In this article, we present the motion, deformation, and coalescence of ferrofluid droplets suspended in a nonmagnetic fluid, subjected to a uniform magnetic field in both vertical and horizontal directions. A coupling between the simplified multiphase lattice Boltzmann method and the self‐correcting scheme is constructed to numerically solve the two‐dimensional flow field and the magnetostatics equations, respectively. The Cahn‐Hilliard equation is employed to seize the diffuse interface between magnetic and nonmagnetic fluids. In order to validate the model, deformation of a ferrofluid droplet suspended in nonmagnetic fluid is simulated as a test case and the results are compared with numerical and experimental results. Furthermore, a detailed analysis on the behavior of falling ferrofluid droplets and the coalescence between a pair of ferrofluid droplets under the effect of different magnetic fields and different droplets configurations are also presented in this article. The results provide significant insight and a better understanding of these phenomena. It is found that for higher values of magnetic bond number and susceptibility, the droplet deformation is significant and the falling process is faster while a reverse behavior is observed for higher values of Eötvös number. Moreover, the magnetic energy density exhibits an interesting behavior in the vicinity of the droplets. It is concentrated between the droplets with a nonuniform distribution when the droplets are close to each other.

中文翻译：

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受均匀磁场作用的铁磁流体液滴的运动，变形和聚结

在本文中，我们介绍了悬浮在非磁性流体中的铁磁流体液滴的运动，变形和聚结，它们在垂直和水平方向上都受到均匀的磁场作用。构造了简化的多相晶格玻尔兹曼方法和自校正方案之间的耦合，以数值方式分别求解二维流场和静磁方程。Cahn-Hilliard方程用于抓住磁性和非磁性流体之间的扩散界面。为了验证该模型，模拟了悬浮在非磁性流体中的铁磁流体液滴的变形作为测试案例，并将结果与​​数值和实验结果进行了比较。此外，本文还详细分析了下落的铁磁流体液滴的行为以及一对铁磁流体液滴在不同磁场和不同液滴构型的影响下的聚结情况。结果为这些现象提供了重要的见识和更好的理解。已经发现，对于更高的磁键数和磁化率值，液滴变形显着且下落过程更快，而对于更高的Eötvös数则观察到相反的行为。此外，磁能密度在液滴附近表现出有趣的行为。当液滴彼此靠近时，其以不均匀的分布集中在液滴之间。