中文摘要：

液滴在固体表面上的铺展行为与润湿特性对许多工业生产过程的研究具有重要意义.根据液滴在光滑表面上的受力情况,建立了液滴平壁铺展的动力学模型.应用润滑近似方法和二维Navier-Stokes方程,建立了液滴沿理想表面铺展的动量和连续性方程.根据建立的方程,应用数值解法求解并详细分析了液滴在铺展过程中膜厚、接触线铺展半径以及铺展速度随时间的变化关系.研究结果表明：液滴的铺展过程可分为扩展和收缩两个阶段,铺展过程伴随着表面能、动能以及各种势能的相互转化,液滴最终的铺展半径大小由固体基面固有的润湿特性所决定;液滴在铺展过程中出现的＂坍塌效应＂与弯曲液面处的Laplace压力差有关;铺展半径随时间变化的标定律近似满足＂1/7＂次方标度律.

英文摘要：

Droplet spreading behavior on a substrate is closely bound up with the wettability of the substrate, and plays a critical role in many industrial applications, such as lubrication, painting, coating, and mineral flotation. In this paper,a dynamical model of droplet spreading on a smooth substrate is established through a mechanical analysis. According to the lubrication approximation theory and Navier-Stokes equation, a general nonlinear evolution equation or equations are derived, including the momentum equation, the continuity equation, and the evolution equation of film thickness.We adopt numerical methods to solve these equations, and also quantitatively analyze the relation among film thickness,spreading radius, speed of wetting contact line and time in detail. The results show that the droplet spreading process is mainly divided into two phases, namely expansion phase and contraction phase. Moreover, the spreading process is along with mutual transformation among surface energy, kinetic energy, and different kinds of potential energies. In addition,the final spreading radius Rfof droplet is determined by the inherent wettability of solid surface, and the ＂collapse effect＂, which emerges at t = 0.006 s in the spreading process, is related to Laplace pressure difference of curved liquid surface. Finally, by controlling the droplet size, we obtain the scaling law of droplet spreading radius with time, which approximately meets R ～ t1/7. The scaling law is validated both experimentally and numerically. The results of this study are expected to enhance our knowledge of the movement of wetting contact line and also provide some guidance for the wetting theory.