Proof of the relationship between the shape of the spherical droplet surface and the principle of free energy minimization

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  • 1. College of Physics,Northwest University,Xian,Shaanxi 710127,China; 2. Department of Mathematics,Hong Kong University of Science and Technology,Kowloon,Hong Kong,China

Received date: 2019-11-08

  Revised date: 2020-03-03

  Online published: 2020-09-24

Abstract

The surface shape of the droplets in the vacuum is determined by the principle of surface free energy minimization. In the case of ignoring droplet gravity,the minimum free energy corresponds to the minimum surfacearea of the droplet. We derive the equations satisfied by the minimum surface under fixed volume constraints,and use the linearized iterative method to numerically solve the equation to prove that the surface is spherical. In addition,we prove that if the final thickness of the super-spreading liquid film is constant,the liquid film spreading shape is also determined by the principle of minimum free energy,and its shape is circular.

Cite this article

JIN Kang, WANG Xin-yi, GUI Kai-hang . Proof of the relationship between the shape of the spherical droplet surface and the principle of free energy minimization[J]. College Physics, 2020 , 39(9) : 17 -22 . DOI: 10.16854 /j.cnki.1000-0712.190512

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