Hassan Md Rifat, Wang Cheng
Department of Mechanical and Aerospace Engineering, Missouri University of Science and Technology, 400 W. 13th St., Rolla, Missouri 65409, United States.
Langmuir. 2021 Nov 16;37(45):13331-13345. doi: 10.1021/acs.langmuir.1c01943. Epub 2021 Nov 3.
This paper reports a numerical investigation on the spreading dynamics of an impinging ferrofluid droplet on solid hydrophilic surfaces (i.e., θ ≤ 60°) in the presence of uniform magnetic fields. A finite element method-based commercial solver is implemented to perform several numerical simulations, which uses a phase-field (PF) method to couple both the flow and magnetic fields. The results demonstrate that a uniform magnetic field is capable of controlling the spreading dynamics of an impinging droplet on hydrophilic substrates. Additionally, the application of a magnetic field results in the generation of a steady-state droplet shape with a reduced base diameter and an increased apex height at higher magnetic Bond numbers at the end of the spreading process. Moreover, as the viscosity of the droplet decreases, the droplet experiences an increase in its primary spreading diameter, which can be even reduced through the implementation of a vertical uniform magnetic field. Additionally, an oscillatory motion appears in a droplet during the spreading phenomenon at lower Ohnesorge numbers (i.e., = 0.023), which is further sustained for a longer period of time in the relaxation phase with increased amplitudes in the case of an extremely low-viscosity droplet (i.e., = 0.002) before attaining a final equilibrium shape. Furthermore, at = 0.002, the droplet undergoes a breakup event after the impact for a short period of time, while the magnetic field induces an elastic behavior in a droplet at lower viscosities (i.e., = 0.023) during the free fall under gravity.
本文报道了在均匀磁场存在下，撞击到固体亲水表面（即θ≤60°）的铁磁流体液滴的铺展动力学的数值研究。采用基于有限元方法的商业求解器进行了多次数值模拟，该求解器使用相场（PF）方法来耦合流场和磁场。结果表明，均匀磁场能够控制撞击到亲水基底上的液滴的铺展动力学。此外，在铺展过程结束时，在较高的磁邦德数下，施加磁场会导致产生一种稳态液滴形状，其底部直径减小，顶点高度增加。而且，随着液滴粘度的降低，液滴的初始铺展直径会增大，通过施加垂直均匀磁场甚至可以减小该直径。此外，在较低的奥内佐格数（即=0.023）下，液滴在铺展现象期间会出现振荡运动，对于极低粘度的液滴（即=0.002），在达到最终平衡形状之前，这种振荡运动在弛豫阶段会持续更长时间，且振幅会增大。此外，在=0.002时，液滴在撞击后短时间内会发生破裂事件，而在重力作用下自由下落期间，磁场会在较低粘度（即=0.023）的液滴中诱导出弹性行为。
