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中文摘要：
近期的实验和分子动力学模拟均表明：圆锥面上粘附液滴能自发地定向运动,且自发定向运动的方向与粘附面的亲水、疏水性质无关.针对这一重要现象,拟从曲面微纳米力学几何化的角度,提供一般性的理论解释.借助于粒子对势,研究了孤立粒子与微纳米硬曲面之间的相互作用,分析了粒子/硬曲面相互作用的几何学基础.可以证实：（a）粒子/硬曲面的作用势均具有统一的曲率化形式,均可以统一地表达成曲面平均曲率和Gauss曲率的函数;（b）基于曲率化的作用势,能够实现曲面微纳米力学的几何化;（c）曲率与曲率的内蕴梯度构成卷曲空间上的驱动力;（d）驱动力方向与曲面的亲水、疏水性质无关,解释了自发定向运动实验.
英文摘要：
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.
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