Comparative study of the lattice Boltzmann models for Allen-Cahn and Cahn-Hilliard equations.

In this paper, a comparative study of the lattice Boltzmann (LB) models for the Allen-Cahn (A-C) and Cahn-Hilliard (C-H) equations is conducted. To this end, a new LB model for the A-C equation is first proposed, where the equilibrium distribution function and the source term distribution function are delicately designed to recover the A-C equation correctly. The gradient term in this model can be computed by the nonequilibrium part of the distribution function such that the collision process can be implemented locally. Then a detailed numerical study on several classical problems is performed to give a comparison between the present model for the A-C equation and the recently developed LB model [H. Liang et al., Phys. Rev. E 89, 053320 (2014)PLEEE81539-375510.1103/PhysRevE.89.053320] for the C-H equation in terms of tracking the interface of two-phase flow. The results show that the present LB model for the A-C equation is more accurate and more stable, and also has a second-order convergence rate in space, while the convergence rate of the previous LB model for the C-H equation is only about 1.5.

Lattice Boltzmann simulation of three-dimensional Rayleigh-Taylor instability.

In this paper, the three-dimensional (3D) Rayleigh-Taylor instability (RTI) with low Atwood number (A(t)=0.15) in a long square duct (12W × W × W) is studied by using a multiple-relaxation-time lattice Boltzmann (LB) multiphase model. The effect of the Reynolds number on the interfacial dynamics and bubble and spike amplitudes at late time is investigated in detail. The numerical results show that at sufficiently large Reynolds numbers, a sequence of stages in the 3D immiscible RTI can be observed, which includes the linear growth, terminal velocity growth, reacceleration, and chaotic development stages. At late stage, the RTI induces a very complicated topology structure of the interface, and an abundance of dissociative drops are also observed in the system. The bubble and spike velocities at late stage are unstable and their values have exceeded the predictions of the potential flow theory [V. N. Goncharov, Phys. Rev. Lett. 88, 134502 (2002)]. The acceleration of the bubble front is also measured and it is found that the normalized acceleration at late time fluctuates around a constant value of 0.16. When the Reynolds number is reduced to small values, some later stages cannot be reached sequentially. The interface becomes relatively smoothed and the bubble velocity at late time is approximate to a constant value, which coincides with the results of the extended Layzer model [S.-I. Sohn, Phys. Rev. E 80, 055302(R) (2009)] and the modified potential theory [R. Banerjee, L. Mandal, S. Roy, M. Khan, and M. R. Guptae, Phys. Plasmas 18, 022109 (2011)]. In our simulations, the Graphics Processing Unit (GPU) parallel computing is also used to relieve the massive computational cost.

Lattice Boltzmann modeling of three-phase incompressible flows.

In this paper, based on multicomponent phase-field theory we intend to develop an efficient lattice Boltzmann (LB) model for simulating three-phase incompressible flows. In this model, two LB equations are used to capture the interfaces among three different fluids, and another LB equation is adopted to solve the flow field, where a new distribution function for the forcing term is delicately designed. Different from previous multiphase LB models, the interfacial force is not used in the computation of fluid velocity, which is more reasonable from the perspective of the multiscale analysis. As a result, the computation of fluid velocity can be much simpler. Through the Chapman-Enskog analysis, it is shown that the present model can recover exactly the physical formulations for the three-phase system. Numerical simulations of extensive examples including two circular interfaces, ternary spinodal decomposition, spreading of a liquid lens, and Kelvin-Helmholtz instability are conducted to test the model. It is found that the present model can capture accurate interfaces among three different fluids, which is attributed to its algebraical and dynamical consistency properties with the two-component model. Furthermore, the numerical results of three-phase flows agree well with the theoretical results or some available data, which demonstrates that the present LB model is a reliable and efficient method for simulating three-phase flow problems.

Phase-field-based multiple-relaxation-time lattice Boltzmann model for incompressible multiphase flows.

In this paper, a phase-field-based multiple-relaxation-time lattice Boltzmann (LB) model is proposed for incompressible multiphase flow systems. In this model, one distribution function is used to solve the Chan-Hilliard equation and the other is adopted to solve the Navier-Stokes equations. Unlike previous phase-field-based LB models, a proper source term is incorporated in the interfacial evolution equation such that the Chan-Hilliard equation can be derived exactly and also a pressure distribution is designed to recover the correct hydrodynamic equations. Furthermore, the pressure and velocity fields can be calculated explicitly. A series of numerical tests, including Zalesak's disk rotation, a single vortex, a deformation field, and a static droplet, have been performed to test the accuracy and stability of the present model. The results show that, compared with the previous models, the present model is more stable and achieves an overall improvement in the accuracy of the capturing interface. In addition, compared to the single-relaxation-time LB model, the present model can effectively reduce the spurious velocity and fluctuation of the kinetic energy. Finally, as an application, the Rayleigh-Taylor instability at high Reynolds numbers is investigated.

Phase-field-based lattice Boltzmann model for axisymmetric multiphase flows.

In this paper, a phase-field-based lattice Boltzmann (LB) model is proposed for axisymmetric multiphase flows. Modified equilibrium distribution functions and some source terms are properly added into the evolution equations such that multiphase flows in the axisymmetric coordinate system can be described. Different from previous axisymmetric LB multiphase models, the added source terms that arise from the axisymmetric effect contain no additional gradients, and therefore the present model is much simpler. Furthermore, through the Chapmann-Enskog analysis, the axisymmetric Chan-Hilliard equation and Navier-Stokes equations can be exactly derived from the present model. The model is also able to deal with flows with density contrast. A variety of numerical experiments, including planar and curve interfaces, an elongation field, a static droplet, a droplet oscillation, breakup of a liquid thread, and dripping of a liquid droplet under gravity, have been conducted to test the proposed model. It is found that the present model can capture accurate interface and the numerical results of multiphase flows also agree well with the analytical solutions and/or available experimental data.

A large iron isotope effect in SmFeAsO(1 - x)F(x) and Ba(1 - x)K(x)Fe(2)As(2).

The recent discovery of superconductivity in oxypnictides with a critical transition temperature (T(C)) higher than the McMillan limit of 39 K (the theoretical maximum predicted by Bardeen-Cooper-Schrieffer theory) has generated great excitement. Theoretical calculations indicate that the electron-phonon interaction is not strong enough to give rise to such high transition temperatures, but strong ferromagnetic/antiferromagnetic fluctuations have been proposed to be responsible. Superconductivity and magnetism in pnictide superconductors, however, show a strong sensitivity to the crystal lattice, suggesting the possibility of unconventional electron-phonon coupling. Here we report the effect of oxygen and iron isotope substitution on T(C) and the spin-density wave (SDW) transition temperature (T(SDW)) in the SmFeAsO(1 - x)F(x) and Ba(1 - x)K(x)Fe(2)As(2) systems. The oxygen isotope effect on T(C) and T(SDW) is very small, while the iron isotope exponent alpha(C) = -dlnT(C)/dlnM is about 0.35 (0.5 corresponds to the full isotope effect). Surprisingly, the iron isotope exchange shows the same effect on T(SDW) as T(C). This indicates that electron-phonon interaction plays some role in the superconducting mechanism, but a simple electron-phonon coupling mechanism seems unlikely because a strong magnon-phonon coupling is included.

Superconductivity at 56 K in samarium-doped SrFeAsF.

We synthesized the samples Sr(1-x)Sm(x)FFeAs with a ZrCuSiAs-type structure. These samples were characterized by resistivity and susceptibility. It is found that substitution of rare earth metal for alkaline earth metal in this system suppresses the anomaly in resistivity and induces superconductivity. Superconductivity at 56 K in nominal composition Sr(0.5)Sm(0.5)FFeAs is realized, indicating that the superconducting transition temperatures in the iron arsenide fluorides can reach as high as that in oxypnictides with the same structure.