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Abstract <p>Using the Schwarz function method, we obtain a new exact solution for the problem of capillary waves on fluid sheets. The reliability of the solution is confirmed by the results of numerical verification of the main boundary equation. It is revealed that the pressure coefficient is the determining physical parameter. Its value makes it possible to predict that one should expect either the capillary wave of a certain type (symmetric or antisymmetric) or the disintegration of the fluid sheet into individual drops. It is shown that the maximum possible length of the capillary wave is approximately 1.6&#xa0;times the thickness of the fluid sheet, regardless of the wave type. The question of reproducing the known exact solution of Kimmersley for this problem remains open.</p>

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Exact Solution for Capillary Waves on Fluid Sheets

  • 期刊论文

  • 发表日期：

    2025年6月1日

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  • M. M. Alimov

摘要

Abstract

Using the Schwarz function method, we obtain a new exact solution for the problem of capillary waves on fluid sheets. The reliability of the solution is confirmed by the results of numerical verification of the main boundary equation. It is revealed that the pressure coefficient is the determining physical parameter. Its value makes it possible to predict that one should expect either the capillary wave of a certain type (symmetric or antisymmetric) or the disintegration of the fluid sheet into individual drops. It is shown that the maximum possible length of the capillary wave is approximately 1.6 times the thickness of the fluid sheet, regardless of the wave type. The question of reproducing the known exact solution of Kimmersley for this problem remains open.