There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

With its roots in kinetic theory and the cellular automaton concept, the lattice-Boltzmann (LB) equation can be used to obtain continuum flow quantities from simple and local update rules based on particle interactions. The simplicity of formulation and its versatility explain the rapid expansion of the LB method to applications in complex and multiscale flows. We review many significant developments over the past decade with specific examples. Some of the most active developments include the entropic LB method and the application of the LB method to turbulent flow, multiphase flow, and deformable particle and fiber suspensions. Hybrid methods based on the combination of the Eulerian lattice with a Lagrangian grid system for the simulation of moving deformable boundaries show promise for more efficient applications to a broader class of problems. We also discuss higherorder boundary conditions and the simulation of microchannel flow with finite Knudsen number. Additionally, the remarkable scalability of the LB method for parallel processing is shown with examples. Teraflop simulations with the LB method are routine, and there is no doubt that this method will be one of the first candidates for petaflop computational fluid dynamics in the near future.

Lattice-Boltzmann Method for Complex Flows

Discrete particle simulation of particulate systems: Theoretical developments

The phase-field method is reviewed against its historical and theoretical background. Starting from Van der Waals considerations on the structure of interfaces in materials the concept of the phase-field method is developed along historical lines. Basic relations are summarized in a comprehensive way. Special emphasis is given to the multi-phase-field method with extension to elastic interactions and fluid flow which allows one to treat multi-grain multi-phase structures in multicomponent materials. Examples are collected demonstrating the applicability of the different variants of the phase-field method in different fields of materials science.

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Phase-field models in materials science

Semisolid metal (SSM) processingis a relatively new technology for metal forming. Different from the conventional metal forming technologies which use either solid metals (solid state processing) or liquid metals (casting) as starting materials, SSM processing deals with semisolid slurries, in which non-dendritic solid particles are dispersed in a liquid matrix. Semisolid metal slurries exhibit distinctive rheological characteristics: the steady state behaviour is pseudoplastic (or shear thinning), while the transient state behaviour is thixotropic. All the currently available technologies for SSM processing have been developed based on those unique rheological properties, which in turn originate from their non-dendritic microstructures. Year 2001 marks the 30th anniversary of the concept of SSM processing. Today, SSM processing has established itself as a scientifically sound and commercially viable technology for production of metallic components with high integrity, improved mechanical properti...

Semisolid metal processing

For gas flows in microchannels, slip motion at the solid surface can occur even if the Mach number is negligibly small. Since the Knudsen number of the gas flow in a long microchannel can vary widely and the Navier-Stokes equations are not valid for Knudsen numbers beyond 0.1, an alternative method that can be applicable to continuum, slip and transition flow regimes is highly desirable. The lattice Boltzmann equation (LBE) approach has recently been expected to have such potential. However, some hurdles need to be overcome before it can be applied to simulate rarefied gas flows. The first major hurdle is to accurately model the gas molecule and wall surface interactions. In addition, the Knudsen number needs to be clearly defined in terms of LBE properties to ensure that the LBE simulation results can be checked against experimental measurements and other simulation results. In this paper, the Maxwellian scattering kernel is adopted to address the gas molecule and surface interactions with an accommodation coefficient (in addition to the Knudsen number) controlling the amount of slip motion. The Knudsen number is derived consistently with the macroscopic property based definition. The simulation results of the present LBE model are in quantitative agreement with the established theory in the slip flow regime. In the transition flow regime, the model captures the Knudsen minimum phenomenon qualitatively. Therefore, the LBE can be a competitive method for simulation of rarefied gas flows in microdevices.

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Lattice Boltzmann simulation of rarefied gas flows in microchannels

In an ideal scenario, a phase field model is able to compute quantitative aspects of the evolution of microstructure without explicit intervention. The method is particularly appealing because it provides a visual impression of the development of structure, one which often matches observations. The essence of the technique is that phases and the interfaces between the phases are all incorporated into a grand functional for the free energy of a heterogeneous system, using an order parameter which can be translated into what is perceived as a phase or an interface in ordinary jargon. There are, however, assumptions which are inconsistent with practical experience and it is important to realise the limitations of the method. The purpose of this review is to introduce the essence of the method, and to describe, in the context of materials science, the advantages and pitfalls associated with the technique.

Phase field method

Passing one electric current pulse through deformed pearlitic steel wires at room temperature causes the formation of cementite particles around 30 nm in size. This is found not only in some particular locations but throughout the cementite area, which reveals a different mechanism from traditional spheroidization of cementite plates because the latter leads to the formation of particles with much large size. Transmission electron microscopy images show electropulse-induced strain relief and formation of fine precipitations. Differential scanning calorimetry analysis demonstrates the additional stored free energy by electropulsing treatment. The raised free energy accounts the increased interface area in finer microstructure of materials. The experiment evidences that the passing electric current in metal has alternated the free energy sequence of various microstructures in comparison with that of current-free system.

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Electropulse-induced cementite nanoparticle formation in deformed pearlitic steels

The influence of electropulsing on the damage of 1045 steel was studied, The results show that electropulsing can substantially increase the strength and ductility of the damaged material, with a little decrease of the Martensite hardness. After the treatment of electropulsing, the microstructure around the crack is modified, and the new structure can prevent the crack from growing, The healing effect of electropulsing on crack is discussed. It is thought that the temperature and thermal compressive stress caused by electropulsing are the main factors causing the healing effect.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0884291400054947

Reversing effect of electropulsing on damage of 1045 steel

Gas flow in microchannels can often encounter tangential slip motion at the solid surface even under creeping flow conditions. To simulate low speed gas flows with Knudsen numbers extending into the transition regime, alternative methods to both the Navier–Stokes and direct simulation Monte Carlo approaches are needed that balance computational efficiency and simulation accuracy. The lattice Boltzmann method offers an approach that is particularly suitable for mesoscopic simulation where details of the molecular motion are not required. In this paper, the lattice Boltzmann method has been applied to gas flows with finite Knudsen number and the tangential momentum accommodation coefficient has been implemented to describe the gas-surface interactions. For fully-developed channel flows, the results of the present method are in excellent agreement with the analytical slip-flow solution of the Navier–Stokes equations, which are valid for Knudsen numbers less than 0.1. The present paper demonstrates that the lattice Boltzmann approach is a promising alternative simulation tool for the design of microfluidic devices.

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Rongshan Qin

Papers

Lattice Boltzmann simulation of rarefied gas flows in microchannels

Phase field method

Electropulse-induced cementite nanoparticle formation in deformed pearlitic steels

Reversing effect of electropulsing on damage of 1045 steel

Gas flow in microchannels - a Lattice Boltzmann method approach