Structure and stress in spherical microstructures
Structure and stress in spherical microstructures
复制标题
球形微结构的结构和应力
DOI：
10.1063/1.442557
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发表时间：
1981
期刊：
影响因子：
--
通讯作者：
H. Davis
中科院分区：
文献类型：
--
作者：
A. H. Falls;L. Scriven;H. Davis
应用非均匀流体的积分理论和梯度理论预测了球界面的结构。理论的非线性积分和微分方程通过使用最先进的有限元技术与牛顿法相结合来求解。数值方法，讨论了一些长度，建议作为一个潜在的工具，解决其他非线性问题的流体统计力学。积分和梯度理论的结果进行了比较，发现是在定性的协议，并在这种协议的强度，梯度理论被用来描述和分析的结构和应力在微观球滴。梯度理论的预测表明，对于小于10个分子宽的液滴，杨-拉普拉斯方程会失效。然而，与通常的估计相反的曲率依赖的表面张力，即使是非常小的滴（说，三个或四个分子宽）的表面张力被发现偏离平面界面的张力很小。
An integral theory and gradient theory of inhomogeneous fluid are used to predict the structure of spherical interfaces. The nonlinear integral and differential equations of the theories are solved by using state‐of‐the‐art finite element techniques, coupled with Newton’s method. The numerical method, discussed at some length, is suggested as a potential tool for solving other nonlinear problems of fluid statistical mechanics. Results of integral and gradient theories are compared and found to be in qualitative agreement and, on the strength of this agreement, gradient theory is used to describe and analyze the structure and stress in microscopic spherical drops. Predictions from gradient theory indicate a breakdown of the Young–Laplace equation for drops smaller than about ten molecules wide. However, contrary to the usual estimate of the curvature dependence of surface tension, the surface tension of even very small drops (say, three or four molecules wide) is found to deviate little from the tension of a planar interface.