We outline a low-order Lagrangian model for the inertial dynamics of spreading and imbibition of a spherical liquid cap on a plane featuring independent cylindrical capillaries without gravity. The analysis predicts the relative roles of radial and axial kinetic energy, reveals the critical Laplace number beyond which the drop oscillates, and attributes the exponent of the initial power-law for contact patch radius vs. time to the form of capillary potential energy just after the liquid sphere touches the plate. © 2017 American Institute of Chemical Engineers AIChE J, 2017

中文翻译：

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毛细管板上液滴的惯性扩散和吸收模型

我们概述了一个低阶拉格朗日模型，该模型用于在没有重力的独立圆柱形毛细管作用下的平面上球形液体帽的扩散和吸收的惯性动力学。该分析预测了径向和轴向动能的相对作用，揭示了临界拉普拉斯数，液滴在该拉普拉斯数之外振荡，并将接触斑半径随时间变化的初始幂律的指数归因于紧随其后的毛细管势能的形式。液体球接触板。©2017美国化学工程师学会AIChE J，2017