Dynamics of Evaporating Droplet Based on Gas Phase Diffusion Model

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

Abstract

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

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.

Figures/Tables 9

Fig.1 Diagram of droplet evaporation on heating substrate

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

Fig.3 Flowchart of calculation

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

Fig.4 Verification of theoretical models

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

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

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

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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