Lattice Boltzmann Study on the Motion of Dual Droplets in Microchannels With Contact Angle Hysteresis
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摘要:
接触角滞后表现为流体在非理想固体表面上运动时前进接触角和后退接触角不同，是两相流体在润湿表面上流动的重要现象。该文采用改进的伪势格子Boltzmann (LB)多组分模型，并与几何润湿边界条件相结合，研究了两个液滴在具有接触角滞后性微通道表面上的运动行为，主要研究了通道内特征数、通道表面性质以及液滴初始参数的影响。研究结果表明：毛细数的增大有助于液滴的移动，然而并不利于液滴的排出，且毛细数的增加对上游液滴的影响大于其对下游液滴的影响；另一方面，接触角滞后性窗口越大，液滴运动和形变更迟缓，但形变程度更明显，两液滴更早地发生合并，但更晚地排出管道；液滴间距的增加使液滴的运动行为在不同阶段表现为不同的模式，但都导致通道中残留小液滴，使得液滴排出通道的时间增加。研究结果还表明：上游液滴和下游液滴的相对尺寸差距越大，越不利于液滴排出管道。
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关键词:
- 接触角滞后性 /
- 格子Boltzmann方法 /
- 液滴相互作用 /
- 剪切流
Abstract:The contact angle hysteresis is defined as the difference between the advancing and receding contact angles, and is an important phenomenon in the two-phase flow on the wet surface. An improved pseudo-potential lattice Boltzmann (LB) multiphase flow model, combined with geometric wetting boundary condition, was employed to study the motion behavior of dual droplets in microchannels with contact angle hysteresis. The effects of the capillary number, the wettability, the contact angle hysteresis window width, the initial distance between the two droplets and the relative size of the droplets on the dynamic behavior of the droplets in the microchannel, were investigated. The research results show that, the increase of the capillary number is conducive to the movement of droplets, but not conducive to the discharge of droplets from the microchannel, and the influence of the capillary number on the upstream droplet is greater than that on the downstream droplet. On the other hand, the larger the contact angle hysteresis window is, the slower the droplet motion and deformation will be, but the more obvious the deformation will be, and the earlier the two droplets will merge but the later they will discharge from the microchannel. In addition, with the increase of the initial distance between the two droplets, the droplet motion mode will differ among different stages, but the duration of the droplet discharge will extend. Correspondingly, the larger the relative size difference between upstream and downstream droplets is, the more difficultly the droplets will discharge from the microchannel.
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Key words:
- contact angle hysteresis /
- lattice Boltzmann method /
- droplet interaction /
- shear flow
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图 4 微通道表面上液滴示意图
Figure 4. A schematic diagram of a droplet on the lower surface of the microchannel
图 5 双液滴在不同时刻的瞬时流型：(a)
$ C_{\rm{a}}=0.2 $ ；(b)$ C_{\rm{a}}=0.5 $ ；(c)$ C_{\rm{a}}=0.8 $ 注 为了解释图中的颜色，读者可以参考本文的电子网页版本，后同。
Figure 5. Instantaneous flow patterns of two droplets at different moments: (a)
$ C_{\rm{a}}=0.2 $ ; (b)$ C_{\rm{a}}=0.5 $ ; (c)$ C_{\rm{a}}=0.8 $ 
图 6 不同毛细数下液滴状态变化时间
Figure 6. Droplet state change time under different capillary numbers
图 7 不同毛细数下的上、下游液滴液-壁接触长度随时间的变化：(a) 上游液滴；(b) 下游液滴
Figure 7. Droplet-wall contact lengths under different capillary numbers: (a) upstream droplets; (b) downstream droplets
图 8 不同滞后性窗口下两液滴的瞬时流型：(a) CA= 45°；(b) CA= 90°；(c) CA= 120°
Figure 8. Instantaneous flow patterns of two droplets under different hysteresis windows: (a) CA= 45°; (b) CA= 90°; (c) CA= 120°
图 9 在不同滞后性窗口下的上、下游液滴液-壁接触长度随时间的变化：(a)上游液滴；(b)下游液滴
Figure 9. Variations of liquid-wall contact lengths with time under different hysteresis windows: (a) upstream droplets; (b) downstream droplets
图 10 不同滞后性窗口下液滴形态变化时刻
Figure 10. Droplet state change moments under different hysteresis windows
图 11 两液滴在
$ S=4R $ ，$6R$ ，$7R$ 下的瞬时流型Figure 11. Instantaneous flow patterns of two droplets for
$S=4R, 6R,7R$ 
图 12 不同间距下液滴形态变化时刻
Figure 12. Droplet state change moments under different drops distance
图 13 两液滴在
$ k_{\rm{r}}=0.6 $ ，$1.0$ ，$1.4$ 下的瞬时流型Figure 13. Instantaneous flow patterns of two droplets for
$ k_{\rm{r}}=0.6,1.0,1.4 $ 
图 14 不同相对大小下的上、下游液滴接触长度随时间的变化：(a) 上游液滴；(b)下游液滴
Figure 14. Variations of liquid-wall contact lengths with time under different droplet relative sizes: (a) upstream droplets; (b) downstream droplets
图 15 不同初始液滴相对大小下液滴状态变化时刻
Figure 15. Droplet state change moments under different initial droplet relative sizes
表 1 网格无关性
Table 1. Grid independence
$ L\times 2H $ $ D $ $ t_{\rm{a}} $ $ t_{\rm{b}} $ $ 300\times100 $ 8 53.5321 67.7234 $ 600\times200 $ 6 54.4856 68.5080 $ 1\;200\times400 $ 6 54.4832 68.5093 
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