In the present study, a fractional-step-based multiphase lattice Boltzmann (LB) method coupled with a solution of a magnetic field evolution is developed to predict the interface behavior in magnetic multiphase flows. The incompressible Navier–Stokes equations are utilized for the flow field, while the Cahn–Hilliard equation is adopted to track the interface, and these governing equations are solved by reconstructing solutions within the LB framework with the prediction–correction step based on a fractional-step method. The proposed numerical model inherits the excellent performance of kinetic theory from the LB method and integrates the good numerical stability from the fractional-step method. Meanwhile, the macroscopic variables can be simply and directly calculated by the equilibrium distribution functions, which saves the virtual memories and simplifies the computational process. The proposed numerical model is validated by simulating two problems, i.e., a bubble rising with a density ratio of 1000 and a viscosity ratio of 100 and a stationary circular cylinder under an external uniform magnetic field. The interfacial deformations of a ferrofluid droplet in organic oil and an aqueous droplet in ferrofluid under the external magnetic field are, then, simulated, and the underlying mechanisms are discussed. Moreover, the rising process of a gas bubble in the ferrofluid is investigated, which shows that the rising velocity is accelerated under the effect of the external magnetic field. All the numerical examples demonstrate the capability of the present numerical method to handle the problem with the interfacial deformation in magnetic multiphase flows.

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基于分数阶的多相晶格玻尔兹曼方法的磁多相流数值研究

在本研究中，基于分数步的多相晶格玻尔兹曼（LB）方法与磁场演化解决方案相结合，可以预测多相磁性流中的界面行为。不可压缩的Navier–Stokes方程用于流场，而Cahn–Hilliard方程用于跟踪界面，并且这些控制方程通过在LB框架内通过基于分数阶的预测校正步骤重建解来求解。步骤方法。所提出的数值模型继承了LB方法的动力学理论的优良性能，并结合了分数步法的优良数值稳定性。同时，可以通过平衡分布函数简单直接地计算宏观变量，这样可以节省虚拟内存并简化计算过程。通过模拟两个问题来验证所提出的数值模型，即气泡在外部均匀磁场下以密度比1000和粘度比100上升以及固定圆柱体上升。然后，模拟了外部磁场下有机油中的铁磁流体液滴和铁磁流体中的含水液滴的界面变形，并探讨了其潜在机理。此外，研究了铁磁流体中气泡的上升过程，这表明在外部磁场的作用下，上升速度加快了。所有的数值例子都证明了本数值方法处理磁多相流界面变形问题的能力。