Abstract The present study concerns the dynamics of ferrofluid droplets in a Newtonian fluid. The incompressible Navier-Stokes (NS) equations are applied for the dynamics of the immiscible magnetic and Newtonian fluids while the Cahn-Hilliard (C-H) equation is adopted to describe the behavior of their interface. A magnetic field coupling lattice Boltzmann (LB) model is developed to solve both the NS equations and the C-H equation. Specially, a mass-correcting term is introduced into the C-H equation, which strongly enforces the mass conservation. The magnetic field is evaluated by a Poisson equation solver with a self-correcting procedure for the static Maxwell equations. The magnetic dipole force is transformed into the magnetic surface force by a rigorous mathematical procedure, which can physically describe the magnetic effect on the interface. Moreover, the magnetic force after this treatment becomes easy-to-implement, which can be directly incorporated into the external force term of the LB model. The capability of the present combination method to simulate the magnetic multiphase flows is demonstrated by three typical numerical examples, i.e., Laplace law for a stationary droplet, a stationary cylinder under an external uniform magnetic field, the deformation of a single ferrofluid droplet. Further, the merging process of multiple-ferrofluid-droplet system in organic oil is investigated. It is found that the elongation of ferrofluid droplet in the direction of magnetic field shows positive impact on the merging process when the orientation of ferrofluid droplets is parallel to the external magnetic field, while negative impact on the merging process when their orientation is perpendicular to the external magnetic field.

中文翻译：

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磁场耦合格子Boltzmann模型及其在多铁磁流体液滴系统合并过程中的应用

摘要 本研究涉及牛顿流体中铁磁流体液滴的动力学。不可压缩的 Navier-Stokes (NS) 方程适用于不混溶的磁性流体和牛顿流体的动力学，而 Cahn-Hilliard (CH) 方程用于描述它们的界面行为。开发了磁场耦合晶格玻尔兹曼 (LB) 模型来求解 NS 方程和 CH 方程。特别地，在 CH 方程中引入了一个质量校正项，它强烈地加强了质量守恒。磁场由泊松方程求解器评估，对静态麦克斯韦方程组具有自校正程序。磁偶极力通过严格的数学程序转化为磁表面力，可以物理描述界面上的磁效应。而且，经过这种处理后的磁力变得容易实现，可以直接纳入LB模型的外力项中。本组合方法模拟磁性多相流的能力通过三个典型的数值例子来证明，即静止液滴的拉普拉斯定律、外部均匀磁场下的静止圆柱体、单个铁磁流体液滴的变形。进一步研究了多铁磁流体-液滴体系在有机油中的融合过程。发现当磁流体液滴的取向平行于外部磁场时，磁流体液滴在磁场方向上的伸长率对合并过程显示出积极的影响，