Abstract
Numerical simulations of lubrication models provide clues for experimentalists about the development of wave structures in thin liquid films. We analyze numerical simulations of a lubrication model for an inclined thin liquid film modified by Marangoni forces due to a thermal gradient and additional localized forcing heating the substrate. Numerical results can be explained through connections to theory for hyperbolic conservation laws predicting wave fronts from Marangoni-driven thin films without forcing. We demonstrate how a variety of forcing profiles, such as Gaussian, rectangular, and triangular, affect the formation of downstream transient structures, including an wave not commonly discussed in the context of thin films. Simulations employing a controlled approximation of a compressive-undercompressive wave pair demonstrate possibilities for applications of localized forcing as microfluidic valve. In the simulations, localized forcing provides a control parameter that can be used to determine mass flux and film profiles.
15 More- Received 17 August 2010
DOI:https://doi.org/10.1103/PhysRevE.82.056320
©2010 American Physical Society