Model for Coiling and Meandering Instability of Viscous Threads

• Nagahiro Shin-ichiro

  Department of Mechanical Engineering, Sendai National College of Technology

• Hayakawa Yoshinori

  Department of Physics, Tohoku University

Abstract

A numerical model for describing both the transient and steady-state dynamics of viscous threads falling onto a plane is presented. The steady-state coiling frequency Ω is calculated as a function of fall height H. In the case of weak gravity, Ω∝H⁻¹ and Ω∝H are obtained for smaller and larger fall heights, respectively. When the effect of gravity is significant, the relation Ω∝H² is observed. These results agree with the scaling laws previously predicted. The critical Reynolds number for the coiling–uncoiling transition is discussed. When the gravity is weak, the transition occurs with hysteretic effects. If the plane moves horizontally at a constant speed, a variety of meandering oscillation modes can be observed experimentally. The present model can also describe this phenomenon. The numerically obtained state diagram for the meandering modes qualitatively agrees with the results of the experiment.

Journal

• Journal of the Physical Society of Japan

  Journal of the Physical Society of Japan 78 (12), 124402-124402, 2009

  THE PHYSICAL SOCIETY OF JAPAN

Keywords

• buckling instability
• liquid rope coiling
• free surface flow
• numerical model

Details

• CRID: 1390282679173496064
• NII Article ID: 130005437178
• NII Article ID: 210000108120
• NII Article ID: 40016879647
• NII Book ID: AA00704814
• DOI: 10.1143/jpsj.78.124402
• ISSN: 13474073
• ISSN: 00319015
• NDL BIB ID: 10480258
• Web Site: http://id.ndl.go.jp/bib/10480258
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I10480258
• Web Site: http://journals.jps.jp/doi/pdf/10.1143/JPSJ.78.124402
• Text Lang: en
• Data Source:
  • JaLC
  • NDL
  • Crossref
  • CiNii Articles
• Abstract License Flag: Disallowed