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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。
By deriving the polar coordinate solution of the internal flow field distribution when the liquid droplets are in the evaporation process, whether the boundary is considering the Marangoni stress or not, the streamline distribution inside the liquid droplet is described in conjunction with the corresponding spherical-cap droplet model When the droplets are subjected to Marangoni stress, the distribution of velocity at a constant ρcosα = with the height of the droplet in polar coordinates. The results of the experiment and the numerical simulation are compared respectively with the analytical results to illustrate the correctness of the analytical formula. At the same time, we can get the distribution of the streamline of the droplet: during the evaporation, the flow rate inside the droplet is the largest at the three-phase interface and the minimum near the center of the substrate. Under the influence of Marangoni stress, the inner part of the droplet generates a circular flow on the symmetry plane, the direction of which is from the center of the droplet to the three-phase interface at the bottom of the droplet. It also shows that Marangoni convection can restrain the “coffee ring” effect.