| Автор | Andreas Münch |
| Дата выпуска | 2000-05-01 |
| dc.description | Thin films of silicon oil driven up an inclined silicon wafer by a thermally induced Marangoni force develop unusual shock profiles involving a non-classical undercompressive shock, if the counteracting parallel component of gravity is sufficiently large (Bertozzi et al 1998 Phys. Rev. Lett. 81 5169-72). They arise as a result of the interaction of a non-convex flux with the fourth-order diffusion generated by surface tension. In this work, we investigate how the dynamical behaviour of the solution is affected by including second-order diffusion resulting from the normal component of gravity; this component was neglected in the previous study. Then the governing equation for the film profile h (x , t ) becomes h<sub>t</sub> + ( h <sup>2</sup> - h <sup>3</sup> )<sub>x </sub> = - ( h <sup>3</sup> h<sub>xxx</sub> )<sub>x </sub> + D ( h <sup>3</sup> h<sub>x</sub> )<sub>x </sub> D 0. The numerical simulations in this paper confirm that neglecting second-order diffusion is justified for small D , but find that for larger D , the structure of the solution changes dramatically. We give a detailed account of the transitions that occur while increasing D and make predictions for future experiments carried out at small inclination angles, corresponding to moderately large D . |
| Формат | application.pdf |
| Издатель | Institute of Physics Publishing |
| Название | Shock transitions in Marangoni gravity-driven thin-film flow |
| Тип | paper |
| DOI | 10.1088/0951-7715/13/3/312 |
| Electronic ISSN | 1361-6544 |
| Print ISSN | 0951-7715 |
| Журнал | Nonlinearity |
| Том | 13 |
| Первая страница | 731 |
| Последняя страница | 746 |
| Аффилиация | Andreas Münch; Zentrum Mathematik, Technische Universität München (H4), D-80290 Munich, Germany |
| Выпуск | 3 |
