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Thermocapillary instability of irradiated transparent liquid films on absorbing solid substrates
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10.1063/1.4811478
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Affiliations:
1 Department of Mechanical and Aerospace Engineering, Graduate School of Engineering, Tottori University, Tottori 680-8552, Japan
a) Electronic mail: fumihiro.saeki@gmail.com
Phys. Fluids 25, 062107 (2013)
/content/aip/journal/pof2/25/6/10.1063/1.4811478
http://aip.metastore.ingenta.com/content/aip/journal/pof2/25/6/10.1063/1.4811478

## Figures

FIG. 1.

Transparent liquid film/absorbing solid substrate system exposed to irradiation.

FIG. 2.

Typical relations between the growth rate ω and wavenumber β.

FIG. 3.

Film thickness dependence of the stability obtained from the thin-substrate model for = 0.001 and = 1. (a) Free surface temperature Θ, (b) energy reflectance , (c) cutoff and most unstable wavenumbers, β and β, and (d) maximum growth rate ω as a function of the film thickness , where the regions indicated by and , which are bounded by vertical dotted lines, correspond to stable and unstable regions, respectively. (e) Growth rate ω as a function of the wavenumber β for various values of .

FIG. 4.

Film thickness dependence of the stability obtained from the generalized model for = 0.001 and = 0.1 (i.e., = 100). (a) Energy reflectance , (b) cutoff and most unstable wavenumbers, β and β, and (c) maximum growth rate ω as a function of the film thickness , where the regions indicated by and , which are bounded by vertical dotted lines, correspond to stable and unstable regions, respectively. (d) Growth rate ω as a function of the wavenumber β for various values of .

FIG. 5.

Substrate thickness dependence of the dispersion relation for and = 0.001. (a) Cutoff and most unstable wavenumbers, β and β, and (b) maximum growth rate ω as a function of the substrate thickness, where β, β, and ω obtained from the generalized model converge to the values indicated by the dotted lines as → ∞. The horizontal scales, and , coincide with each other by conversion to the dimensional quantity . (c) Growth rate ω as a function of the wavenumber β, as obtained from the generalized model for various values of . The dashed curve in (c) indicates the trajectory of (β, ω).

FIG. 6.

Film thickness dependence of the stability obtained from the generalized model, where all parameter values are the same as in Fig. , but () ≡ 0. (a) Cutoff and most unstable wavenumbers, β and β, and (b) maximum growth rate ω as a function of the film thickness . (c) Growth rate ω as a function of the wavenumber β for various values of .

FIG. 7.

Growth rate ω as a function of the wavenumber β, as obtained from the generalized model for = 0.001, = 0.1, and various values of that satisfies in the case of . The solid and dotted curves are for the cases of and () ≡ 0, respectively. The inset shows the energy reflectance as a function of the film thickness , where and are the thicknesses corresponding to minima of the curve, and and are the thicknesses corresponding to maxima of the curve.

FIG. 8.

Incident light intensity dependence of the dispersion relation obtained from the generalized model for and = 0.1. (a) Cutoff and most unstable wavenumbers, β and β, and (b) maximum growth rate ω as a function of the incident light intensity . (c) Growth rate ω as a function of the wavenumber β for various values of , where the dashed curve indicates the trajectory of (β, ω).

## Tables

Table I.

Physical properties at 298 K, where the optical constants correspond to those at λ = 632.8 nm. For details, see Ref. and references therein.

Table II.

Nondimensional parameters.

/content/aip/journal/pof2/25/6/10.1063/1.4811478
2013-06-24
2014-04-20

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