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. Comparison of the one-dimensional theory with two-dimensional computations and experimental results is given.
thin films • fluid dynamics • thermocapillary valve • Marangoni forcing • lubrication theory