simulation. Such a lattice gas is similar to standard lattice gases, but its collision operator is informed by an underlying MD simulation. This can be considered an optimal lattice gas implementation because it allows for the representation of any system that can be simulated with MD. We show here that equilibrium behavior of the popular lattice Boltzmann algorithm is consistent with this optimal lattice gas. This comparison allows us to make a more accurate identification of the expressions for temperature and pressure in lattice Boltzmann simulations, which turn out to be related not only to the physical temperature and pressure but also to the lattice discretization. We show that for any spatial discretization, we need to choose a particular temporal discretization to recover the lattice Boltzmann equilibrium.

Fluctuating lattice Boltzmann method for the diffusion equation.

We derive a fluctuating lattice Boltzmann method for the diffusion equation. The derivation removes several shortcomings of previous derivations for fluctuating lattice Boltzmann methods for hydrodynamic systems. The comparative simplicity of this diffusive system highlights the basic features of this first exact derivation of a fluctuating lattice Boltzmann method.

Nanomole-Scale Assignment and One-Use Kits for Determining the Absolute Configuration of Secondary Alcohols.

Two different protocols were developed and optimized to address the need for (1) high sensitivity or (2) convenient utilization in the determination of the absolute configuration of secondary alcohols. The first protocol uses the competing enantioselective conversion (CEC) method to determine configuration on nanomole scale. Reactions were conducted with 145 nmol of the substrate using a 50 µL microsyringe as the reaction vessel, and the absolute configuration was assigned via qualitative determination of the fast reaction by thin-layer chromatography. This protocol resulted in a 50-fold reduction in material required from previous CEC method studies. The approach was evaluated with benzylic and ß-aryl systems. The second protocol was optimized to address the needs of practicing medicinal chemists. A one-use CEC kit was developed, where the fast reaction was identified by (1)H NMR spectroscopy and thin-layer chromatography. The CEC reaction conditions developed for the microsyringe protocol and the one-use kit both displayed data consistent with pseudo-first-order kinetics in substrate. Therefore, the lower limit of sensitivity for the substrate is limited only by the ability to effectively detect the reaction conversions between alcohol substrate and ester product.

Phase separation and the 'coffee-ring' effect in polymer-nanocrystal mixtures.

The coupling between the 'coffee-ring' effect and liquid-liquid phase separation is examined for ternary mixtures of solvent, polymer and semiconductor nanocrystal. Specifically, we study mixtures of toluene, polystyrene (PS) and colloidal silicon nanocrystals (SiNCs) using real-space imaging and spectroscopic techniques to resolve the kinetic morphology of the drying front for varied molecular weight of the PS. Our results demonstrate that the size of the polymer has a significant impact on both phase-separation and drying, and we relate these observations to simulations, measured and predicted binodal curves, and the observed shape of the flow field at the contact line. The results inform a deposition process that reduces the influence of drying instabilities for low-molecular-weight polymers while paving the way for more detailed and generic computational descriptions of drying instabilities in complex fluids.

Kinetic analysis of the HBTM-catalyzed esterification of an enantiopure secondary alcohol.

A detailed kinetic analysis of the homobenzotetramisole-mediated esterification of the enantiopure secondary alcohol (1R,2S)-2-phenylcyclohexanol is presented. The results of this analysis show that the reaction is first order in the homobenzotetramisole catalyst, first order in (1R,2S)-2-phenylcyclohexanol, and first order in propionic anhydride. Initial rates, the turnover frequency of the catalyst, and "different excess" plots were utilized in this evaluation. Additionally, a "same excess" plot revealed no noticeable catalyst decomposition or product inhibition during the course of the reaction.