基于参数变分法的液滴形状建模分析

doi:10.12066/j.issn.1007-2861.2508

摘要/Abstract

摘要： 参数方程形式对刻画亲水和疏水液滴模型起到了统一化作用.考虑重力对液滴形状的影响,分别对二维液滴模型和轴对称条件下的三维液滴模型引入参数方程,基于二维Young-Laplace方程推导出二维液滴轮廓函数关系式,利用液滴表面自由能加上重力势能最小化条件下的轴对称液滴形状分析方法,结合变分法推导出参数方程下三维液滴形状的控制方程及其相应的接触角公式.进一步比较两种模型下的液滴形状与实验数据之间的差异.数据表明,本模型数值模拟与实验结果具有较高的契合度.

关键词: 液滴形状, 表面张力, 接触角, 数学模型

Abstract: The parametric equation form plays a unifying role in characterizing hydrophilic and hydrophobic droplet models. Considering the influence of gravity on droplet shapes, parametric equations were introduced into the two-dimensional droplet model and the three-dimensional droplet model under axisymmetric conditions, respectively. Based on the two-dimensional Young– Laplace equation, the functional relationship of the two-dimensional droplet proflle was derived. By utilizing the axisymmetric droplet shape analysis method under the condition of minimizing the droplet surface free energy and the gravitational potential energy, combined with the variational method, the governing equation of the three-dimensional droplet shape and its corresponding contact angle formula under the parametric equation were derived. Furthermore, the difierences between the droplet shapes in the two models and the experimental data were compared. The data indicate that the numerical simulation of this model has a high degree of agreement with the experimental results.

Key words: droplet shape, surface tension, contact angle, mathematical model

中图分类号:

O176.1

刘亚楠, 王远弟, 黄廷恩, 张鹏. 基于参数变分法的液滴形状建模分析[J]. 上海大学学报(自然科学版), 2026, 32(3): 554-564.

LIU Yanan, WANG Yuandi, HUANG Tingen, ZHANG Peng. Analysis of droplet shape modeling based on parametric variational method[J]. Journal of Shanghai University（Natural Science Edition）, 2026, 32(3): 554-564.

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