Lattice Boltzmann Model for the Incompressible Navier–Stokes Equation

In this paper a lattice Boltzmann (LB) model to simulate incompressible flow is developed. The main idea is to explicitly eliminate the terms of o(M ²), where M is the Mach number, due to the density fluctuation in the existing LB models. In the proposed incompressible LB model, the pressure p instead of the mass density ρ is the independent dynamic variable. The incompressible Navier–Stokes equations are derived from the incompressible LB model via Chapman–Enskog procedure. Numerical results of simulations of the plane Poiseuille flow driven either by pressure gradient or a fixed velocity profile at entrance as well as of the 2D Womersley flow are presented. The numerical results are found to be in excellent agreement with theory.     

Accuracy analysis of high-order lattice Boltzmann models for rarefied gas flows

In this work, we have theoretically analyzed and numerically evaluated the accuracy of high-order lattice Boltzmann (LB) models for capturing non-equilibrium effects in rarefied gas flows. In the incompressible limit, the LB equation is shown to be able to reduce to the linearized Bhatnagar–Gross–Krook (BGK) equation. Therefore, when the same Gauss–Hermite quadrature is used, LB method closely resembles the discrete velocity method (DVM). In addition, the order of Hermite expansion for the equilibrium distribution function is found not to be directly correlated with the approximation order in terms of the Knudsen number to the BGK equation for incompressible flows. Meanwhile, we have numerically evaluated the LB models for a standing-shear-wave problem, which is designed specifically for assessing model accuracy by excluding the influence of gas molecule/surface interactions at wall boundaries. The numerical simulation results confirm that the high-order terms in the discrete equilibrium distribution function play a negligible role in capturing non-equilibrium effect for low-speed flows. By contrast, appropriate Gauss–Hermite quadrature has the most significant effect on whether LB models can describe the essential flow physics of rarefied gas accurately. Our simulation results, where the effect of wall/gas interactions is excluded, can lead to conclusion on the LB modeling capability that the models with higher-order quadratures provide more accurate results. For the same order Gauss–Hermite quadrature, the exact abscissae will also modestly influence numerical accuracy. Using the same Gauss–Hermite quadrature, the numerical results of both LB and DVM methods are in excellent agreement for flows across a broad range of the Knudsen numbers, which confirms that the LB simulation is similar to the DVM process. Therefore, LB method can offer flexible models suitable for simulating continuum flows at the Navier–Stokes level and rarefied gas flows at the linearized Boltzmann model equation level.     

Lattice constants of Langmuir-Blodgett films measured by atomic force microscopy

Langmuir-Blodgett (LB) films are examples of soft organic and related biological samples. Therefore it is essential to make sure that the mechanical scanning process does not disturb the specimen. We describe atomic force microscopy measurements of the lattice constants of Cd arachidate LB films. A lattice constant d_hk is revealed correctly by scanning parallel to the corresponding lattice line [hk]. Scanning in deviating directions enlarges the lattice spacing. The phenomena are explained with a simple model. Previous studies where such artefacts have not been reported are discussed.     

On the generalized Hermite-based lattice Boltzmann construction,lattice sets,weights, moments,distribution functions and high-order models

The influence of the use of the generalized Hermite polynomial on the Hermite-based lattice Bofiz- mann （LB） construction approach, lattice sets, the thermal weights, moments and the equilibrium distribution function （EDF） are addressed. A new moment system is proposed. The theoretical possibility to obtain a unique high-order Hermite-based singel relaxation time LB model capable to exactly inatch some first hydrodynamic inoments thermally i） on-Cartesian lattice, ii） with thermal weights in the EDF, iii） whilst the highest possible hydrodynamic moments that are exactly reatched are obtained with the shortest on-Cartesian lattiee sets with some fixed real-valued temperatures, is also analyzed.     

Improved yield in molecular electronic devices using amino-style molecules

Molecular electronic devices were fabricated with amino-style derivatives as redox-active components. These molecules are amphiphilic to allow monolayer formation by the Langmuir–Blodgett (LB) method, and this LB monolayer is inserted between two metal electrodes. On measuring the current–voltage (I–V) characteristics, it was found that the Al/amino style LB monolayer/Al devices show remarkable hysteresis and switching behavior, so that they can be used as memory devices at ambient conditions, when an aluminum oxide layer exists on the bottom electrode. From the results of I–V measurements, we acquired values of the switching voltage and some large on/off ratios in the case of the ASBC-18 molecule. Also, we improved the yield of the molecular electronic device by reducing the area of the device and by inserting a Ti protecting layer between the top metal electrode and the amino style LB monolayer.     

Simulation of microchannel flow using the lattice Boltzmann method

For microchannel flow simulation, the slip boundary model is very important to guarantee the accuracy of the solution. In this paper, a new slip model, the Langmuir slip model, instead of the popularly used Maxwell slip model, is incorporated into the lattice Boltzmann (LB) method through the non-equilibrium extrapolation scheme to simulate the rarefied gas flow. Its feasibility and accuracy are examined by simulations of microchannel flow. Although, for simplicity, in this paper our recently developed LB model is used to solve the flow field, this does not prevent the present boundary scheme from easily incorporating other LB models, for example the more advanced collision model with multiple relaxation times. In addition, the existing non-equilibrium extrapolation LB boundary scheme for macroscopic flows can be recovered naturally from the present scheme when the Knudsen number .     

Interactions between a cavitation bubble and solidification front under the effects of ultrasound: Experiments and lattice Boltzmann modeling

The phenomena of melting and dendritic fragmentation are captured by using an in-situ device during the ultrasound-assisted solidification of a succinonitrile-acetone (SCN-ACE) alloy. The experimental results show that the dendrite arms detach from primary trunk due to the melting of the solid phase, which is caused by a moving ultrasound cavitation bubble. To quantify the interactions between the ultrasound cavitation bubble and the solidification front, a coupled lattice Boltzmann (LB) model is developed for describing the fields of temperature, flow, and solid fraction, and their interactions. The multi-relaxation-time (MRT) scheme is applied in the LB model to calculate the liquid-gas flow field, while the Bhatnagar–Gross–Krook (BGK) equation is executed to simulate the evolution of temperature. The kinetics of solidification and melting are calculated according to the lever rule based on the SCN-ACE phase diagram. After the validation of the LB model by an analytical model, the morphologies of the cavitation bubble and solidification front are simulated. It is revealed that the solidification interface melts due to the increase of the temperature nearby the cavitation bubble in ultrasonic field. The simulated morphologies of the cavitation bubble and solidification front are compared well with the experimental micrograph. Quantitative investigations are carried out for analyzing the melting rate of the solidification front under different conditions. The simulated data obtained from LB modeling and theoretical predictions reasonably accord with the experimental results, demonstrating that the larger the ultrasonic intensity, the faster the melting rate. The present study not only reveals the evolution of the solidification front shape caused by the cavitation bubbles, which is invisible in the ultrasound-assisted solidification process of practical alloys, but also reproduces the complex interactions among the temperature field, acoustic streaming, and multi-phase flows.     

Error analysis and correction for Lattice Boltzmann simulated flow conductance in capillaries of different shapes and alignments

We study the relative error in conductance calculations, for simulated flow of a single component single phase fluid through a capillary in three dimensions, by the Lattice Boltzmann (LB) method with bounce-back boundary conditions. The relative error with respect to analytical results for capillary cross-sections of circular, triangular and square shapes are calculated as a function of the cross-section diameter, a, and for different alignment of the cross-section relative to the underlying lattice grid. It is shown, when the shapes are not aligned perfectly to the lattice, that the relative error decreases systematically with the size, a, as ～1/a when a is evaluated by mapping the computed cross-sectional area, in terms of the enclosed number of grid points, to the respective geometrical shapes concerned. For perfectly aligned geometries, viz. the square capillary aligned to the LB lattice grid or rotated with its side along the diagonal of the LB grid, the relative error decreases as ～1/a². A simple method is suggested to locate the boundary wall depending on its orientation relative to the grid, such that the exact conductance of the new shape matches the LB computed conductance.     

Lattice Boltzmann modeling and simulation of compressible flows

In this mini-review we summarize the progress of Lattice Boltzmann (LB) modeling and simulating compressible flows in our group in recent years. Main contents include (i) Single-Relaxation-Time (SRT) LB model supplemented by additional viscosity, (ii) Multiple-Relaxation-Time (MRT) LB model, and (iii) LB study on hydrodynamic instabilities. The former two belong to improvements of physical modeling and the third belongs to simulation or application. The SRT-LB model supplemented by additional viscosity keeps the original framework of Lattice Bhatnagar-Gross-Krook (LBGK). So, it is easier and more convenient for previous SRT-LB users. The MRT-LB is a completely new framework for physical modeling. It significantly extends the range of LB applications. The cost is longer computational time. The developed SRT-LB and MRT-LB are complementary from the sides of convenience and applicability.     

Improved crystallinity,spatial arrangement and monodispersity of submicron La0.7Ba0.3MnO3 powders: A citrate chelation approach

The perovskite manganite systems have been the materials of tremendous interest due to their strong correlation between structure, transport and magnetism. These materials in their single-crystal form show colossal magneto-resistance (CMR), but the applied fields are very high (∼1–5 T). The polycrystalline samples do show high low-field magneto-resistance (LFMR), but good amount of control over particle sizes and grain-boundary distribution is required, which is well known but less realized in practical approaches. In this context, we report on synthesis and manipulation of polycrystalline La_0.7Ba_0.3MnO₃ (LBMO) submicron powders using citric acid chelation. The Citrate-gel route is used to synthesize poly-dispersed LBMO powders which are subjected to citrate chelation for a duration of 0 (LB0) to 4 h(LB4) . The samples show improved ordering in X-ray diffraction patterns. Raman spectroscopy scans indicate changed mode signatures due to the probable chelating process, which alters the surface morphology. X-ray photoelectron microscopy shows an evidence of fine citrate layer on the grain boundaries. Low temperature B–H curves exhibit fine hysteresis loops for all samples, while room temperature B–H curves shows paramagnetic response. Scanning electron microscopy images showed the formation of well arranged, connected, mono-dispersed grains of LB4 sample, as against polydispered LB0. The magneto-resistance (at H=100 kOe) is seen to enhance for LB4 at its transition temperature (75%, as compared to LB0, where it is 60%), which can be attributed to the well-controlled inter-grain tunneling phenomenon and thin insulating regions in between, created due to citrate chelation, which probably enhances the scattering phenomenon and its susceptibility to applied fields. As citric acid is known to chelate Mn ions, it probably chelates the smaller LB particulate structure and leaves behind citrate-connected submicron grains of LBMO, which are seen to be well engineered.     

Lattice Boltzmann model for combustion and detonation

In this paper we present a lattice Boltzmann model for combustion and detonation. In this model the fluid behavior is described by a finite-difference lattice Boltzmann model by Gan et al. [Physica A, 2008, 387: 1721]. The chemical reaction is described by the Lee-Tarver model [Phys. Fluids, 1980, 23: 2362]. The reaction heat is naturally coupled with the flow behavior. Due to the separation of time scales in the chemical and thermodynamic processes, a key technique for a successful simulation is to use the operator-splitting scheme. The new model is verified and validated by well-known benchmark tests. As a specific application of the new model, we studied the simple steady detonation phenomenon. To show the merit of LB model over the traditional ones, we focus on the reaction zone to study the non-equilibrium effects. It is interesting to find that, at the von Neumann peak, the system is nearly in its thermodynamic equilibrium. At the two sides of the von Neumann peak, the system deviates from its equilibrium in opposite directions. In the front of von Neumann peak, due to the strong compression from the reaction product behind the von Neumann peak, the system experiences a sudden deviation from thermodynamic equilibrium. Behind the von Neumann peak, the release of chemical energy results in thermal expansion of the matter within the reaction zone, which drives the system to deviate the thermodynamic equilibrium in the opposite direction. From the deviation from thermodynamic equilibrium, Δ _m *, defined in this paper, one can understand more on the macroscopic effects of the system due to the deviation from its thermodynamic equilibrium.     

Immiscible multicomponent lattice Boltzmann model for fluids with high relaxation time ratio

An immiscible multicomponent lattice Boltzmann model is developed for fluids with high relaxation time ratios, which is based on the model proposed by Shan and Chen (SC). In the SC model, an interaction potential between particles is incorporated into the discrete lattice Boltzmann equation through the equilibrium velocity. Compared to the SC model, external forces in our model are discretized directly into the discrete lattice Boltzmann equation, as proposed by Guo et al. We develop it into a new multicomponent lattice Boltzmann (LB) model which has the ability to simulate immiscible multicomponent fluids with relaxation time ratio as large as 29.0 and to reduce ‘spurious velocity’. In this work, the improved model is validated and studied using the central bubble case and the rising bubble case. It finds good applications in both static and dynamic cases for multicomponent simulations with different relaxation time ratios.     

Time-domain interferometry experiments using multi-line nuclear absorbers

Langmuir-Blodgett (LB) films of octadecanoyl hydroxamic acid (C18N) complexed with Fe^3?+? ions have been prepared at various subphase pH values. The LB films consisting of different number of layers were investigated by ⁵⁷Fe conversion electron M?ssbauer spectroscopy (CEM) at room temperature. The CEM detector contained a piece of α-iron, enriched with ⁵⁷Fe, using as an internal standard. The M?ssbauer pattern of the C18N/Fe LB films is a doublet with parameters δ = 0.35?mm/s and Δ = 0.74?mm/s. A gradual increase of the relative occurrence of the doublet compared to the sextet of the internal standard was observed with the increasing number of layers, indicating the nearly uniform distribution of Fe among the LB layers.     

Lattice Boltzmann simulation of fluid flows in two-dimensional channel with complex geometries

Boundary conditions (BCs) play an essential role in lattice Boltzmann (LB) simulations. This paper investigates several most commonly applied BCs by evaluating the relative L₂-norm errors of the LB simulations for two-dimensional (2-D) Poiseuille flow. It is found that the relative L₂-norm error resulting from FHML's BC is smaller than that from other BCs as a whole. Then, based on the FHML's BC, it formulates an LB model for simulating fluid flows in 2-D channel with complex geometries. Afterwards, the flows between two inclined plates, in a pulmonary blood vessel and in a blood vessel with local expansion region, are simulated. The numerical results are in good agreement with the analytical predictions and clearly show that the model is effective. It is expected that the model can be extended to simulate some real biologic flows, such as blood flows in arteries, vessels with stenosises, aneurysms and bifurcations, etc.     

Monolayer characteristics and spectroscopic study of benz(b)fluoranthene assembled in Langmuir Blodgett films mixed with stearic acid

Excellent Langmuir Blodgett (LB) films of benz(b)fluoranthene (B(b)F) have been prepared by mixing with stearic acid (SA). The surface pressure vs. area per molecule isotherms (π–A) of B(b)F mixed with SA at different mole fraction reveal that the area per molecule decreases with increasing mole fractions of B(b)F. The area per molecule vs. mole fraction shows that there is positive deviation of the experimental data to the idealized one. This indicates formation of aggregation of B(b)F molecules in the SA matrix. Spectroscopic properties of B(b)F in solution and in mixed LB films have been compared by absorption, steady state fluorescence, phosphorescence spectroscopy and lifetime measurements. Bathochromic shift in absorption and emission spectrum suggests the formation of some kind of aggregates in LB film. Decrease in fluorescence and phosphorescence lifetime is compared to that of pure B(b)F also supports the formation of different sized aggregates in the mixed film.     

Lattice Boltzmann Simulations of Blood Flow: Non-Newtonian Rheology and Clotting Processes

The numerical simulation of thrombosis in stented aneurysms is an important issue to estimate the efficiency of a stent. In this paper, we consider a Lattice Boltzmann (LB) approach to bloodflow modeling and we implement a non-Newtonian correction in order to reproduce more realistic flow profiles. We obtain a good agreement between simulations and Casson’s model of blood rheology in a simple geometry. Finally we discuss how, by using a passive scalar suspension model with aggregation on top of the LB dynamics, we can describe the clotting processes in the aneurysm     

Multiple-Relaxation-Time Lattice Boltzmann Approach to Richtmyer-Meshkov Instability

The aims of the present paper are twofold. At first, we further study the Multiple-Relaxation-Time (MRT) Lattice Boltzmann (LB) model proposed in [Europhys. Lett. 90 (2010) 54003]. We discuss the reason why the Gram-Schmidt orthogonalization procedure is not needed in the construction of transformation matrix M; point out a reason why the Kataoka-Tsutahara model [Phys. Rev. E 69 (2004) 035701(R)] is only valid in subsonic flows.The von Neumann stability analysis is performed. Secondly, we carry out a preliminary quantitative study on the Richtmyer-Meshkov instability using the proposed MRT LB model. When a shock wave travels from a light medium to a heavy one, the simulated growth rate is in qualitative agreement with the perturbation model by Zhang-Sohn. It is about half of the predicted value by the impulsive model and is closer to the experimental result. When the shock wave travels from a heavy medium to a light one, our simulation results are also consistent with physical analysis.     

Optimal preconditioning of lattice Boltzmann methods

A preconditioning technique to accelerate the simulation of steady-state problems using the single-relaxation-time (SRT) lattice Boltzmann (LB) method was first proposed by Guo et al. [Z. Guo, T. Zhao, Y. Shi, Preconditioned lattice-Boltzmann method for steady flows, Phys. Rev. E 70 (2004) 066706-1]. The key idea in this preconditioner is to modify the equilibrium distribution function in such a way that, by means of a Chapman–Enskog expansion, a time-derivative preconditioner of the Navier–Stokes (NS) equations is obtained. In the present contribution, the optimal values for the free parameter γ$\gamma$ of this preconditioner are searched both numerically and theoretically; the later with the aid of linear-stability analysis and with the condition number of the system of NS equations. The influence of the collision operator, single- versus multiple-relaxation-times (MRT), is also studied. Three steady-state laminar test cases are used for validation, namely: the two-dimensional lid-driven cavity, a two-dimensional microchannel and the three-dimensional backward-facing step. Finally, guidelines are suggested for an a priori definition of optimal preconditioning parameters as a function of the Reynolds and Mach numbers. The new optimally preconditioned MRT method derived is shown to improve, simultaneously, the rate of convergence, the stability and the accuracy of the lattice Boltzmann simulations, when compared to the non-preconditioned methods and to the optimally preconditioned SRT one. Additionally, direct time-derivative preconditioning of the LB equation is also studied.     

Molecular assembly and photophysical properties of Langmuir-Blodgett films with novel lanthanide complexes of long chain para-dodecanoyl and para-myristoyl oxybenzoate

Several ultrathin luminescent Langmuir-Blodgett (LB) films have been prepared by using the subphase containing the rare earth ions (Eu³⁺, Dy³⁺). The effect of the rare earth ions on the monolayer of p-dodecanoyloxybenzoate (12-OBA) and p-myristoyloxybenzoate (14-OBA) was investigated. IR spectra showed the rare earth ions were bound to the carboxylic acid head groups and the coordination took place between the polar head group and the rare earth ions. The layer structure of the LB films was demonstrated by low-angle X-ray diffraction. The AFM study revealed that the LB films were uniform and crack free, and the films mainly consisted of closely packed grains with an average size of 241 nm. The LB films can give off strong fluorescence, and the signal can be detected from a single layer. The characteristic luminescence behaviors of LB films have been discussed compared with those of the complexes.     

Neutron measurements around a TN85-type storage cask with high-active waste

Several types of casks have been deposited in the German interim storage facility for spent fuel assemblies and vitrified high-active waste (HAW) at Gorleben since 1995, most of them of the CASTOR^® type. In 2008 a delivery of 11 TN85-type casks arrived. They belong to the Transnuclear/Areva cask family and, compared to the flasks of the German (GNS) CASTOR^® type, they differ in the neutron shielding design.Generally, radiation exposure of personnel during transportation and storage of casks containing spent fuel and vitrified waste is caused by mixed photon/neutron fields. Frequently, especially at casks for vitrified waste from reprocessing, neutrons are the major component of radiation exposure.Spectrometric and dosimetric investigations were made around a cask of the TN85-type. Neutron fluence spectra and reference values of the ambient dose equivalent H*(10) were measured by means of a Bonner sphere spectrometer (BSS) at several locations on the cask surface and in its environment. Moreover, commercial area dosemeters, LB6411 neutron monitors and conventional AD 6-type photon dosemeters were used. In addition, the responses of two electronic personal dosemeters for mixed fields (EPD-N2, DMC 2000GN) and a TLD albedo dosemeter were investigated.The neutron spectra obtained from the BSS are presented and compared with former measurements at CASTOR^® type casks. The relative responses of the LB6411 survey meter and the individual dosemeters are discussed. The LB6411 monitor indicates H*(10) around the TN85 cask with tolerable measuring uncertainties. The personal dosemeters provide acceptable results for photons but overestimate the neutron dose considerably.