On self-similar thermal rupture of thin liquid sheets

Mark Bowen, B. S. Tilley

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

We consider the dynamics of a symmetrically heated thin incompressible viscous fluid sheet. We take surface tension to be temperature dependent and consequently the streamwise momentum equation includes the effects of thermocapillarity, inertia, viscous stresses, and capillarity. Energy transport to the surrounding environment is also included. We use a long-wave analysis to derive a single nondimensional system which, with appropriate choices of Reynolds number, recovers two previously studied cases. In both cases, we find conditions under which sufficiently large-amplitude initial temperature profiles induce film rupture in finite time, notably without the inclusion of disjoining pressures from van der Waals effects. When the Reynolds number is large, the similarity solution is governed by a balance of inertia and capillarity near the rupture location, analogous to the isothermal case. When the Reynolds number is small, the thermocapillary transients induce the same similarity solution over intermediate times that is found for the drainage of lamellae in foams. For O(1) Reynolds numbers, the dynamics are governed initially by the large Reynolds number evolution, and then a transition over several orders of magnitude in the sheet thickness needs to take place before the small Reynolds number similarity solution is observed.

Original languageEnglish
Article number102105
JournalPhysics of Fluids
Volume25
Issue number10
DOIs
Publication statusPublished - 2013 Oct 23

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Reynolds number
liquids
inertia
viscous fluids
lamella
drainage
planetary waves
foams
temperature profiles
interfacial tension
inclusions
momentum
temperature
energy

ASJC Scopus subject areas

  • Condensed Matter Physics

Cite this

On self-similar thermal rupture of thin liquid sheets. / Bowen, Mark; Tilley, B. S.

In: Physics of Fluids, Vol. 25, No. 10, 102105, 23.10.2013.

Research output: Contribution to journalArticle

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