应用数学和力学2011，Vol.32Issue(5)：509-521,13.DOI:10.3879/j.issn.1000-0887.2011.05.001
曲率的形状梯度和经典梯度:微纳米曲面上的驱动力
Shape Gradient and Classical Gradient of Curvatures: Driving Forces on Micro/Nano Curved Surfaces
摘要
Abstract
Recent experiment and molecule dynamics simulation showed that adhesion droplet on conical surface could move spontaneously and directionally.Besides, this spontaneous and directional motion was independent of the hydrophilicity and hydrophobicity of the conical surface.Aimed at this important phenomenon, a general theoretical explanation was provided from the viewpoint of the geometrization of micro／nano mechanics on curved surfaces.Based on the pair potentials of particles, the interactions between an isolated particle and a micro／ nano hard-curved-surface were studied, and the geometric foundation for the interactions between the particle and the hard-curved-surface were analyzed.The following results are derived: (a) The potential of the particle／hard-curved-surface is of the unified curvature-form (i.e.the potential is always a unified function of the mean curvature and Gauss curvature of the curved surface); (b) On the basis of the curvature-based potential, the geometrization of the micro／nano mechanics on hard-curved-surfaces can be realized; (c) Curvatures and the intrinsic gradients of curvatures form the driving forces on curved spaces; (d) The direction of the driving force is independent of the hydrophilicity and hydrophobicity of the curved surface, which explains the experimental phenomenon of spontaneous and directional motion.关键词
微纳米曲面/曲率/形状梯度/经典梯度/驱动力Key words
micro／nano curved surfaces/ curvatures/ shape gradient/ classical gradient/ driving forces分类
数理科学引用本文复制引用
殷雅俊,陈超,吕存景,郑泉水..曲率的形状梯度和经典梯度:微纳米曲面上的驱动力[J].应用数学和力学,2011,32(5):509-521,13.基金项目
国家自然科学基金资助项目(10872114 （）
10672089 （）
10832005 （）
11072125) （）
