Localized Marangoni forcing in driven thin films

We consider the use of localized Marangoni forcing to produce a thermocapillary “microfluidic valve” that allows us to control the downstream flow of a thin film of viscous fluid. To this end, we analyze the influence of this localized forcing on a flow driven by a combination of uniform Marangoni stresses and gravity in a one-dimensional model. Long-time solutions approach states that can be categorized in two classes, where the film thickness downstream of the forcing is: (I) determined by the upstream thickness, or (II) controlled by the forcing amplitude. The type II solutions are stable stationary hydraulic jumps for thin films. We give careful attention to the relation between the forcing and the downstream film flow for the resulting bi-stable solutions. We include a comparison of the one-dimensional theory with two-dimensional computations and experimental results.