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Slow rupture of viscous films between parallel needles

Published online by Cambridge University Press:  05 February 2007

SOFYA V. CHEPUSHTANOVA  and
IGOR L. KLIAKHANDLER
SOFYA V. CHEPUSHTANOVA
Affiliation:
Department of Mathematical Sciences, Michigan Technological University, 1400 Townsend Drive, Houghton, MI 49931-1295, USA
IGOR L. KLIAKHANDLER
Affiliation:
Department of Mathematical Sciences, Michigan Technological University, 1400 Townsend Drive, Houghton, MI 49931-1295, USA
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Abstract

Experiments and theory on the rupture of a free plane viscous film are reported. The relatively thick film, with a typical thickness of the order of 0.1–0.6 mm, rests between two long parallel needles. When the film is punctured, a hole is formed with the rim on the front. The hole expands, reaches the needles, and propagates along them with a constant velocity of the order of 2–50 cm s−1. The Reynolds numbers for the present experiments are relatively small, 0.002 ≤ Re ≤ 0.34. A crude theory for propagation velocity of the rim is proposed; the theory compares well with the experimental data. The rupture profile is visually similar to a U-shaped curve. Crude equations for the rupture profile are derived, and their solutions are consistent with the experimental observations. A theory for propagation velocity and profile of the rupture, applicable to all Reynolds numbers, is proposed.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 573 , February 2007 , pp. 297 - 310
Copyright
Copyright © Cambridge University Press 2007

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