基于参数变分法的液滴形状建模分析

doi:10.12066/j.issn.1007-2861.2508

Abstract

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

CLC Number:

O176.1

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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URL: https://www.journal.shu.edu.cn/EN/10.12066/j.issn.1007-2861.2508

https://www.journal.shu.edu.cn/EN/Y2026/V32/I3/554

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Analysis of droplet shape modeling based on parametric variational method

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