Li Qiuxiang, Chai Zhenhua, Shi Baochang, Liang Hong
National Laboratory of Coal Combustion, Huazhong University of Science and Technology, Wuhan 430074, China.
School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Oct;90(4):043015. doi: 10.1103/PhysRevE.90.043015. Epub 2014 Oct 21.
In this paper, we present a numerical study on the deformation and breakup behavior of liquid droplet past a solid circular cylinder by using an improved interparticle-potential lattice Boltzmann method. The effects of the eccentric ratio β, viscosity ratio λ between the droplet and the surrounding fluid, surface wettability, and Bond number (Bo) on the dynamic behavior of the liquid droplet are considered. The parameter β represents the degree that the solid cylinder deviates from the center line, and Bo is the ratio between the inertial force and capillary force. Numerical results show that there are two typical patterns, i.e., breakup and no breakup, which are greatly influenced by the aforementioned parameters. When β increases to a critical value βc, the droplet can pass the circular cylinder without a breakup, otherwise, the breakup phenomenon occurs. The critical eccentric ratio βc increases significantly with increasing Bo for case with λ>1, while for the case with λ<1, the viscosity effects on the βc is not obvious when Bo is large. For the breakup case, the amount of deposited liquid on the tip of the circular cylinder is almost unaffected by β. In addition, the results also show that the viscosity ratio and wettability affect the deformation and breakup process of the droplet. For case with λ<1, the viscosity ratio plays a minor role in the thickness variations of the deposited liquid, which decreases to a nonzero constant eventually; while for λ>1, the increase of the viscosity ratio significantly accelerates the decrease of the deposited liquid, and finally no fluid deposits on the cylinder. In term of the wettability, there occurs continuous gas phase trapped by the wetting droplet, but this does not happen for nonwetting droplet. Besides, for λ<1, the time required to pass the cylinder (tp) decreases monotonically with decreasing contact angle, while a nonmonotonic decrease appears for λ>1. It is also found that tp decreases monotonically with increasing Bo and is less sensitive to λ at a large Bo.
在本文中，我们使用改进的粒子间势格子玻尔兹曼方法对液滴绕过固体圆柱的变形和破碎行为进行了数值研究。考虑了偏心比β、液滴与周围流体之间的粘度比λ、表面润湿性和邦德数（Bo）对液滴动力学行为的影响。参数β表示固体圆柱偏离中心线的程度，Bo是惯性力与毛细力的比值。数值结果表明，存在两种典型模式，即破碎和不破碎，这两种模式受上述参数的影响很大。当β增加到临界值βc时，液滴可以绕过圆柱而不破碎，否则会发生破碎现象。对于λ>1的情况，临界偏心比βc随Bo的增加而显著增加，而对于λ<1的情况，当Bo较大时，粘度对βc的影响不明显。对于破碎情况，圆柱尖端上沉积的液体量几乎不受β的影响。此外，结果还表明，粘度比和润湿性会影响液滴的变形和破碎过程。对于λ<1的情况，粘度比在沉积液体厚度变化中起次要作用，最终厚度减小到一个非零常数；而对于λ>1的情况，粘度比的增加显著加速了沉积液体的减少，最终圆柱上没有流体沉积。就润湿性而言，湿润液滴会捕获连续的气相，但非湿润液滴则不会。此外，对于λ<1的情况，绕过圆柱所需的时间（tp）随接触角的减小而单调减小，而对于λ>1的情况则出现非单调减小。还发现tp随Bo的增加而单调减小，并且在较大的Bo时对λ不太敏感。
