马朗戈尼效应
润滑理论
机械
马兰戈尼数
润滑
对流
流量(数学)
蒸发
有限元法
拉普拉斯方程
材料科学
热力学
边值问题
化学
物理
复合材料
量子力学
作者
Hua Hu,Ronald G. Larson
出处
期刊:Langmuir
[American Chemical Society]
日期:2005-03-26
卷期号:21 (9): 3972-3980
被引量:776
摘要
We study the effects of Marangoni stresses on the flow in an evaporating sessile droplet, by extending a lubrication analysis and a finite element solution of the flow field in a drying droplet, developed earlier. The temperature distribution within the droplet is obtained from a solution of Laplace's equation, where quasi-steadiness and neglect of convection terms in the heat equation can be justified for small, slowly evaporating droplets. The evaporation flux and temperature profiles along the droplet surface are approximated by simple analytical forms and used as boundary conditions to obtain an axisymmetric analytical flow field from the lubrication theory for relatively flat droplets. A finite element algorithm is also developed to solve simultaneously the vapor concentration, and the thermal and flow fields in the droplet, which shows that the lubrication solution with the Marangoni stress is accurate for contact angles as high as 40 degrees. From our analysis, we find that surfactant contamination, at a surface concentration as small as 300 molecules/microm(2), can almost entirely suppress the Marangoni flow in the evaporating droplet.
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