Geodesic
Features of the behavior of a liquid film heated from above and placed over deep liquid
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 12, pp. 2082-2090

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The features of rupture occurring in a liquid film lying on deep liquid are studied. A thermal load applied to the film free surface leads to its deformation and rupture. The process is studied using a mathematical model describing the motion of a thin viscous nonisothermal liquid layer. The model is based on the two-dimensional Navier–Stokes equations. To solve them, the boundary conditions on the film-gas and film-liquid interfaces are written in explicit form. The effect of the thermal load on the film rupture is analyzed numerically depending on the Marangoni number and the stresses on the film-liquid interface. The results of solving model problems are presented. 
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     author = {A. S. Ovcharova},
     title = {Features of the behavior of a liquid film heated from above and placed over deep liquid},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {2082--2090},
     publisher = {mathdoc},
     volume = {53},
     number = {12},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_12_a12/}
}
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A. S. Ovcharova. Features of the behavior of a liquid film heated from above and placed over deep liquid. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 12, pp. 2082-2090. http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_12_a12/