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Abstract

The thermocapillary migration of droplets on a solid surface is widely used in daily life and industrial fields. Regulating droplet thermocapillary migration by changing surface wettability has received extensive attention. According to the lubrication theory and slip boundary conditions, we establish a mathematical model of the thermocapillary migration dynamics of a droplet on wettability-confined tracks subjected to a uniform temperature gradient. Combined with the contact line dynamics, a method of determining the velocity of the contact line in a different direction of the three-dimensional droplet is proposed, the simulation is carried out with FreeFEM++. The evolution of droplet migration is examined, and the effects of track width and wettability on the droplet migration dynamics are emphatically investigated. The results show that the main part of the droplet moves from the high-temperature region to the low-temperature region, the trailing edge of the droplet forms a small bulge during the movement, and a thin liquid film is formed between the bulge and the main part of the droplet. The droplet spreading perpendicular to the track direction is inhibited and remains pinned after shrinking to the track edge. Negative correlation between the velocity of the advancing contact line and the track width is observed. The velocity of the advancing line first rapidly and then slowly decrease to a steady state. The squeezing effect caused by the wettability confined perpendicular to the track direction accelerates the thermocapillary migration of the droplet on the track in the initial short time. The enhanced track wettability increases the initial velocity of the receding contact line but has little effect on its stable value. The velocity of the advancing contact line is positively correlated with track wettability. Changing the track width is possibly easier to regulate the thermocapillary migration of a droplet than varying the track wettability.

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Corresponding author:Ye Xue-Min,yexuemin@163.com

Funds:Project supported by the National Natural Science Foundation of China (Grant No. 51876065) and the Natural Science Foundation of Hebei Province, China (Grant No. A2015502058).

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网格数目	液滴前进接触角θ_a	液滴前进接触线移动速度u_a/10^–4	计算所需 CPU时长/h
4584	0.1506	1.721	3.15
10028	0.1534	1.779	8.02
15578	0.1536	1.781	14.21

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物性参数	符号 / 单位	典型数量级
液滴厚度	$ \widetilde{H}/ {\rm{m}}$	10^–4
长度特征尺度	$ \widetilde{L}/ {\rm{m}}$	10^–3
液体黏度	$\widetilde{\mu }/ ({\rm{Pa} }{\cdot} {\rm{s} })$	10^–3
液体密度	$\widetilde{\rho }/ ({\rm{kg} }{\cdot} {\rm{m} }^{-3} )$	10³
传热系数	$\widetilde{\alpha }/({\rm{kW} }{\cdot}{\rm{m} }^{-2}{\cdot}{\rm{K} }^{-1} )$	1—10
壁面温度	$ \widetilde{T}/{\rm{K}} $	10³—10²
界面张力	$\widetilde{\sigma }/ ({\rm{N} }{\cdot} {\rm{m} }^{-1} )$	10^–2
特征速度	$\widetilde{U}=\dfrac{\widetilde{\sigma }_{ {T}_{0} }-\widetilde{\sigma }_{ {T}_{\rm{m} } } }{\widetilde{H}/\left(\tilde{\mu }\tilde{L}\right)}/ ({\rm{m} }{\cdot} {\rm{s} }^{-1}$)	10^–4—1

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无量纲参数	定义式	取值范围
小量ε	${\varepsilon }=\widetilde{H}/\widetilde{L}$	10^–2—10^–1
邦德数Bo	$ Bo=\widetilde{\rho }g{\widetilde{H}}^{2}/\widetilde{\mu }U $	10^–2—10^–1
温度梯度$ \varGamma $	$\varGamma =\dfrac{(d{\widetilde{T} }_{\rm{w} }/{\rm{d}}\widetilde{x})\widetilde{L} }{ {\widetilde{T} }_{\rm{m} }-{\widetilde{T} }_{0} }$	10^–3—10^–2
毛细数C	$ C=\dfrac{{\varepsilon }^{2}{\widetilde{\sigma }}_{{\widetilde{T}}_{\rm{m}}}}{{\widetilde{\sigma }}_{{\widetilde{T}}_{0}}-{\widetilde{\sigma }}_{{\widetilde{T}}_{\rm{m}}}} $	10^–2—10^–1
界面温度敏感系数$\varOmega_{\rm{i}} $	$ {\varOmega }_{\rm{i}}=\dfrac{{\widetilde{\alpha }}_{T\rm{i}}({\widetilde{T}}_{\rm{m}}-{\widetilde{T}}_{0})}{{\widetilde{\sigma }}_{{\rm{i}, \widetilde{T}}_{0}}-{\widetilde{\sigma }}_{{\rm{l}\rm{g}, \widetilde{T}}_{\rm{m}}}} $	0—10²

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Vol. 72, Issue 2 - 2023-01-20

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