中文摘要：

由于碰撞壁面后液滴内部流动的复杂性，以及气-液-固三相间的相互作用，对液滴碰撞壁面形态变化的数学理论研究有较大的难度，因此所见者多为实验和数值模拟。本文通过对液滴受力状态的分析，得到了惯性力、黏性力和表面张力带经验系数的表达式，并进一步建立了液滴碰撞壁面振荡模型，得到了液滴铺展半径的振荡表达式，以及表面张力、黏性系数等参数对液滴铺展的影响。最后通过与液滴衰减振荡数值模拟结果的对比，确定了液滴振荡模型中的修正系数，验证了模型的可行性。

英文摘要：

Due to the complexity inside the drop after impact on solid surfaces and the interaction among gas, liquid and solid phases, it is difficult to investigate the shape variation of the drop through the theoretical analysis, and most studies have focused on experiments and numerical simulations. In this paper, expressions for empirical coefficients of inertia, viscosity and surface tension are acquired by analyzing the force state. The drop oscillation model after impact is built further. The expression of the drop spreading radius, and the effects of surface tension and viscosity on the spreading process are obtained. Finally, the correction factor in the drop oscillation model is determined and the feasibility of the model is verified by comparing the computational results with the numerical results.