Thermocapillary instability of irradiated transparent liquid films on absorbing solid substrates

Abstract

The thermocapillary instability of irradiated transparent liquid films on absorbing solid substrates is investigated by means of linear stability analysis. Under such circumstances, incident light passes through a film and is absorbed by the substrate, and the film is then heated by the heat influx across the interface with the substrate. The optical absorption in the substrate is affected by optical reflection. The energy reflectance varies periodically with the film thickness due to optical interference between light waves reflected from the gas-liquid and liquid-solid interfaces. The periodic variation of the reflectance strongly affects the film stability, which also varies periodically with the film thickness. Characteristic scales of the instability are also affected by the substrate thickness and incident light intensity. While qualitative aspects of the stability can be easily obtained from the analysis based on a simplified model that is derived under the thin-substrate assumption, the quantitative evaluation for the case of substrates of moderate to large thickness should be based on a more generalized model that allows for substrates of arbitrary thickness.

Oscillatory thermocapillary instability of a film heated by a thick substrate

“…Effectively, we assume that the substrate-film thermal conductivity and thickness ratios are large. Although we obtain a dispersion relation that is similar to that of Saeki et al (2013), it is important to note that they did not observe oscillatory modes. This may be due to a limited examination of model parameter values in their investigation.The manuscript proceeds as follows: in §2, we present the dimensional equations of motion and boundary conditions for a deformable liquid layer heated by a thick substrate.…”

“…Thus, in the present work, we investigate the emergence of oscillatory instability for the simpler problem: a film heated by a thick solid substrate. To do so, we initially follow the work by Saeki et al (2011Saeki et al ( , 2013 that considered the linear analysis of a coupled filmsubstrate model, which induces thermocapillary film deformation driven by laser heating. In the present work we follow their asymptotic assumptions so that the full heat equation of the substrate is retained at leading order in the long-wave expansion of the governing equations.…”

On efficient asymptotic modelling of thin films on thermally conductive substrates

“…2011; Shklyaev et al. 2012; Saeki, Fukui & Matsuoka 2013) whereas the heat loss/gain from the film to the substrate has been modelled variously by (i) a constant temperature (Oron & Peles 1998; Oron 2000; Saeki et al. 2011), (ii) constant flux (Atena & Khenner 2009; Shklyaev et al.…”

“…In later work, Saeki et al. (2013) developed similar leading-order equations for film temperature when the film is optically transparent. In this case the film temperature dependence on is slaved to the inclusion of radiative heat losses.…”

“…Again, various modelling approaches have been taken in the literature: we note for example that Saeki et al. (2011, 2013) present a detailed model for laser energy that involves complicated expressions for the optical properties; whereas Trice et al. (2007) propose a simpler approach (to be discussed later) in which these properties are approximated.…”