TY - JOUR

T1 - Thermally induced van der Waals rupture of thin viscous fluid sheets

AU - Bowen, Mark

AU - Tilley, B. S.

N1 - Funding Information:
M.B. gratefully acknowledges the support of a Global Studies Grant from the University of Tokyo and the hospitality of Worcester Polytechnic Institute, where part of this research was undertaken. We also wish to thank the referees for their constructive comments which improved the manuscript.

PY - 2012/3/14

Y1 - 2012/3/14

N2 - We consider the dynamics of a thin symmetric fluid sheet subject to an initial temperature profile, where inertia, viscous stresses, disjoining pressures, capillarity, and thermocapillarity are important. We apply a long-wave analysis in the limit where deviations from the mean sheet velocity are small, but thermocapillary stresses and heat transfer from the sheet to the environment are significant and find a coupled system of partial differential equations that describe the sheet thickness, the mean sheet velocity, and the mean sheet temperature. From a linear stability analysis, we find that a stable thermal mode couples the velocity to the interfacial dynamics. This coupling can be utilized to delay the onset of rupture or to promote an earlier rupture event. In particular, rupture can be induced thermally even in cases when the heat transfer to the surrounding environment is significant, provided that the initial phase shift between the initial velocity and temperature disturbances is close to φ = π/2. These effects suggest a strategy that uses phase modulation in the initial temperature perturbation related to the initial velocity perturbation that assigns priority of the rupture events at particular sites over several spatial periods.

AB - We consider the dynamics of a thin symmetric fluid sheet subject to an initial temperature profile, where inertia, viscous stresses, disjoining pressures, capillarity, and thermocapillarity are important. We apply a long-wave analysis in the limit where deviations from the mean sheet velocity are small, but thermocapillary stresses and heat transfer from the sheet to the environment are significant and find a coupled system of partial differential equations that describe the sheet thickness, the mean sheet velocity, and the mean sheet temperature. From a linear stability analysis, we find that a stable thermal mode couples the velocity to the interfacial dynamics. This coupling can be utilized to delay the onset of rupture or to promote an earlier rupture event. In particular, rupture can be induced thermally even in cases when the heat transfer to the surrounding environment is significant, provided that the initial phase shift between the initial velocity and temperature disturbances is close to φ = π/2. These effects suggest a strategy that uses phase modulation in the initial temperature perturbation related to the initial velocity perturbation that assigns priority of the rupture events at particular sites over several spatial periods.

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U2 - 10.1063/1.3693700

DO - 10.1063/1.3693700

M3 - Article

AN - SCOPUS:84859340353

VL - 24

JO - Physics of Fluids

JF - Physics of Fluids

SN - 1070-6631

IS - 3

M1 - 032106

ER -