极坐标下Marangoni应力对静止液滴蒸发过程的影响

Analysis of the Effects of Marangoni Stresses on the Microflow in Evaporating Sessile Droplet

通过推导液滴在蒸发过程中,边界是否考虑Marangoni应力作用时,其内部流场分布的极坐标解析式,并结合相应的球冠液滴模型,来描述液滴内部的流线分布情况,以及液滴在受到Marangoni应力作用时,极坐标下ρcosα=常数处速度随液滴高度的分布规律。并分别使用实验与数值模拟结果与解析结果进行对比,从而说明解析式的正确性。同时从液滴的流线的分布得出:液滴在蒸发过程中,其内部的流动速率在三相界面处最大,在靠近基板的中心处最小。受Marangoni应力作用的影响,液滴内部在其对称面上产生了环流,其方向在液滴底部是从液滴中心流向三相界面的,同时也说明了Marangoni对流可以抑制"咖啡环"效应。

Deducing the streamlines expressions under polar coordinate system with whether there is a Marangoni stress or not on interfere of the droplet,and through building the corresponding spherical cap model to obtain the streamlines inside the droplet and velocities at different polar angles and pole diameters inside the droplet with the effect of Marangoni stress.The results got by analytic expressions without the Marangoni stress are verified with experimental results in literatures,the results got by analytic expressions with the Marangoni stress are verified with experimental results in literatures and simulation results.It can be concluded that streamlines are the most intensive in the three-phase line and the most sparsely at the center of the droplet during the evaporation.Under the influence of Marangoni stress,circulations produced inside the droplet,and the direction of them are from the three-phase line to the apex along the interfere,from the center to the three-phase line at the bottom of the droplet.So it can be demonstrated that Marangoni convection can inhibit the ＂coffee ring＂ effect.