Healing of thermocapillary film rupture by viscous heating

• Published in: Journal of fluid mechanics 2019-08, Vol.872, p.308-326
• Main Authors: Kirkinis, E., Andreev, A. V.
• Format: Article
• Language: English
• Subjects: Critical temperature; Healing; Heat transfer; Heating; High temperature effects; Instability; Mechanics; Partial differential equations; Physics; Rupture; Rupturing; Shear stress; Stability; Substrates; Surface tension; Temperature dependence; Temperature differences; Temperature gradients; Tension; Thin films; Vapor phases; Velocity; Viscosity; Vortices; Wavelength
• ISSN: 0022-1120; 1469-7645
• DOI: 10.1017/jfm.2019.338

Thin liquid films sitting on a heated solid substrate and surrounded by a colder ambient gas phase are strongly affected by surface-shear stresses induced by surface tension and temperature gradients, as well as by viscous and capillary forces. The temperature dependence of surface tension may lead to thinning of liquid-film depressions promoting instability which takes place when a critical temperature difference $\unicode[STIX]{x0394}\unicode[STIX]{x1D717}_{cr}$ between the substrate and the ambient gas phase is exceeded. In this article we show theoretically that viscous heating, previously neglected in related literature, may delay or suppress the thermocapillary instability and leads to film healing. The viscous heating effect, by inhibiting heat transfer, prevents the system from reaching the critical value $\unicode[STIX]{x0394}\unicode[STIX]{x1D717}_{cr}$ required to bring about instability. As a consequence, the system remains within the stability region, suppressing film rupture. The presence of the viscous heating effect leads to a persistent circulating motion of two counter-rotating vortices lying diametrically opposite to a depression of the liquid–gas interface reducing the wavelength of disturbances to one half of its initial value. This effect has yet to be observed in experiment.