TY - JOUR

T1 - Model for coiling and meandering instability of viscous threads

AU - Nagahiro, Shin Ichiro

AU - Hayakawa, Yoshinori

PY - 2009/12

Y1 - 2009/12

N2 - 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 ∝ H 2 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.

AB - 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 ∝ H 2 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.

KW - Buckling instability

KW - Free surface flow

KW - Liquid rope coiling

KW - Numerical model

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U2 - 10.1143/JPSJ.78.124402

DO - 10.1143/JPSJ.78.124402

M3 - Article

AN - SCOPUS:73949133649

SN - 0031-9015

VL - 78

JO - Journal of the Physical Society of Japan

JF - Journal of the Physical Society of Japan

IS - 12

M1 - 124402

ER -