Journal
INTERNATIONAL JOURNAL OF THERMAL SCIENCES
Volume 107, Issue -, Pages 209-219Publisher
ELSEVIER FRANCE-EDITIONS SCIENTIFIQUES MEDICALES ELSEVIER
DOI: 10.1016/j.ijthermalsci.2016.03.021
Keywords
Meniscus instability; Evaporating meniscus; Thin films
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Funding
- Natural Sciences and Engineering Research Council of Canada
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The stability of an evaporating meniscus in a narrow channel is theoretically investigated. A non-linear differential equation is derived using the lubrication approximation and taking into account evaporation, long-range molecular forces, surface tension, vapor recoil, thermocapillarity and viscous forces. Using a linear stability analysis, the susceptibility of the film to instability is studied. Three different base state profiles are used: flat replenished thin film, modified Young-Laplace profile and curved thin film. The last base state most accurately reflects an evaporating meniscus; however, its implementation requires the numerical solution of the non-linear thin-film equations. A shooting technique together with a fourth order Runge-Kutta method is used to obtain the curved thin-film profiles. The results obtained for each base state are analyzed and limitations are discussed. The curved thin-film base profile predicts strong instability for higher wall superheats. The growth rates are found to be positive (destabilizing) in the thin-film region and become negative (stabilizing) towards the intrinsic meniscus. The results indicate that the instability most likely originates in the evaporating thin-film region. Part II of the presented paper is devoted to experimental investigation. (C) 2016 Elsevier Masson SAS. All rights reserved.
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