基于气相扩散模型的液滴蒸发动力学特性

doi:10.19596/j.cnki.1001-246x.8854

摘要/Abstract

摘要：

基于润滑理论和气相扩散与液滴蒸发之间的相互耦合作用, 建立液滴在均匀壁温固体基底上蒸发的数学模型, 推导出基于气相扩散模型的液滴厚度演化方程; 结合液滴接触线动力学求解准静态气相场, 通过数值计算分析气相作用下马兰戈尼数(Ma)和佩克莱数(Pe_k)对液滴蒸发进程的影响。结果表明: 与单边模型相比, 采用气相扩散模型时的液滴蒸发进程更慢、接触半径更小、蒸发速率更低, 其结果与实验结果更符合; 在气相扩散模型下, 减小Ma可增大液滴蒸发速率, 促进液滴蒸发; 增大Pe_k, 液滴附近的气体密度增大, 液滴蒸发速率加快。

关键词: 液滴蒸发, 气相扩散模型, 润滑理论, 动力学特性, 扩散效应

Abstract:

Based on the lubrication theory and the coupling between gas phase diffusion and droplet evaporation, a mathematical model of droplet evaporation on a solid substrate with uniform wall temperature is established, and the evolution equation of droplet thickness based on the gas phase diffusion model is derived. The quasi-static gas phase field is solved with the droplet contact line dynamics, and the influence of Ma and Pe_k on the droplet evaporation under the effect of gas phase is discussed through numerical simulation. The results show that under the same parameters, the droplet evaporation process of the gas phase diffusion model is slower than that of the one-sided model, and the contact radius and the evaporating rate is decreased, and the results are more consistent with the experimental results. Under the gas phase diffusion model, the droplet evaporating rate is increased and the droplet evaporation process is shortened by reducing Ma, thereby promoting droplet evaporation. By increasing Pe_k, the gas density near the droplet is densified, and the droplet evaporation is enhanced.

Key words: droplet evaporation, gas phase diffusion model, lubrication theory, dynamics characteristics, diffusion effect

熊天桐, 叶学民, 谢雄飞, 李春曦. 基于气相扩散模型的液滴蒸发动力学特性[J]. 计算物理, 2025, 42(2): 182-191.

Tiantong XIONG, Xuemin YE, Xiongfei XIE, Chunxi LI. Dynamics of Evaporating Droplet Based on Gas Phase Diffusion Model[J]. Chinese Journal of Computational Physics, 2025, 42(2): 182-191.

图/表 9

图1 加热基底上液滴蒸发示意图

Fig.1 Diagram of droplet evaporation on heating substrate

图2 (a) 液相与(b)气相计算区域及网格

Fig.2 Domain and grid of (a) liquid and (b) gas phases

图3 计算流程图

Fig.3 Flowchart of calculation

表1 网格无关性验证

Table 1 Validation of grid independence

气相和液相网格		节点数/个	网格数/个	x_cr	与方案3的相对误差	计算时长/h
方案1	液相	300	600	1.150 36	0.41%	2.8
方案1	气相	200	32 439	1.150 36	0.41%	2.8
方案2	液相	500	1 000	1.149 56	0.34%	5.4
方案2	气相	400	56 345	1.149 56	0.34%	5.4
方案3	液相	800	1 600	1.145 67		18.7
方案3	气相	600	94 327	1.145 67		18.7

图4 计算模型验证

Fig.4 Verification of theoretical models

图5 Ma对液滴演化特征参数影响(a) 接触线；(b) 接触角；(c) x=0处的液滴蒸发率分布；(d) 液滴蒸发剩余质量；(e) t=104液滴蒸发速率分布

Fig.5 Effect of Ma on characteristic parameters of droplet evolution (a) contact line; (b) contact angle; (c) droplet evaporation rate distribution at x=0; (d) remaining mass of droplet evaporation; (e) droplet evaporation rate distribution at t=104

图6 Ma对气-液界面参数影响(a) t=104时表面张力x方向的变化；(b)气-液界面密度演化

Fig.6 Effect of Ma on parameters at gas-liquid interface (a) variation of the surface tension in x direction at t=104; (b) density evolution of gas-liquid interface

图7 Pek对液滴演化特征参数的影响(a) 接触线；(b) 接触角；(c) t=104时的液滴蒸发率分布；(d) 液滴蒸发剩余质量

Fig.7 Effect of Pek on characteristic parameters of droplet evolution (a) contact line; (b) contact angle; (c) droplet evaporation rate distribution at t=104; (d) remaining mass of droplet evaporation

图8 不同Pek时ρg|int的时间演化和t=104时的气相密度分布(a) 气-液界面密度演化；(b) Pek=1.3时气相密度分布；(c) Pek=1.5时气相密度分布；(d) Pek=1.8时气相密度分布

Fig.8 Gas phase density distribution at different Pek and gas phase density distribution at t=104 (a) density evolution of gas-liquid interface; (b) gas phase density distribution at Pek=1.3; (c) gas phase density distribution at Pek=1.5; (d) gas phase density distribution at Pek=1.8

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