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 N 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.
© 2010 American Physical Society
Levy, R, Rosenthal, S, Wong, J. Engineering flow states with localized forcing in a thin Marangoni-driven inclined film. Phys Rev E. 2010;82(5): 1-12.