Thermally induced van der Waals rupture of thin viscous fluid sheets

Mark Bowen, B. S. Tilley

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

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.

Original languageEnglish
Article number032106
JournalPhysics of Fluids
Volume24
Issue number3
DOIs
Publication statusPublished - 2012 Mar 14

Fingerprint

viscous fluids
heat transfer
perturbation
planetary waves
phase modulation
inertia
partial differential equations
temperature profiles
temperature
phase shift
disturbances
deviation
fluids

ASJC Scopus subject areas

  • Condensed Matter Physics

Cite this

Thermally induced van der Waals rupture of thin viscous fluid sheets. / Bowen, Mark; Tilley, B. S.

In: Physics of Fluids, Vol. 24, No. 3, 032106, 14.03.2012.

Research output: Contribution to journalArticle

@article{70f9e2cf9ef545e6a01198079837abf1,
title = "Thermally induced van der Waals rupture of thin viscous fluid sheets",
abstract = "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.",
author = "Mark Bowen and Tilley, {B. S.}",
year = "2012",
month = "3",
day = "14",
doi = "10.1063/1.3693700",
language = "English",
volume = "24",
journal = "Physics of Fluids",
issn = "1070-6631",
publisher = "American Institute of Physics Publising LLC",
number = "3",

}

TY - JOUR

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

AU - Bowen, Mark

AU - Tilley, B. S.

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.

UR - http://www.scopus.com/inward/record.url?scp=84859340353&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84859340353&partnerID=8YFLogxK

U2 - 10.1063/1.3693700

DO - 10.1063/1.3693700

M3 - Article

VL - 24

JO - Physics of Fluids

JF - Physics of Fluids

SN - 1070-6631

IS - 3

M1 - 032106

ER -