Droplet profiles under the influence of van der Waals forces
Droplet profiles under the influence of van der Waals forces
复制标题
DOI：
10.1017/s0956792501004478
复制
发表时间：
2001-06
影响因子：
1.9
通讯作者：
E. Minkov;A. Novick-Cohen
中科院分区：
文献类型：
--
作者：
E. Minkov;A. Novick-Cohen
我们研究了货车德瓦耳斯力对蒸气气氛中固体基底上液滴全局能量最小化分布的影响，假设液滴具有均匀的横截面。我们证明了对于排斥货车德瓦耳斯力以及对于某些短程排斥-长程吸引力，存在唯一的全局极小化轮廓。尽管该轮廓必须包含垂直边界段，但垂直边界段的高度A通常可以被证明为比液滴的总高度B小一个数量级。特别是，当液滴足够大，Hamaker常数足够小，并且吸引力足够温和时，情况就是这样。在仅存在排斥力的情况下，对于实际的参数值，当B为毫米量级时，A为埃量级。此外，当在距液滴边缘的距离Δ 0处经由内切圆构造测量接触角时，规定了尽管出现垂直段但仍满足杨氏定律的条件，其中A [Lt ] Δ 0 [Lt ] B。
We study the effect of van der Waals forces on globally energy minimizing profiles for liquid droplets which lie on a solid substrate in a vapour atmosphere and which are assumed to have a uniform cross-section. We prove that for repulsive van der Waals forces as well as for certain short range repulsive-long range attractive forces, there exists a unique globally minimizing profile. Although this profile necessarily contains vertical bounding segments, the height A of the vertical bounding segments can often be demonstrated to be order of magnitude smaller that the overall height B of the droplet. This is the case, in particular, when the droplet is sufficiently large, the Hamaker constant is sufficiently small, and the attractive forces are sufficiently mild. In the presence of repulsive forces only, A is on the order of angströms when B is on the order of millimeters, for realistic parameter values. Moreover, conditions are prescribed under which Young's law is satisfied to leading order despite the appearance of the vertical segments, when the contact angle is measured via an inscribed circle construction at a distance ξ0 from the edge of the droplet, where A [Lt ] ξ0 [Lt ] B.