Abstract The initial spreading dynamics of a droplet has been studied for decades, however, the mechanism of such phenomenon is still not well known and an efficient prediction model considering combined effects of each influence factor for this process is absent. In present study, numerical simulations for the early stage droplet spreading are carried out based on a modified MPS method with up-to-date viscosity model, pressure Poisson equation, pressure gradient model as well as improved boundary conditions. Influences of the contact angle, viscosity and surface tension force are individually investigated, and their effects are properly characterized by dimensionless contact angle Θ, Reynolds number Re and Bound number Bo. Results show that the droplet spreading radius can be modeled as r/R0 = β(t*)α, where α and β are functions of dimensionless numbers above. Parameters α and β of the contact radius’ power-law growth in all simulations are adopted as inputs to determine coefficients in droplet spreading correlation. The proposed correlation generates pretty close predicted results whose relative errors are less than 5% comparing with experimental values. Present research provides a picture on how the initial contact between the liquid drop and solid surface develops, and it could be a fundamental research for more complicated droplet behaviors e.g. the droplet impact and collision.

中文翻译：

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基于数值模拟的早期液滴扩散建模

摘要 液滴的初始扩散动力学已经研究了几十年，然而，这种现象的机制仍然不为人所知，并且缺乏考虑该过程的每个影响因素的组合效应的有效预测模型。在目前的研究中，基于改进的 MPS 方法与最新的粘度模型、压力泊松方程、压力梯度模型以及改进的边界条件，对早期液滴扩散进行了数值模拟。分别研究了接触角、粘度和表面张力的影响，并通过无量纲接触角 Θ、雷诺数 Re 和结合数 Bo 适当地表征了它们的影响。结果表明，液滴扩散半径可以建模为 r/R0 = β(t*)α，其中 α 和 β 是上述无量纲数的函数。所有模拟中接触半径的幂律增长的参数α和β被用作确定液滴扩散相关系数的输入。所提出的相关性产生了非常接近的预测结果，与实验值相比，其相对误差小于 5%。目前的研究提供了关于液滴和固体表面之间初始接触如何发展的图片，它可能是更复杂的液滴行为（例如液滴撞击和碰撞）的基础研究。所提出的相关性产生了非常接近的预测结果，与实验值相比，其相对误差小于 5%。目前的研究提供了关于液滴和固体表面之间初始接触如何发展的图片，它可能是更复杂的液滴行为（例如液滴撞击和碰撞）的基础研究。所提出的相关性产生了非常接近的预测结果，与实验值相比，其相对误差小于 5%。目前的研究提供了关于液滴和固体表面之间初始接触如何发展的图片，它可能是更复杂的液滴行为（例如液滴撞击和碰撞）的基础研究。